François Kuonen
email: fkuonen@stanford.edu

Isabelle Surbeck

Kavita Y Sarin

Monique Dontenwill

Curzio Ruegg

Michel Gilliet

Anthony E Oro

Olivier Gaide

TGF-β, FIBRONECTIN AND INTEGRIN α5β1 PROMOTE INVASION IN BASAL CELL CARCINOMA

Basal cell carcinoma (BCC) is the most frequent human cancer and is becoming an important health problem in an ageing population. Based on their clinical and histological characteristics, thick BCC are typically divided into low-risk nodular and high-risk infiltrative subtypes, although the underlying mechanisms are poorly understood. We have identified molecular mechanisms that explain the aggressiveness of high-risk infiltrative BCC, with a potential direct clinical impact. In this study, we first show that fibroblasts, TGFβ and fibronectin are found preferentially in infiltrative human BCC. This allowed us to develop in vivo models for the study of infiltrative BCC, which in turn let us confirm the role of TGFβ in inducing peritumoral fibronectin deposition and tumor infiltration. We then show that fibronectin promotes adhesion and migration of BCC cell lines through integrin α5β1-mediated phosphorylation of focal adhesion kinase (FAK). Fittingly, inhibition of integrin α5β1 and phospho-FAK both prevent fibronectin-induced migration of BCC cells in vitro as well as BCC infiltration in vivo. Altogether our results open important insights into the pathogenesis of aggressive infiltrative BCC, and identify integrin α5β1 or FAK inhibition as promising strategies for the treatment of advanced BCC.

INTRODUCTION

Basal cell carcinoma (BCC) is the most common skin cancer, affecting more than 50% of Caucasians during their lifetime [START_REF] Kasper | Basal cell carcinoma -molecular biology and potential new therapies[END_REF]. Virtually 100% of BCC, independently of their clinical or histological subtype, depend on a deregulated Hedgehog (Hh) signaling pathway ultimately leading to the activation of Gli transcription factors (Epstein, 2008, Rubin and[START_REF] Rubin | Targeting the Hedgehog pathway in cancer[END_REF]. However, despite this molecular homogeneity, BCC can display very different morphological aspects and have varying clinical prognoses [START_REF] Kasper | Basal cell carcinoma -molecular biology and potential new therapies[END_REF][START_REF] Telfer | Guidelines for the management of basal cell carcinoma[END_REF]. Whereas superficial, micro-nodular and even thick nodular BCC are considered as low-risk tumors, infiltrative BCC are associated with higher tumor recurrence after surgery and lower response to radiotherapy [START_REF] Breuninger | Prediction of subclinical tumor infiltration in basal cell carcinoma[END_REF][START_REF] Caccialanza | Radiotherapy of morphea-type basal cell carcinoma: results in 127 cases[END_REF][START_REF] Piccinno | Dermatologic radiotherapy in the treatment of extensive basal cell carcinomas: a retrospective study[END_REF]. Consequently, a better understanding of the functional determinants of nodular and infiltrative phenotypes is of high clinical relevance. Interestingly, some insights into the pathogenesis of BCC subtypes were obtained from a large genomic analysis of human BCC, which identified additional genetic mutations in MYCN, PPP6C and PTPN14 in infiltrative BCC [START_REF] Bonilla | Genomic analysis identifies new drivers and progression pathways in skin basal cell carcinoma[END_REF]. However, it must be noted that the impact of these mutations was neither validated in vitro nor in vivo.

Recently, accumulating evidences point out the role of the tumor-stroma interactions in BCC infiltration. Tumor-associated macrophages (TAM) were shown to act on BCC progression through paracrine activation of cyclo-oxygenase 2 (COX-2) [START_REF] Tjiu | Tumor-associated macrophage-induced invasion and angiogenesis of human basal cell carcinoma cells by cyclooxygenase-2 induction[END_REF]. Similarly, carcinoma-associated fibroblasts (CAF) were reported to promote BCC invasion through paracrine activation of c-MET in BCC tumor cells [START_REF] Marsh | alpha vbeta 6 Integrin promotes the invasion of morphoeic basal cell carcinoma through stromal modulation[END_REF][START_REF] Tjiu | Tumor-associated macrophage-induced invasion and angiogenesis of human basal cell carcinoma cells by cyclooxygenase-2 induction[END_REF]. Chiu et al. showed the implication of CXCR4-induced angiogenesis in infiltrative BCC [START_REF] Chu | Stromal cell-derived factor-1alpha (SDF-1alpha/CXCL12)-enhanced angiogenesis of human basal cell carcinoma cells involves ERK1/2-NF-kappaB/interleukin-6 pathway[END_REF]. Altogether, these observations support the role of the microenvironment in BCC progression, although functional validation is currently lacking, as there is no appropriate in vivo mouse model of infiltrative BCC.

The tumor stroma is composed of a bio-active network of proteins forming the extra-cellular matrix (ECM). Importantly, low-risk nodular BCC present histologically as well-defined tumor nests in a loose myxoid stroma. They mostly display a continuous basement membrane and split retraction at the tumor-stroma interface. On the contrary, high-risk infiltrative BCC are defined histologically by irregular tumor strands in a densely-packed fibrotic stroma, in which basement membrane and split retraction are mostly absent [START_REF] Barsky | Desmoplastic basal cell carcinomas possess unique basement membrane-degrading properties[END_REF][START_REF] Crowson | Basal cell carcinoma: biology, morphology and clinical implications[END_REF][START_REF] Kallioinen | Discontinuity of the basement membrane in fibrosing basocellular carcinomas and basosquamous carcinomas of the skin: an immunohistochemical study with human laminin and type IV collagen antibodies[END_REF]. These histological observations suggest that ECM modifications may play a role in BCC subtype and progression. Modifications of the ECM network actually appear early during cancer progression and are associated with tumor progression [START_REF] Barcellos-Hoff | The evolution of the cancer niche during multistage carcinogenesis[END_REF][START_REF] Butcher | A tense situation: forcing tumour progression[END_REF][START_REF] Levental | Matrix crosslinking forces tumor progression by enhancing integrin signaling[END_REF][START_REF] Lorusso | The tumor microenvironment and its contribution to tumor evolution toward metastasis[END_REF] and poor prognosis [START_REF] Conklin | Aligned collagen is a prognostic signature for survival in human breast carcinoma[END_REF]. Because the impact of the ECM on BCC progression has not yet been studied, we focused our work on this important field.

In this study, we show that TGFβ and fibronectin are highly expressed in the peritumoral stroma of infiltrative BCC. Using two different BCC allograft models, we show that TGFβ induces peritumoral fibronectin and confers infiltrative features to BCC. Consistently, fibronectin promotes the migration of BCC tumor cells in vitro through integrin α5β1 binding and downstream phosphorylation of focal adhesion kinase (FAK). Both integrin α5β1 and FAK inhibition prevent fibronectin-induced migration. Consistently, silencing of FAK expression in tumor cells, inhibition of phospho-FAK with the tyrosine kinase inhibitor PF-562271 or the integrin α5β1 inhibitor K34C all prevent TGFβ-induced infiltration in vivo. Altogether, these results reveal the pivotal role of TGFβ-induced peritumoral fibronectin in BCC progression and suggest that FAK inhibitors, available in the clinics, may be used for the treatment of advanced infiltrative BCC.

RESULTS

TGFβ is associated with peritumoral fibronectin deposition and the transition from nodular to infiltrative phenotype in human BCC samples and mouse models.

Peritumoral fibrosis has been shown to confer poor prognosis in several tumor types (Barcellos-Hoff et al., 2013, Cirri and[START_REF] Cirri | Cancer associated fibroblasts: the dark side of the coin[END_REF]. Regarding skin tumors, peritumoral fibrotic stroma is observed in advanced and aggressive infiltrative BCC [START_REF] Crowson | Basal cell carcinoma: biology, morphology and clinical implications[END_REF], suggesting that modifications of the ECM may be responsible for BCC progression. Among the various ECM components of the fibrotic response, fibronectin has been reported as the most strongly expressed upon fibroblast activation in chronic fibrosis [START_REF] Wynn | Cellular and molecular mechanisms of fibrosis[END_REF]. In order to determine the relationship between fibrosis and BCC infiltration, human BCC samples were collected and stained for fibronectin and S100A4, a marker for carcinoma-associated fibroblasts [START_REF] Kalluri | The biology and function of fibroblasts in cancer[END_REF]. Haematoxylin-eosin (HE) stains were performed on adjacent slides to determine BCC subtype. Higher levels of fibronectin and higher density of S100A4 + fibroblasts were found at the periphery of infiltrative compared to nodular BCC (Figures 1a and1b). Importantly, previously-treated or -biopsied tumor samples were excluded from our study. Hence, secondary modification of fibronectin expression due to inflammation or tissue repair after treatment can be safely excluded. To get an insight into the molecular drivers of peritumoral fibrosis in BCC, human samples were tested by quantitative real-time PCR for various secreted cytokines reported to promote fibronectin deposition. Among the various cytokines tested, TGFβ was found to be significantly higher in infiltrative compared to nodular BCC, both at the mRNA and protein levels (Supplementary Figure S1a and Figure 1c). These results suggest that TGFβ may be a key regulator of fibronectin induction and tumor infiltration in BCC.

To test this hypothesis in vivo, we induced "nodular-like" BCC by co-injecting the human UW_BCC_T2 cell line with mouse embryonic fibroblasts (MEFs) subcutaneously into NODSCID immunosuppressed mice. In this model, recombinant TGFβ was injected repeatedly into UW_BCC_T2 growing tumors (Supplementary Figure 1b). At the time of sacrifice, no difference in tumor growth (volume) was observed (Supplementary Figure 1c). However, higher levels of fibronectin as well as morphological changes reminiscent of human infiltrative BCC were found in tumors injected with recombinant TGFβ compared to controls. (Figures 1d and1e). Additional stainings for Ki67 as well as cleaved Caspase 3 did not show any difference in proliferation and apoptosis levels, respectively (Supplementary Figure 1d). Reduced E-cadherin, without associated N-cadherin enhancement upon TGFβ suggested a possible incomplete epithelial-to-mesenchymal transition (EMT) in this model (Supplementary Figure 1e). Interestingly, murine ASZ_001 cells co-injected with MEFs in NOD-SCID mice spontaneously formed "infiltrative-like" BCC. In this model, we neutralized TGFβ1 in tumor cell using lentiviral-mediated expression of TGFβ1-targeting short hairpin (sh)-RNA (Supplementary Figure 1f). When co-injected wit MEF (Supplementary Figure 1b), TGFβ1-silencing reduced tumor growth, peritumoral fibronectin and partially restored a "nodular-like" phenotype (Figures 1f and1g; Supplementary Figure S1c). Taken together, these results strongly suggest that TGFβ plays a key role in peritumoral fibronectin deposition as well as in the switch from a nodular to an infiltrative phenotype. Moreover, they help to address the current lack of in vivo models for the study of infiltrative BCC.

Increased BCC adhesion and migration on fibronectin is mediated by integrin α5β1.

ECM proteins have been shown to provide a scaffold that favors tumor cell migration and invasion [START_REF] Pickup | The extracellular matrix modulates the hallmarks of cancer[END_REF]. We therefore decided to explore whether BCC cells may adhere to deposited fibronectin in vitro. Using an adhesion assay, we found that both the human UW_BCC_T2 and murine ASZ_001 BCC cell lines are able to adhere very efficiently to fibronectin when compared to control (uncoated) or collagen I, the most abundant ECM component (Figures 2a and2b). Interestingly, long-term cultures on fibronectin revealed phenotypic modifications such as reduced cell-to-cell contacts and longer cytoplasmic extensions, suggestive of greater cell motility (Figure 2c). To address this question, we used the previously described wound-healing assay [START_REF] Liang | In vitro scratch assay: a convenient and inexpensive method for analysis of cell migration in vitro[END_REF][START_REF] Polacheck | Tumor cell migration in complex microenvironments[END_REF] either on uncoated or fibronectin-coated dishes. For both UW_BCC_T2 and ASZ_001 cell lines, fibronectin-coating promoted cell migration (Figures 2d-f).

Integrin α5β1 is a main fibronectin receptor, binding to its RGD domain [START_REF] Schaffner | Integrin alpha5beta1, the Fibronectin Receptor, as a Pertinent Therapeutic Target in Solid Tumors[END_REF]. Interestingly, we observed a significant expression of integrin α5β1 at the mRNA (not shown), and more importantly at the protein level in both UW_BCC_T2 and ASZ_001 cell lines (Figure 3a). To test the functional implication of integrin α5β1, we used both K34C, a recently developed pharmacologic inhibitor of integrin α5β1 [START_REF] Ray | Single cell tracking assay reveals an opposite effect of selective small non-peptidic alpha5beta1 or alphavbeta3/beta5 integrin antagonists in U87MG glioma cells[END_REF] and P1D6, an anti-human integrin α5β1 blocking antibody. K34C significantly reduced UW_BCC_T2 and ASZ_001 cells adhesion on fibronectin in a dose-dependent manner (Figure 3b). Similar results were obtained using P1D6 blocking antibody on UW_BCC_T2 cells (Figure 3c). Consistently, K34C inhibitor prevented fibronectin-induced migration of UW_BCC_T2 and ASZ_001 cells (Figure 3d). Similar results were obtained using P1D6 blocking antibody on UW_BCC_T2 cells (Figure 3e). Migration time-courses are shown in Supplementary Material (Supplementary Figures S2a-c). Importantly, neither K34C nor P1D6 did affect UW_BCC_T2 and ASZ_001 cell growth on fibronectin (Supplementary Figures S2d-f), suggesting a specific effect of integrin α5β1 in mediating fibronectininduced cell migration. Taken together, these results show that fibronectin promotes efficiently the migration of BCC cells through a mechanism implicating integrin α5β1 binding.

Fibronectin adhesion to integrin α5β1 induces focal adhesion kinase (FAK) phosphorylation both in vitro and in vivo.

FAK activation has been observed in various types of cancers and is widely associated with poor prognosis [START_REF] Gabarra-Niecko | FAK regulates biological processes important for the pathogenesis of cancer[END_REF]. It is a key mediator between extracellular adhesion to ECM and intracellular regulation of actin-cytoskeleton organization and cell motility. Integrin binding to ECM typically activates FAK through autophosphorylation at tyrosine 397 (Y397), providing a binding site for downstream activating molecules implicated in proliferation, survival and motility [START_REF] Tilghman | Focal adhesion kinase as a regulator of cell tension in the progression of cancer[END_REF]. We suspected that this mechanism could also be at play in BCC, and checked the phosphorylation status of FAK at Y397 in BCC cells lines, upon adhesion to fibronectin. As predicted by our model, we observed high levels of phosphorylated FAK (phospho-FAK) at the cell membrane of BCC growing on fibronectin but not on those growing on poly-l-lysine (Figure 4a). Consistently, K34C (Figures 4b and4d) and P1D6 antibody (Figures 4c and4d), both efficiently prevented FAK phosphorylation, bringing proof that this event is mediated by α5β1 integrin. Reduced FAK phosphorylation upon K34C and P1D6 treatments were confirmed by western blot (Figure 4e and Supplementary Figures S3a andS3b). Importantly, we observed preferential FAK phosphorylation in infiltrative-like areas of BCC injected with TGFβ (Figure 4f).

FAK mediates fibronectin-induced migration in vitro and TGFβ-induced infiltration in vivo.

To test the functional role of FAK in fibronectin-induced migration, we silenced FAK expression in tumor cells through lentiviral-mediated expression of FAK-targeting shRNA. Significant reduction in FAK level was confirmed at both the mRNA (not shown) and protein levels in both UW_BCC_T2 and ASZ_001 cell lines (Supplementary Figures S4a andS4b). In both cell lines, FAK silencing efficiently prevented fibronectin-induced migration in vitro (Figure 5a and Supplementary Figure S4c). In contrast to integrin α5β1 inhibition, FAK silencing also significantly reduced tumor cell growth in vitro (Supplementary Figure S4d). This difference may be explained by the implication of phospho-FAK in mediating tumor cell growth through alternative integrins [START_REF] Desgrosellier | Integrins in cancer: biological implications and therapeutic opportunities[END_REF]. We then tested the effect of FAK silencing in vivo (Supplementary Figure S4e). Consistently with the in vitro observations, FAK silencing in UW_BCC_T2 significantly prevented both tumor growth and TGFβ-induced infiltration in vivo (Figures 5b and5c; Supplementary Figure S4f). Similarly, FAK silencing in ASZ_001 prevented both tumor growth and spontaneous infiltration in vivo (Figures 5d and5e; Supplementary Figure S4g).

Taken together, these results identify integrin α5β1-dependent FAK phosphorylation as a key regulator of BCC cell adhesion and migration on fibronectin in vitro as well as infiltration in vivo.

Phospho-FAK inhibitor PF-562271 prevents fibronectin-induced migration in vitro and TGFβ-induced infiltration in vivo.

Having identified FAK as a key factor driving BCC invasiveness, we aimed to determine if this finding could have clinical implications. To support integrin α5β1 / phospho-FAK implication in human BCC progression, both were quantified in human BCC samples using immunohistochemistry. As expected, whereas integrin α5β1 was barely expressed in nodular BCC, significant expression was found in infiltrative BCC (Figure 6a). Similarly, phospho-FAK was found preferentially in highly infiltrative BCC (Figure 6a). Taken together with our previous findings, this strongly suggested that phospho-FAK targeting may prevent BCC infiltration in human.

Efficient inhibitors of FAK activity are available [START_REF] Golubovskaya | Targeting FAK in human cancer: from finding to first clinical trials[END_REF][START_REF] Slack-Davis | Cellular characterization of a novel focal adhesion kinase inhibitor[END_REF] and tested successfully in Phase I clinical trials for patients with solid advanced tumors [START_REF] Infante | Safety, pharmacokinetic, and pharmacodynamic phase I dose-escalation trial of PF-00562271, an inhibitor of focal adhesion kinase, in advanced solid tumors[END_REF]. We therefore hypothesized that they could also prevent expansion of aggressive BCC. We started by testing the effect of PF-562271, an enzymatic phospho-FAK inhibitor [START_REF] Infante | Safety, pharmacokinetic, and pharmacodynamic phase I dose-escalation trial of PF-00562271, an inhibitor of focal adhesion kinase, in advanced solid tumors[END_REF], in vitro and observed that it could efficiently prevent fibronectin-induced migration of BCC cells (Figure 6b and Supplementary Figures S5a). Similarly to FAK silencing, PF-562271 also significantly reduced tumor cell growth on fibronectin in vitro (Supplementary Figures S5b). Stimulated by these results we set up to test whether FAK inhibition also impinged tumor migration in vivo, by monitoring the effect of PF-562271 in our allograft models of invasive BCC (Supplementary Figure S5c). Mice bearing UW_BCC_T2/MEF tumors were injected intratumorally with recombinant TGFβ and simultaneously treated with or without the inhibitor. While PF-562271 did impinge on the growth of tumors (Supplementary Figure S5d), it also significantly prevented TGFβinduced infiltrative phenotype (Figures 6c and6e). Similarly, PF-52271 efficiently prevented both tumor growth (Supplementary Figure S5e) and spontaneous infiltration of ASZ_001/MEF tumors (Figures 6d and6e). The lack of biovailability data regarding integrin α5β1 inhibitor K34C unfortunately precludes from systemic administration at the time being. Nevertheless, as a proof-of-concept, we performed repeated intratumoral injection of K34C (Supplementary Figure S5c) that partially prevented TGFβ-induced infiltration in UW_BCC_T2/MEF tumors as well as spontaneous infiltration in ASZ_001/MEF tumors, without impacting tumor growth (Figures 6c-e; Supplementary Figures 5d and5e). Altogether, these results implicate TGFβ, fibronectin, and FAK phosphorylation through integrin α5β1 as a molecular pathway driving a phenotypic switch from nodular BCC to invasive BCC, with potential direct clinical benefits.

DISCUSSION

Here, we bring important insights in the field of aggressive BCC, setting up in vivo models for the study of infiltrative BCC and revealing the role of TGFβ-induced fibronectin in promoting tumor cell motility through integrin α5β1-mediated FAK phosphorylation.

The first key finding is the central implication of TGFβ-induced fibronectin as a functional link between fibrotic stroma and infiltrative phenotype during BCC progression. The dense peritumoral network induced upon TGFβ injection in our murine model is consistent with the previous report of TGFβ as the most potent activator of chronic fibrosis [START_REF] Meng | TGF-beta: the master regulator of fibrosis[END_REF]. Importantly, chronic fibrosis is a self-amplifying process, in which remodeled ECM sustains myofibroblast differentiation and release/activation of latent TGFβ [START_REF] Annes | Making sense of latent TGFbeta activation[END_REF][START_REF] Munger | Cross talk among TGF-beta signaling pathways, integrins, and the extracellular matrix[END_REF]. By analogy, initiation and maintenance of peritumoral fibrosis upon tumor-derived TGFβ expression may benefit from a self-amplifying loop [START_REF] Kojima | Autocrine TGF-beta and stromal cell-derived factor-1 (SDF-1) signaling drives the evolution of tumor-promoting mammary stromal myofibroblasts[END_REF]. Once activated, stromal TGFβ-induced remodeling may induce secretion of various ECM components and ECM-remodeling molecules that potentially contribute to tumor progression [START_REF] Ueha | Cellular and molecular mechanisms of chronic inflammationassociated organ fibrosis[END_REF]. Our work definitively contributes to define TGFβ-induced fibronectin as a key functional connector between fibrotic stroma and BCC tumor progression, resulting in the concomitant transition from a loose myxoid towards a dense fibrotic stroma and from a nodular towards an infiltrative tumor phenotype [START_REF] Crowson | Basal cell carcinoma: biology, morphology and clinical implications[END_REF]. As fibronectin is considered one of the most upregulated protein upon TGFβ stimulation (Rybinski et al., 2014, White and[START_REF] White | Fibronectin splice variants: understanding their multiple roles in health and disease using engineered mouse models[END_REF], it is not surprising to find high levels of fibronectin in various chronic fibrotic processes as excessive scarring (keloids), systemic sclerosis, chronic radiodermatitis or desmoplastic tumors [START_REF] Berman | Pentoxifylline inhibits the proliferation of human fibroblasts derived from keloid, scleroderma and morphoea skin and their production of collagen, glycosaminoglycans and fibronectin[END_REF][START_REF] Dooley | Modulation of collagen type I, fibronectin and dermal fibroblast function and activity, in systemic sclerosis by the antioxidant epigallocatechin-3-gallate[END_REF][START_REF] Kelsh | EDA Fibronectin in Keloids Create a Vicious Cycle of Fibrotic Tumor Formation[END_REF][START_REF] Roberts | Transforming growth factor beta stimulates the expression of fibronectin and of both subunits of the human fibronectin receptor by cultured human lung fibroblasts[END_REF][START_REF] Tien | Pancreatic carcinoma cells stimulate proliferation and matrix synthesis of hepatic stellate cells[END_REF][START_REF] Walker | The complexities of breast cancer desmoplasia[END_REF]. Importantly, several fibrotic skin events (like scars and chronic radiodermatitis among others) increase the risk to develop BCC [START_REF] Handa | Multiple pigmented basal cell carcinomas arising in the normal-appearing skin after radiotherapy for carcinoma of the cervix[END_REF][START_REF] Kowal-Vern | Burn scar neoplasms: a literature review and statistical analysis[END_REF][START_REF] Serrano-Ortega | Basal cell carcinoma arising in professional radiodermatitis of the nail[END_REF]. Further functional studies will be needed to link fibrotic events with the increased susceptibility to develop BCC.

As epithelial-to-mesenchymal transition (EMT) is reported in wound healing process and fibrosis [START_REF] Li | Pathophysiology of acute wound healing[END_REF], one intriguing question is whether EMT is required during the nodular to infiltrative transition. Our data support the hypothesis that EMT may act as a driver of BCC progression, as TGFβ, fibronectin and integrin α5β1 were all implicated in EMT [START_REF] Cicchini | TGFbeta-induced EMT requires focal adhesion kinase (FAK) signaling[END_REF][START_REF] Maschler | Tumor cell invasiveness correlates with changes in integrin expression and localization[END_REF][START_REF] Massague | TGFbeta in Cancer[END_REF][START_REF] Park | Mammary epithelial cell interactions with fibronectin stimulate epithelialmesenchymal transition[END_REF]. Moreover, despite the absence of N-cadherin detection, we demonstrated reduced Ecadherin in vivo upon TGFβ injection. Similarly, Papanikolaou et al. recently observed reduced E-cadherin levels as well as increased membranous integrin-linked kinase (ILK) at the invasive front of infiltrative BCC [START_REF] Papanikolaou | ILK expression in human basal cell carcinoma correlates with epithelial-mesenchymal transition markers and tumour invasion[END_REF], resulting in a shift from cell-to-cell contacts to cell-to-stroma interactions that is mediated by integrins. Further studies will be needed to study these intriguing observations. The second key finding is the functional implication of phospho-FAK downstream of integrin α5β1 activation. In fact, we showed that phospho-FAK inhibition recapitulates the effect of integrin α5β1 inhibition in term of fibronectin-induced migration in vitro and TGFβ-induced infiltration in vivo. However, phospho-FAK inhibition also prevented tumor cell proliferation on fibronectin in vitro, as well as tumor growth in vivo, whereas integrin α5β1 inhibition did not. Most integrins bind and activate FAK through their β subunit. Some however activate specific Src-family kinases (SFK) through their α subunit (as α1, α5 or αV) or exert a positional control over adjacent receptor tyrosine kinases (RTKs), which in turn affect FAK activity [START_REF] Alavi | Role of Raf in vascular protection from distinct apoptotic stimuli[END_REF][START_REF] Giancotti | Positional control of cell fate through joint integrin/receptor protein kinase signaling[END_REF], Hood et al., 2003[START_REF] Miranti | Sensing the environment: a historical perspective on integrin signal transduction[END_REF][START_REF] Wary | The adaptor protein Shc couples a class of integrins to the control of cell cycle progression[END_REF][START_REF] Wary | A requirement for caveolin-1 and associated kinase Fyn in integrin signaling and anchorage-dependent cell growth[END_REF]. These complex and specific interactions between integrins, SFK, adjacent RTK and various cofactors modulate FAK activation and dictate specific downstream effector pathways, as cell proliferation, cell survival or cell migration [START_REF] Desgrosellier | Integrins in cancer: biological implications and therapeutic opportunities[END_REF]Cheresh, 2010, Guo and[START_REF] Guo | Integrin signalling during tumour progression[END_REF]. Our data suggest that FAK is required for both cell proliferation and migration through different activation routes in BCC. While integrin α5β1 specifically mediates fibronectin-induced migration, further studies will be needed to decipher the mechanisms of FAK-mediated proliferation. Altogether, our data identify FAK inhibition as a promising therapy for advanced BCC. Importantly, various phospho-FAK inhibitors have been recently developed, some with proven clinical success [START_REF] Golubovskaya | Targeting FAK in human cancer: from finding to first clinical trials[END_REF][START_REF] Infante | Safety, pharmacokinetic, and pharmacodynamic phase I dose-escalation trial of PF-00562271, an inhibitor of focal adhesion kinase, in advanced solid tumors[END_REF][START_REF] Slack-Davis | Cellular characterization of a novel focal adhesion kinase inhibitor[END_REF]. The precise place of FAK inhibitors along surgery, radiotherapy or Smoothenedinhibitors naturally remains to be clarified.

In conclusion, this work suggests that TGFβ, fibronectin, integrin α5β1 and phospho-FAK act together as key regulators in driving a dense fibrotic peritumoral stroma and BCC infiltration. We bring experimental evidence for the role of TGFβ in peritumoral fibronectin deposition and BCC infiltration in murine models of infiltrative BCC and identify integrin α5β1-mediated phosphorylation of FAK, upon fibronectin adhesion, as a mechanism regulating BCC cell motility. The clinical relevance of our experiments is validated by the observation of increased TGFβ, fibronectin as well as membranous phospho-FAK in human infiltrative BCC. Hence, this work extends our understanding of the biology of aggressive infiltrative BCC and provides an essential step toward better prevention and improved treatment of BCC.

MATERIALS AND METHODS

Cell lines and cell culture.

UW_BCC cell line was generously provided by Dr. V. Spiegelman (Madison, WI). UW_BCC_T2 were obtained as previously described [START_REF] Bal | Mutations in ACTRT1 and its enhancer RNA elements lead to aberrant activation of Hedgehog signaling in inherited and sporadic basal cell carcinomas[END_REF]. ASZ_001 cell line was generously provided by Dr. E. Epstein (Oakland, CA). For all experiments, cells were grown in M154CF (Invitrogen, Basel, Switzerland) supplemented with 10% FBS, 1% P/S and CaCl2 0.05mM. 293T cells were obtained from ATCC (Manassas, VA). Dermal mouse embryonic fibroblasts (MEF) were obtained from 13.5 days-old C57BL/6 embryos as described in (A, 2007). 293T and MEF were grown in DMEM (Invitrogen, basel, Switzerland) supplemented with 10% FBS and 1% P/S. Cell lines were assessed for mycoplasma using the MycoSeq Mycoplasma real-time PCR detection kit (ThermoFisher Scientific, Waltham, MA) and frozen stocks were used for a maximum of 2 months.

Mouse model and drug treatment.

Adult male (5-7 weeks of age) NOD-SCID mice were used as host animals for grafted tumors. Primary tumors were initiated by injection of UW_BCC_T2 (5×10 5 cells/mouse) or ASZ_001 (5×10 5 cells/mouse) tumor cells together with MEF (1.5×10 6 cells/mouse) subcutaneously in 100μl of PBS:Matrigel 1:1. For intratumoral injection, mouse recombinant TGFβ1 (R&D Systems, Minneapolis, MN) was dissolved in 0.1% BSA, 4mM HCl and diluted in PBS before injection. PF-562271 inhibitor (MedKoo Biosciences, Chapel Hill, NC) was dissolved in DMSO and diluted in 5% DMSO (H2O) for oral gavage. K34C inhibitor was dissolved in DMSO and diluted in 0.2% DMSO (PBS) for intratumoral injections. Tumor volume was assessed as previously described [START_REF] Kuonen | Inhibition of the Kit ligand/c-Kit axis attenuates metastasis in a mouse model mimicking local breast cancer relapse after radiotherapy[END_REF]. Infiltration was assessed on HE stainings in every quarter of a Chalkley grid (0= nodular; 1= slightly infiltrative; 2= infiltrative) and summed. For every slide, an infiltrative score from 0 (highly nodular) to 8 (highly infiltrative) was obtained. Mice were housed under standard conditions, and animal care was in compliance with the protocols approved by the Institutional Animal Care and Use Committee (IACUC) at Stanford University.

Human BCC samples.

Study on human samples obtained in Switzerland was approved by the cantonal ethical authority (VD, Switzerland) and written informed consents were obtained from participants. Study on human samples obtained from Stanford University was approved by the Stanford University Institutional Review Board (Stanford, CA), with a waiver ofconsent from participants.

Statistical analyses.

Statistical comparisons were performed by a two-tailed Student's t test or one-way ANOVA with Tukey's post test for multiple comparisons. Statistical analyses were performed using GraphPad Prism (La Jolla, CA). The data were considered to be significantly different when p < 0.05.

A more complete and detailed description of the methods is included in Supplementary Materials and Methods.

Figure 1 .

 1 Figure 1. TGFβ is associated with peritumoral fibronectin deposition and the transition from nodular to infiltrative phenotype in human BCC samples and mouse models.(a) Fibronectin and S100A4 stainings of nodular and infiltrative human BCC tumors. (b) Quantification of the stainings shown in (a). (c) Quantification of TGFβ at the protein level measured in nodular and infiltrative human BCC. (d) Fibronectin and HE stainings of UW_BCC_T2/MEF tumors injected either with PBS (control) or recombinant TGFβ (400ng/injection, 3×/week). (e) Quantification of fibronectin and infiltration in UW_BCC_T2/MEF tumors shown in (d). (f) Fibronectin and HE stainings of ASZ_001_ns/MEF and ASZ_001_TGFβshRNA/MEF tumors. (g) Quantification of fibronectin and infiltration in tumors shown in (f). Scale bars indicate 100μm. Columns and error bars represent the mean ± SD for n ≥ 5 samples or mice per group. *p < 0.05, **p < 0.01 and ***p < 0.001.

Figure 2 .

 2 Figure 2. Fibronectin promotes BCC adhesion and migration. (a)Crystal violet staining of adhesion assays performed with UW_BCC_T2 and ASZ_001 on BSA, collagen I or fibronectin. Scale bars indicate 1mm. (b) Quantification of adhesion assays shown in (a). (c) Crystal violet staining of long-term clonogenic assays performed with UW_BCC_T2 and ASZ_001 on uncoated or fibronectin-coated plates. (d) Timecourse and crystal violet staining of migration assays performed with UW_BCC_T2 on uncoated or fibronectin-coated plates. (e) Timecourse and crystal violet staining of migration assays performed with ASZ_001 on uncoated or fibronectin-coated plates. (f) Tumor cell velocity measured from migration assays performed in (d) and (e). Scale bars indicate 100μm (unless specified). Columns and error bars represent the mean ± SD for n ≥ 3 per group. *p < 0.05, **p < 0.01 and ***p < 0.001.

Figure 3 .

 3 Figure 3. BCC adhesion and migration on fibronectin is mediated by integrin α5β1.

( a )

 a Flow cytometry analysis of integrin α5 and β1 subunits on UW_BCC_T2 and ASZ_001. (b) Crystal violet staining and quantification of UW_BCC_T2 and ASZ_001 adhesion to fibronectin when treated with DMSO or K34C. (c) Crystal violet staining and quantification of UW_BCC_T2 adhesion to fibronectin when treated with isotype (control) or P1D6 antibodies. (d) Crystal violet staining and quantification of UW_BCC_T2 and ASZ_001 migration on fibronectin when treated with DMSO or K34C.(e) Crystal violet staining and quantification of UW_BCC_T2 migration on fibronectin when treated with isotype (control) or P1D6 antibodies. Scale bars indicate 1mm in (b) and (c), and 100μm in(d) and (e). Columns and error bars represent the mean ± SD for n ≥ 3 per group. *p < 0.05, **p < 0.01 and ***p < 0.001.

Figure 4 .

 4 Figure 4. Fibronectin adhesion to integrin α5β1 induces FAK phosphorylation. (a) Phospho-FAK immunostainings of UW_BCC_T2 and ASZ_001 on poly-L-lysine or fibronectin. (b) Phospho-FAK immunostainings of UW_BCC_T2 and ASZ_001 on fibronectin treated with DMSO or K34C. (c) Phospho-FAK immunostainings of UW_BCC_T2 on fibronectin treated with isotype (control) or P1D6 antibodies. (d) Quantification of membranous phospho-FAK shown in (b) and (c). (e) Western blots for phospho(Y397)-and total-FAK in UW_BCC_T2 and ASZ_001 on fibronectin treated with DMSO or K34C, and UW_BCC_T2 on fibronectin treated with isotype (control) or P1D6 antibodies. (f) Phospho-FAK stainings and quantification in nodular-compared to infiltrative-like areas of UW_BCC_T2 tumors injected with TGFβ. Scale bars indicate 100μm. White arrowheads indicate membranous phospho-FAK. Scale bars indicate 20μm (unless specified). Columns and error bars represent the mean ± SD for n ≥ 3 per group. *p < 0.05, **p < 0.01 and ***p < 0.001.

Figure 5 .

 5 Figure 5. FAK mediates fibronectin-induced migration in vitro and TGFβ-induced infiltration in vivo. (a) Crystal violet staining and quantification of migration assays performed with UW_BCC_T2_ns or UW_BCC_T2_FAKshRNA and ASZ_001_ns or ASZ_001_FAKshRNA cells on uncoated or fibronectin-coated plates. (b) HE stainings of UW_BCC_T2_ns/MEF or UW_BCC_T2_FAKshRNA/MEF tumors injected either with PBS or recombinant TGFβ (400ng/injection, 3×/week). (c) Quantification of infiltration in tumors shown in (b). (d) HE stainings of ASZ_001_ns/MEF or ASZ_001_FAKshRNA/MEF tumors.

Figure 6 .

 6 Figure 6. Phospho-FAK inhibition prevents fibronectin-induced migration in vitro and TGFβinduced infiltration in vivo.

( a )

 a Pictures and quantification of integrin α5β1 and phospho-FAK stainings in human nodular and infiltrative BCC. (b) Crystal violet staining and quantification of UW_BCC_T2 and ASZ_001 migration on fibronectin treated with DMSO or PF-562271. (c) HE stainings of UW_BCC_T2/MEF tumors injected either with PBS or recombinant TGFβ (400ng/injection, 3×/week) and simultaneously treated with either DMSO, PF-562271 (50mg/kg, 1×/day) or K34C (50μl at 20μM).

J Invest Dermatol. Author manuscript; available in PMC 2019 May 01.

ACKNOWLEDGEMENTS

This work was supported by a MD-PhD clinician fellowship from CHUV-FBM (to FK), a Swiss National Research Foundation fellowship (to FK), a Fondation René Touraine fellowship (to FK), the Swiss National Research Foundation grant 31003A_159824 (to CR) and the NIH R01ARO46786 grant (to AO). We acknowledge Hanson Zhen for his help with the isolation of dermal mouse embryonic fibroblasts.

Supplementary Material

Refer to Web version on PubMed Central for supplementary material.


M Benchikhi

R El Ouatib

L Er-Rakho

S Guillemet-Fritsch

B Durand

F Olivie

K Kassmi

Morphological and electric characterizations of a nanometric material α-CuMoO 4 for photovoltaic application

Keywords: CuMoO 4, soft chemistry, semiconductor, nanoparticles, conventional caking, spark plasma sintering, forbidden band width, morphology. Résumé CuMoO4, chimie douce, semi-conducteur, nanoparticules, frittage conventionnel, frittage SPS, largeur de bande interdite, morphologie

The work presented in this publication concerns the elaboration by soft chemistry and the structural, morphological and physical characterizations of semiconductors with metallic Oxides CuMoO 4 . Particularly, we study the caking of powders of molybdate of copper: conventional sintering and Spark Plasma Sintering (SPS). The characterization by Xrays diffraction analyses (DRX) and scanning electronic microscopy (SEM) show that the ceramic obtained by SPS at 300°C

for 5 min has a densification of 98.0 %, superior to that of the ceramic sintered in a conventional way (94.8 %), with a grain size (0.2 µm) significantly lower than that obtained by conventional sintering (2.0 µm). The study of the electric properties by the method of the current-voltage measurements (I-V) of the non doped ceramic CuMoO 4 shows on one hand, the semiconductor character of the material and on the other hand, a clear improvement of the thermal activation of the carriers in the case of the ceramic obtained by SPS at 300°C. The width of the forbidden gap (Eg) deducted from these measurements is 1.8 ± 0.1 eV.

Introduction

La recherche de ressources alternatives d'énergie est devenue une question cruciale de nos jours [START_REF] Clark | Changing the Atmosphere Expert Knowledgeand Environmental Governance[END_REF][START_REF] Iskander | Recent developments of applying solar photovoltaic technologies in Malta[END_REF]. Beaucoup de recherches scientifiques ont été développées dans le secteur des sources illimitées d'énergie telles que la production d'électricité par la transformation d'énergie solaire [START_REF] Wijesundera | [END_REF][START_REF] Sebastian | Role of substrate temperature in controlling properties of sprayed CuInS 2 absorbers[END_REF]. La majorité des études concerne la réalisation de nouveaux matériaux nanométriques, permettant la réalisation des cellules photovoltaïques (PV) de faible coût et de propriétés électriques et de rendement meilleurs que ceux des cellules à base de semi-conducteurs classiques (Si,…). Depuis plusieurs décennies, un effort important de la recherche sur les nanomatériaux est consacré au développement et à l'amélioration des méthodes de synthèse. En effet, le contrôle des caractéristiques morphologiques des particules nanométriques de matériaux présente un grand intérêt pour optimiser leurs propriétés dans des domaines d'application photovoltaïque. De nombreuses méthodes de synthèse aussi bien physiques que chimiques ont été développées pour permettre l'obtention des matériaux présentant des caractéristiques morphologiques bien définies. Les méthodes physiques telles que l'ablation laser [5], la pulvérisation cathodique [START_REF] Benchikhi | Ceramics International[END_REF], l'évaporation [START_REF] Wagner | [END_REF], et l'électrodéposition [8] sont basées sur la décomposition d'un matériau massif afin d'en réduire la taille. Ces méthodes nécessitent généralement des installations lourdes et coûteuses sans pour autant forcément assurer l'obtention de préparations homogènes (films uniformes, composition chimique stable, etc.). Les méthodes chimiques quant à elles, sont moins onéreuses, plus accessibles et consistent à faire croître les particules en utilisant des précurseurs (molécules, complexes, etc.) comme entités de départ. Parmi un grand nombre de techniques d'élaboration par voie chimique, on peut citer la synthèse solvothermale [9][10][11][12][13], la précipitation [14][15][16], la méthode Péchini [17,18], le procédé glycinenitrate [19], la méthode sels fondus [20] et la voie sol-gel [21,22]. L'objectif de ce travail est de proposer de nouveaux matériaux nanostructurés photo-actifs pour la conversion photovoltaïque. Deux études sont réalisées :

-matériau CuMoO 4 fritté par la méthode conventionnelle. Ces matériaux sont élaborés par voie de chimie douce des matériaux nanométriques à base de cuivre et de molybdène (Cu-Mo), -matériau CuMoO 4 fritté par voie conventionnelle et sous charge par Spark Plasma Sintering (SPS) à basse température. Les différents matériaux sont caractérisés par diffraction des Rayons X(DRX), microscopie électronique à balayage (MEB) et électriquement à partir du banc DLTS automatisé.

Résultats et discussions

Synthèse de la poudre CuMoO4

La synthèse de la variété alpha du molybdateCuMoO 4 a été faite par voie de chimie douce au Laboratoire LPCMI de Casablanca, en mettant en oeuvre la pyrolyse d'un complexe polymérisable synthétisé selon la méthode de Pechini [17][18]. La figure 1 résume les étapes de cette synthèse.

. Frittage

Le frittage de la poudre du matériau α-CuMoO 4 (Figure 2) a été réalisé, de façon conventionnelle au laboratoire du CIRIMAT de Toulouse, et par SPS à la plate Forme Nationale de Frittage Flash (PNF2) de Toulouse:  La méthode conventionnelle [START_REF] Sebastian | Role of substrate temperature in controlling properties of sprayed CuInS 2 absorbers[END_REF]: L'oxyde α-CuMoO 4 a été fritté à l'air en présence d'un liant organique (Rhodoviol), par traitement thermique avec une vitesse de chauffe de 2,5°C/mn d'un cru obtenu par compression uniaxiale, suivant la procédure classique. L'optimisation du cycle thermique du frittage et notamment la durée du palier, a permis d'obtenir un matériau fritté présentant un taux de densification de 95% (Figure 3).  La méthode de frittage flash, SPS : Cette technique est intéressante car elle permet de fritter à des températures beaucoup plus basses et des durées beaucoup plus courtes que celles requises pour des frittages «conventionnels ». Les poudres de molybdates CuMoO 4 (Figure 3) sont introduites dans une matrice en carbure de tungstène sans aucun liant. Le chauffage est assuré par un courant électrique pulsé de faible tension et très forte intensité avec application d'une pression pendant tout le cycle thermique. L'enregistrement du retrait des pastilles crues est effectué in situ directement dans l'enceinte du SPS sous atmosphère d'argon. Différents paramètres de frittage, la température, la durée du palier, la pression appliquée, ont été optimisés en vue d'obtenir une densification la plus élevée possible. Dans les conditions optimales de température et de palier (300°C, 5 min), la pression a également été optimisée. On obtient une densité maximale pour une pression de 225 MPa, i.e 97,70 %.

Caractérisation DRX et MEB

La caractérisation par diffraction des Rayons X(DRX) et par microscopie électronique à balayage (MEB) de la poudre obtenue a été réalisée au CIRIMAT. Les diagrammes de diffraction X des céramiques du matériau CuMoO4, après frittage, conventionnel et SPS à basse température (Figure 4), montrent la conservation de la phase α-CuMoO 4 pour les deux types de frittage. On constate également un élargissement des pics de diffraction pour la céramique frittée par SPS attribuable à la conservation d'une taille de cristallites beaucoup plus faible. Les micrographies MEB des céramiques (Figure 5) confirment que le frittage flash conduit à une céramique avec une taille de grains (0,2 µm) dix fois plus faible que celle de la céramique frittée par la méthode conventionnelle (2,0 µm).

Caractérisation électrique des céramiques du matériau α-CuMoO4 2.4.1. Densité de courant et résistivité

Les propriétés électriques de l'oxyde α-CuMoO 4 ont été étudiées au LAAS/CNRS (Toulouse). Le matériau α-CuMoO 4 fritté (Figure 3) est métallisé face avant et face arrière par une couche d'or par évaporation, puis déposé et soudé à un substrat en silicium par une couche d'aluminium. Ce substrat constitue un support nécessaire aux mesures DLTS (Figure 6). Le banc DLTS permet de relever les caractéristiques courant-tension en fonction de la température et en conséquence d'analyser l'activation thermique des porteurs de charges libres et d'estimer la largeur de la bande interdite (Eg) du matériau α-CuMoO 4 . Lorsque la pastille est chauffée à 450 K pendant 5 min, il apparait un comportement ohmique et le matériau α-CuMoO 4 montre les propriétés électriques d'un semi-conducteur, dépendantes de la température et du type de frittage :  Dans le cas d'un frittage normal, le matériau a un caractère ohmique et les densités de courant observées sont très faibles (inférieures à 10 -6 A/cm 2 ). La résistivité du matériau diminue avec la température à partir de 360K environ. Ceci montre la présence des porteurs de charges libres dont la création et la densité augmentent avec la température.  Dans le cas d'un frittage SPS, les densités de courant sont nettement plus importantes que celles obtenues par frittage conventionnel, en particulier après chauffage du matériau. Lorsque la tension appliquée est de 10V et la température de l'ordre de 450K, la densité de courant (résistivité) augmente (diminue) d'un facteur de 20 pour un frittage SPS avant chauffage et de 100 après chauffage.

L'ensemble des résultats montre des propriétés électriques dépendantes de la température, similaires à celles des semiconducteurs conventionnels au silicium [22]. Dans la suite, nous analysons la largeur de bande interdite de chaque type de matériau (frittage conventionnel et SPS).

 (.cm) T (°K)

Fig. 8 : Résistivité du matériau α-CuMoO 4 en fonction de la température et du type de frittage.

Largeur de la bande interdite

Nous avons estimé la largeur de la bande interdite (Eg) du molybdate de cuivre à partir de la relation qui régit les semi-conducteurs au silicium [START_REF] Sze | Physics of semiconductor devices[END_REF]:

(1) où ; K B est la constante de Boltzmann. Le tracé de la résistance R du matériau suivant cette relation (Figure 9) montre un comportement linéaire, pour chaque cas de matériau. Ceci traduit que le matériau synthétisé possède bien les propriétés d'un semi-conducteur dont la largeur de bande interdite (Eg) peut être déterminée par la relation 1. A partir de la pente de chaque caractéristique, nous avons déterminé et reporté dans le tableau 1 les valeurs de Eg pour chaque type de matériau. Il apparait que :

2,0x10

 Avant traitement thermique, la largeur de bande de la céramique α-CuMoO 4 frittée par SPS, 1,89 eV est du même ordre de grandeur que celle de la céramique frittée par voie conventionnelle, 1.71-1.94 eV. Ces valeurs sont en accord avec celles trouvées pour des céramiques α-CuMoO 4 , frittées par la méthode conventionnelle (2,00 eV).  Le recuit à 450 K de la céramique frittée à basse température par SPS influe sur l'activation des porteurs de charges et en particulier sur le gap (Eg). L'ensemble des résultats obtenus montre la faisabilité du semi-conducteur nanométrique α-CuMoO 4 , fritté par la méthode SPS à basse température. Le matériau obtenu présente des grains de taille voisine de 200 nm et un gap de l'ordre de 2 eV. Afin de réduire la résistivité du matériau, des études sont en cours sur la possibilité d'augmenter le nombre de porteurs de charge par des dopages de type N ou P.

Frittage conventionnel

Frittage SPS Avant chauffage

Après chauffage Eg (eV) 1,71 -1,937 1,89 0,35 Tableau 1 : Largeur de la bande interdite du matériau α-CuMoO 4 .

Conclusion

Les premiers résultats obtenus sur le matériau α-CuMoO 4 montrent que la taille des grains et les propriétés électriques du matériau dépendent fortement du type de frittage (conventionnel ou SPS à basse température). Les résultats obtenus mettent en évidence :

 Le frittage SPS à basse température conduit à des céramiques de faible taille de grains. Les tailles de grains des céramiques obtenues sont de l'ordre de 200 nm (soit une réduction d'un facteur de 10 par rapport au frittage conventionnel).  les propriétés électriques des matériaux sont similaires à celles des semiconducteurs conventionnels : lorsque la température augmente la densité de courant augmente et la résistivité diminue.  le matériau α-CuMoO 4 possède les propriétés d'un semi-conducteur de bande interdite de largeur de l'ordre de 2 eV. Ces dernières valeurs sont en bon accord avec celles de la littérature dans le cas d'un matériau proche de celui de CuMoO 4 .

Remerciements-Ce

Références

Figure 1 :

 1 Figure 1: Procédé d'élaboration du composé α-CuMoO 4 [6].

Figure 2 :

 2 Figure 2 : Machine SPS de la Plate Forme de frittage Flash.

Figure 3 :

 3 Figure 3 : Poudre et matériau α-CuMoO 4 .

Figure 4 :

 4 Figure 4 : Diagramme DRX du matériau α-CuMoO 4 fritté par la méthode conventionnelle (a) et par SPS (b).

Figure 5 :

 5 Figure 5 : Micrographie MEB du matériau CuMoO 4 fritté par la méthode conventionnelle (a) et SPS (b).

Figure 6 :

 6 Figure 6 : Banc de mesure DLTS du LAAS. Les caractéristiques densité de courant-tension typiques ainsi que la résistivité du matériau en fonction de la température sont représentées sur les figures 7 et 8. Toutes les céramiques ont été caractérisées dans les mêmes conditions.

Fig. 7 :

 7 Fig. 7: Caractéristiques densité de courant-tension du matériau α-CuMoO 4 en fonction de la température et du type de frittage.

12 :

 12 Frittage SPS, après chauffage à 450 °K, : Frittage SPS, avant chauffage à 450 °K, : Frittage normal.

: 1 )Figure 9 :

 19 Figure 9 : Tracé permettant d'estimer la bande interdite du matériau α-CuMoO 4

  travail est soutenu par le Comité Franco -Marocain 'Action Intégrée N° MA/09/205 et la Convention CNRS/CNRST N° Chimie 14/11.

Matériau CuMoO4.


J Lochner

J Gain

S Perche

A Peytavie

E Galin

E Guérin

Interactive Authoring of Terrain using Diffusion Models

Styles palette

Figure 1: Our diffusion-based terrain authoring framework empowers users to iteratively combine terrain stylization with feature sketching.

Here, an artist first sketches a simple ridge and forked drainage network, then makes their style selection (outlined in red) before adding further details.

Introduction

The need for authoring tools that enable digital artists to create convincing heightfield terrains suited to a particular aesthetic or functional rôle is widespread in computer graphics applications, such as film, games, training, and simulation. Using scanned real-world terrain often does not suffice, since landforms may be missing or not arranged acceptably. Once authored, a bare heightfield is typically layered with surface detail to depict earth, rock, grass, plants, trees, rivers, and bodies of water, representing a complete natural scene.

The effective authoring of synthetic terrain is a notoriously difficult problem to solve for many reasons. First, achieving perceptual realism is a challenge due to the complexity of the underlying physical processes that interact to shape terrain. For example, shifting tectonic plates, gradual erosive forces, and even natural disasters contribute to terrain formation. Second, the sheer variety of formative processes gives rise to a correspondingly wide range of distinctive landforms, from plains to mountains and every style inbetween. Third, authoring tools should afford a balance between design economy and precision so that artists can achieve envisaged results (precision) as tersely and rapidly as possible (economy). Finally, allied to this is the need for a computationally efficient realtime or interactive generation process to enable cycles of iterative design. Ideally, a terrain authoring framework should produce perceptual realism, landform diversity, both economical and precise authoring, and interactive response.

To address this, terrain authoring has historically been built on a foundation of procedural, simulation, or example-based techniques [GGP * 19]. Recently, these have been complemented by generative machine learning, where deep neural networks -including Convolutional Neural Networks (CNNs) [ACA18, KSR20] and Conditional Generative Adversarial Networks (CGANs) [GAMA20, ZLZ * 22, ZLB * 19, ZCZ * 20, NJSR22] -are tasked with learning the complex patterns and mutual dependencies between terrain features, given abundant real-life data, and conditioned on user inputs, such as user sketches or style selection. Unfortunately, these strategies suffer from repetition and gridding artifacts with sparse inputs [START_REF] Guérin | Manual of Digital Earth[END_REF], tend to tackle only specific sub-tasks (e.g., super-resolution) rather than providing an overarching authoring framework, and also, with a few exceptions [START_REF] Li | Generating terrain data for geomorphological analysis by integrating topographical features and conditional generative adversarial networks[END_REF], focus primarily on mountainous regions, ignoring plains, cliffs, and canyons.

Inspired by evidence of the effectiveness of Denoising Diffusion Probabilistic Models (DDPMs) in conditional image generation [Luo22] with high sample diversity [DN21], we develop a feature-rich terrain authoring framework that performs cascaded applications of diffusion models. Our framework supports interactive authoring through style selection and feature sketching (see Figure 1), followed by a finalizing amplification step. Performance is sufficient to enable near real-time updates (∼ 8Hz) during sketching, with additional iterative quality refinement taking place in the background between strokes. To achieve this, we balance sample quality and inference speed by trading off terrain resolution, number of sampling timesteps, and memory footprint. The resulting synthesized terrains encompass a wide range of landforms and evidence improved structural and perceptual realism. Specifically, we found the results of diffusion to be structurally sound but sometimes missing in fine-scale detail so that users in our perceptual study were able to differentiate between real and generated landscapes in certain cases, but not in others.

Related Work

Traditionally, digital terrain generation techniques, as surveyed by Galin et al. [GGP * 19], have been partitioned into three categories: procedural modeling, geomorphological simulation, and datadriven synthesis. Procedural approaches algorithmically reverseengineer terrain based on characteristics of the final appearance using a collection of techniques that include constrained multiresolution noise, diffusion, and deformation. Simulation seeks to replicate the physical processes of uplift and erosion involved in landscape formation. However, our focus in this paper is on data-driven methods that exploit the extensive high-quality corpus of scanned realworld terrain data and offer the prospect of effective user control, interactive performance, and perceptual realism.

The earliest data-driven methods repurposed texture synthesis for terrain generation by cutting, reassembling, and joining terrain fragments at a patch or pixel level [LWZ * 06,ZSTR07]. Subsequent research built on this foundation to improve: realism by altering patch blending [TGM12] and fixing global drainage [SD21,SD22], performance through GPU acceleration [TGM12, GMM15], and authoring control by extending beyond ridge and valley sketching [START_REF] Gain | Parallel, realistic and controllable terrain synthesis[END_REF]. Compared to machine learning, the upside is that these methods can operate parsimoniously with as little as a single source terrain, but the downside is that re-assembly is localized and, despite some attempts at improvement [SD21], does not always respect global properties, such as realistic drainage patterns.

Sparse modeling [GDGP16, AAC * 17] represents another example-based approach. It is underpinned by compressed sensing theory and relies on a dictionary of reusable terrain patches, which are sampled and blended at run-time to construct a terrain. However, these techniques suffer from the same limitations as texture synthesis methods and lend themselves more to compression and amplification than authoring [GGP * 19].

Inspired by the success of image-to-image translation [IZZE17], Guérin et al. [GDG * 17] were the first to apply machine learning to terrain authoring. They use a conditional generative adversarial network trained on the pairing of real terrains and extracted ridge and valley line maps to enable the interactive generation of plausible terrain from user sketches. This approach is flexible enough to support a range of authoring tools and tasks, including in-filling missing areas of a DEM, user support for painting average elevations or water occupancy [START_REF] Valencia-Rosado L | Generation of synthetic elevation models and realistic surface images of river deltas and coastal terrains using cgans[END_REF], and upsampling with erosion detail, but suffers from gridding and repetition artifacts when the user inputs are not sufficiently detailed.

A standard CGAN or CNN pipeline generates a single outcome even though two-dimensional user sketches are highly underdetermined. In reality, the same sketched configuration of ridge and valley lines could plausibly lead to various landforms, representing different terrains types or styles. An obvious solution to this stylization problem is to train separate synthesizers for each terrain type, but this inherently limits the number of styles and is a bar to transitional regions that mix styles. Better strategies involve making the training and synthesis conditional on a multi-dimensional style discriminator [ZLZ * 22] or selecting variations from a latent space [NJSR22].

Depending on the details of the scanning campaign, Digital Elevation Models (DEMs) of real-world terrain can have varying resolutions, from as fine as 1 to as coarse as 90 meters per pixel. As a consequence, resolution amplification (otherwise known as upsampling or super-resolution) is a common application area for machine learning that has seen various recent experiments in modifying CGAN [ZCZ * 20, ZLB * 19] and CNN [KSR20, ACA18] architectures.

The vast majority of these data-driven methods have used adaptations of texture synthesis, CNNs, or CGANs specialized for terrain generation. However, in the space of image-to-image translation, of which user-guided terrain synthesis is a specific instance, Denoising Diffusion Probabilistic Models (DDPMs, or simply, diffusion models) have recently emerged as a highly-competitive alternative [HJA20, YZS * 22] in terms of task versatility and perceptual image quality. The focus of this paper is thus on exploring the applicability of this class of generative models to terrain synthesis, while at the same time expanding the richness of the authoring toolset.

Overview

Our framework supports authoring in two complementary forms: feature sketching and example-based stylization. At a high level, feature sketching provides users with an intuitive way to specify the type and placement of features on the landscape, while stylization controls the overall appearance of the resulting terrain (using examples for guidance). As demonstrated in Figure 7, users are provided with tools to sketch cliff, valley, and ridge lines at different levels of prominence. This expands significantly on the typical toolset offered by machine learning interfaces. Notably, blank areas in the sketch are nevertheless populated with plausible features, but this can be suppressed by painting with a flattening brush. Furthermore -in the interests of iterative refinement -users are offered a palette of available styles, both before and after sketch input, to control the overall terrain character.

By design, the combination of a style and detailed sketch map provides a signature sufficient for terrain reconstruction, meaning a user-provided terrain can be imported, matched, and then edited. This idea is demonstrated in Figure 3, where localized changes can be made to an existing terrain in a manner that balances realism and user intent.

As is typical in machine learning this is realized by separating the architecture into a pre-processing and training phase, and an online generation phase (see Figure 2). Our data preparation (described in section 4), centers around the training and utilization of CNN-based classifiers to remove terrain that contains recording errors or artificial features, followed by signature extraction and model training.

In terms of models, our framework is built upon two different types of diffusion-based terrain synthesizers (detailed in section 5). First, our sketch-to-terrain model S generates terrain from a signature that combines a sketch and style vector. Second, our terrainupscaling models U 1 and U 2 enhance the small-scale details of terrain in a realistic way, being able to increase terrain resolution from 153m per pixel to 19.1m per pixel and from 19.1m per pixel to 2.39m per pixel, respectively. Thus, in a similar fashion to Ho et al. [HSC * 22], we cascade these diffusion models (i.e., using the output of one as input to the next) to achieve high-resolution terrain synthesis. As demonstrated in Figure 4, this results in a 64× resolution increase, in a manner that preserves the global structure of the output terrain.

Data Preparation

We obtained raw elevation and co-registered satellite data from the United States Geological Survey (USGS). To select suitable regions, we submitted a user-defined mask created by taking into account elevation, gradient, and population-density maps of North America. This approach ensures that the final dataset includes a diverse selection of landforms. The corresponding ∼ 6 million tiles (stored individually as 256 × 256 float arrays) were downloaded at the highest available resolution of ∼ 2.39 meters per pixel.

Preprocessing

Unfortunately, many of the downloaded tiles contain recording errors, making them unusable for training. Failure to remove such data would degrade output quality, with artifacts or sampling errors replicated (or even magnified) in the synthesized terrains [GGP * 19]. We first performed a combination of algorithmic and manual labeling of approximately 350 000 derivative images. More specifically, we defined a list of simple heuristics to identify abnormal changes in elevation, followed by a manual moderation process to ensure edge-cases were correctly labeled. This initial batch was then used to train a CNN classifier based on EfficientNetV2 [TL21] to filter the remaining tiles. We also removed terrains containing man-made structures (see Figure 5[bottom]), such as buildings, roads, and farmland. To this end, an additional classifier was trained on around 200 000 manually-labeled satellite images. Note that it is specifically for this purpose that we downloaded registered satellite data, which is not used in the remainder of the pipeline.

Filtering out artificial elements was performed iteratively, continually improving and expanding the training set until a satisfactory validation accuracy was achieved. Once again, this was done by manually reviewing subsets of the predictions made by the classifier. Only tiles free from artifacts and artificial structures were included in the final dataset, resulting in 3.84 million usable tiles (covering an area of 1.44 million km 2 ).

As is typical in machine learning, GPU memory limitations impose a cap on image size -256 × 256 pixels per image in our case. To meet this requires a careful balance between terrain extent (area) and resolution (detail). Accordingly, we chose a terrain extent of roughly 5 × 5 km 2 since this is large enough to encompass significant features (such as mountains, river gorges, and canyons) while also exhibiting feature diversity and is thus suitable for many terrain applications. By concatenating source DEMs in an 8×8 grid and downsampling to the desired 256 × 256 pixel resolution we obtain a final extent of ≈ 4.9 × 4.9 km 2 and sampling resolution of ∼ 19.1m per pixel.

After concatenation and downsampling, we were left with approximately 200 000 terrain tiles. By applying combinations of vertical and horizontal flips, and 90-degree rotations, we were able to enlarge our dataset eightfold, for a total of 1 600 000 terrain images.

Signature Extraction

It is clearly infeasible to require hand-drawn feature sketches for hundreds of thousands of terrains. Instead, we concentrate on algorithmic derivation of feature sketches from heightmap sources, with a specific focus on ridge and drainage networks, cliff lines, and flat regions.

Drainage networks are detected by simulating water flow over a terrain and identifying regions with high water accumulation. Individual streams are labeled according to their Strahler order. This is a numerical measure of branching complexity [START_REF] Horton R | Erosional development of streams and their drainage basins; hydrophysical approach to quantitative morphology[END_REF]Str57] that provides a way to rank the importance of rivers in a network. We then invert the terrain and apply the same algorithm to detect ridge lines. Cliff lines are extracted by applying Canny edge detection [Can86] on the normalized heightmap and then selecting lines that correspond to steep terrain (i.e., high average slope magnitude). Lastly, we mark regions in the terrain as flat if they have a low average slope magnitude.

The process of deriving a feature sketch is subject to several pre-and post-processing steps. First, as suggested by Guérin et al. [GDG * 17], we apply a light Gaussian blur prior to feature extraction with the intention of making synthesis more robust to imprecise sketches. After extraction, we randomly select features to display weighted by their Strahler order and water accumulation value so as to emulate sketches containing varying extent and concentration of detail. Sketches are further enhanced by widening important ridge, drainage, and cliff lines in the scene (based on Strahler order or steepness). We also perform minor postprocessing to fill in gaps, remove small artifacts, and smooth edges.

Parameter

Options Selected Finally, each sketch is stored as an RGBA image, with one feature class per channel.

Model

The other component of the terrain signature is a style vector, which is based on histograms of slope and both normalized and un-normalized elevation. Each histogram consists of 16 bins, with appropriate bin ranges selected to enforce a uniform distribution over the training set. These bin ranges are used consistently across all subsequent training and inference. To compute a style vector for an individual terrain, we compute the 3 histograms according to these ranges and concatenate them to form a single 48-dimensional vector.

Training data for the upsampling models are generated in a selfsupervised manner: downsampling the original terrain images by a factor of 8 using nearest neighbor interpolation. The models are then trained to predict terrains at the original resolution, given the down-scaled images as input.

Diffusion-based Synthesis

Diffusion models draw inspiration from non-equilibrium thermodynamics [START_REF] Sohl-Dickstein | Deep unsupervised learning using nonequilibrium thermodynamics[END_REF], where the core idea is to systematically destroy the structure in a data distribution by iteratively adding noise to a sample and then learning to reverse this process. After training, new samples can be generated by passing pure noise through this learned denoising process.

We use a time-conditioned U-Net [RFB15, DN21], augmented with cross-attention and skip-connections, as the backbone of our architecture (denoted as f θ in Figure 6). It processes an image, formed from the concatenation of noise and a feature sketch, by progressively lowering the resolution, passing it through a bottleneck, and then upscaling this representation back to its original resolution. As is standard practice, the U-Net is trained with a denoising objective to iteratively remove noise from an image [SHC * 21].

With regard to model hyperparameters, we carefully examine the trade-off between sample quality and inference speed. For our sketch-to-terrain model S, we focus on providing users with nearimmediate feedback during authoring without significantly impacting the realism of the synthesized terrain. Early experimentation revealed that although smaller models lead to a decrease in fine details, they are generally capable of producing terrains with a consistent global structure. This is a reasonable compromise given the availability of amplification techniques to account for the lost detail [ZLB * 19, ZCZ * 20, ACA18, KSR20]. Details of the chosen hyperparameters and implementation of the method can be found in Table 1 and in the official repository, respectively.

As illustrated in Figure 6, the feature sketch, x, is concatenated with the noisy image, yt , at each timestep t. Aligning the sketch with the noisy terrain enables direct and localized manipulation of terrain features. In contrast, example-based stylization serves as a means of controlling the global aesthetic of the terrain, with synthesized terrains containing similar landform characteristics to those present in the provided examples. This is achieved by forming a single 48-element style vector based on histograms of slope and elevation (both normalized and un-normalized). This process (denoted as τ) ensures that deviations from the norm are accentuated in the generated styles. These style vectors are then passed to the intermediate layers of the U-Net, which utilize a cross-attention mechanism [VSP * 17]. For consistency, we use the same architecture for upscaling as the sketch-to-terrain model, with the only exception being the type of input image (i.e., low-resolution terrain instead of a feature sketch). We also provide additional guidance through exemplar terrains and their corresponding style vectors, allowing the synthesized terrains to include characteristic features of specific landform classes (e.g., sharp ridge lines). Since upscaling is only performed as a post-processing step, users may select a larger number of sampling timesteps (250 -1000) to achieve higher quality, without the need for interactive feedback.

Model and Training Hyperparameters

In terms of tuning, early tests demonstrated that although performance improves with larger models (base dimensions, channel multipliers, and ResNet blocks), this comes at the cost of substantially longer training and sampling times (or even out-of-memory errors). Given our focus on interactive authoring, it is important to select model parameters that balance quality and performance. Accordingly, we tested the parameter options listed in Table 1, by training each model for 72 hours on a machine with an Nvidia ® A100 GPU (20GB). We split our dataset into training (90%), validation (5%), and testing (5%) subsets.

In terms of optimal parameters, in keeping with Saharia et al.

[SHC * 21, SCC * 22], we did not observe any benefits from dropout, likely because regularisation is not needed due to the volume of source data.

We use a batch size of 8 as the largest value that does not result in out-of-memory errors. We also find that a learning rate of 1e-4 with a ReduceLROnPlateau scheduler and an L2 loss produces the best FID outcomes.

As observed by Chen et al. [Che23], the appropriate noise scheduler is task-specific, and depends on model size, image size and dataset statistics. We find that a linear (1e-6, 1e-2) DDIMScheduler [SME20] provides the best results in our case.

Results

With the exception of visualization software, our entire framework is coded in Python. The diffusion models are implemented using Hugging Face's diffusers library (with PyTorch backend) [vPPL * 22] due to the memory optimizations and additional inference parameters it provides. Our authoring interface uses Blender's ® Python API, enabling seamless integration with existing artist workflows. The hypsometric terrain views were rendered in Mitsuba 0.6, while photorealistic landscape images were rendered with Vue ® .

Training was conducted on a workstation equipped with a partitioned Nvidia ® A100 GPU (20GB), while evaluation and testing were performed on a desktop computer equipped with an Intel ® Core™ i9-10980XE CPU @ 3.00GHz and NVidia ® RTX 3090 (24GB).

Hydrological Validation

Hydrological consistency is an important criterion for determining not only the geological but also the perceptual realism of a synthetic terrain [RKv * 22]. One form of evaluation is to compute and visualize the drainage of a terrain. The upstream drainage area a of point p is the amount of water that flows through p, and is proportional to the area of the surface where every downstream route passes through p. As an additional measure, we compute the average breaching volume b for each case. This is defined as the volume of material removed by the minimal breaching required to ensure free drainage off the terrain [START_REF] Barnes R | Priority-flood: An optimal depression-filling and watershed-labeling algorithm for digital elevation models[END_REF] divided by terrain area. Values reported in Figure 8 demonstrate that our method outperforms comparator techniques and is on par with erosion simulation. A notable exception is a method described by Scott and Dodgson [SD21], which specifically performs a complete post-processing multi-resolution breaching to improve the realism of image-based synthesis methods: in that case, the resulting average breaching volume is 0.

Balancing Quality and Performance

As illustrated in Figures 15 and16, our sketch-to-terrain model is capable of generating high-fidelity terrains faithful to user inputs in the form of feature sketches and style selections. This is complemented by upscaling models that introduce high-frequency detail that is cognizant of the low-frequency source (see Figure 9). We also see significant improvement over the current state-of-the-art when generating terrain from sparse input sketches. In these cases, our results show plausible and consistent structures and are free of the artifacts typical of other methods (see Figures 16 and17).

Next, we consider the necessary trade-off between response rate and output quality. One strength of diffusion models is that they rely on an iterative generation process involving a sequence of sampling timesteps during which output quality improves at a diminishing rate [DN21]. Since the time required for an individual timestep remains relatively constant (at around 40Hz in our case) this allows a time limit to be imposed on synthesis, so long as the user is willing to accept the consequent quality level. Conversely, a quality threshold can be set with the generation time determined during execution.

To explore this dynamic, we compared terrain quality as a function of the number of timesteps using the following standard image distance metrics: Learned Perceptual Image Patch Similarity (LPIPS) [ZIE * 18], and Fréchet Inception Distance (FID) [HRU * 17]. Despite a clear decline in quality when using fewer timesteps (as shown in Figure 10, particularly at less than 25 timesteps), we, nevertheless, find that the global structure of the terrain is well-maintained (see Figure 12). Furthermore, we compared our results to the current stateof-the-art deep learning model for sketch-to-terrain synthesis [GDG * 17] on the basis of LPIPS and FID scores (see Figure 10). Their implementation uses conditional Generative Adversarial Networks (cGANs) for image-to-image translation, based on the Pix2Pix [IZZE17] architecture. As evidenced by the significantly lower FID scores for t ≥ 15, our model more closely matches the underlying distribution of real terrains. Similarly, our model produces better LPIPS scores for t ≥ 25, which is indicative of a perceptual image similarity closer to the target terrains.

Our framework supports two modes of fixed-duration operation: real-time response during active sketching (5 timesteps in 0.125s at a rate of 8Hz), and interactive updates once the pen is lifted (up to 250 timesteps in 6.25s). In fact, diffusion iterations can continue in the background during unrelated activities, such as viewing, tool selection, and parameter setting so that the terrain is progressively refined.

Perceptual Study

We tested the perceived realism of terrains obtained from our framework, the real ground truth data and a cGAN model [GDG * 17] with an internet-administered user study (n = 41 participants). The comparator cGAN model was trained on exactly the same dataset as the diffusion model using the code from the original paper [GDG * 17].

The experiment design employed a 2AFC (two-alternative forced choice) protocol in which participants were required to choose on each trial between two landscapes drawn from real, diffusion-synthesized and CGAN-synthesized sets. Their selection was based on the question: "Which terrain looks more realistic (left or right)?", with the order of presentation (left or right) randomized. The number of pairings of treatments (Real vs. cGAN, Real vs. Ours, and Ours vs. cGAN) was also balanced. The landscapes were fixed at a 256 × 256 resolution and rendered with a hypsometric texture from an oblique angle and rotated to left and right about the vertical axis over a period of 10 seconds to aid depth discrimination.

To address the known differences in perception between landscape styles and their constituent landforms [SD22, RKv * 22] we partitioned the trials into four distinct categories: cliffs, hills, mountains, and flatland (which nevertheless contained some detail, such as coastlines and river courses). In order to avoid selection bias, we first performed k-means clustering on the style vector of the input dataset to group terrains by category (with k = 4). Then for each treatment and category, we randomly selected a set of 10 signatures based on the style distance from the centroid of the cluster, with 5 above and 5 below the median distance to provide diversity. The original terrain was retained for the real treatment, while the corresponding signature was used to generate terrain in the case of the diffusion and cGAN models. We avoided performing resolution amplification so as to ensure parity between real and generated data. The extent of terrains was kept constant at 5 × 5 km 2 across all trials.

Each participant was presented with 26 trials (3 treatment parings with 2 repetitions for each of the 4 landscape categories and 2 additional repeated control pairs). The duplicate controls were chosen at random, with a participant's data excluded due to inconsistency if both controls differed from their original selections. We introduced further randomization by drawing each categorytreatment sample without repetition from a pool of 10, meaning that the experiment dataset contained 120 terrains (10 pool elements ×3 treatments ×4 categories).

A demographic questionnaire was completed by each participant beforehand to determine familiarity with real landscapes (regularity of experiencing natural landscapes) and gaming (regularity of playing games depicting outdoor environments).

We obtained participants via convenience sampling with the majority being students and academics. After exclusion due to inconsistency, we analyzed data from n = 41 participants of whom 37% hiked and 54% gamed either weekly or monthly (see Table 2). We then undertook a Bayesian statistical analysis partitioned by category with the probability of treatment t (real, ours, or cGAN) modeled as a Bernoulli random variable with associated probability θt . For statistical significance, we derived the credible intervals corresponding to 95% of each probability density function (see Figure 14), implying that if the intervals for two treatments in a category do not intersect then they credibly represent distinct distributions. For the purposes of inspection, Figure 11 shows the terrains most and least favored by participants grouped by treatment and category.

Our analysis indicates that users are able to reliably distinguish real from generated terrains in the case of hills, but not plains, cliffs, and mountains (see Figure 14). In fact, our method outperforms cGANs for plains and hills and, surprisingly, even real terrains in the case of plains. Our tentative conclusion is that these differences are primarily due to viewers favouring terrains with well-defined erosion detail (as borne out by Figures 11 and13). Such detail is visible because we use a fractional Laplacian to enhance high frequencies in our rendering. The cGAN approach lacks any discernible notion of style and this impacts its performance in certain categories. It also has a tendency to produce small grid artifacts [GDG * 17]. While this clearly harms the realism of terrain upon close inspection, such artifacts can pass for plausible detail at medium viewing distances or when viewed for a short amount of time. Finally, it is worth noting that these categorical differences support the view [SD22] that perceptual experiments really should treat terrain types separately.

Limitations

Based on the success of sketching and stylization, we attempted to extend the authoring toolset to include elevation constraints: with the idea that users would be able to specify the elevation of key features, such as mountain peaks and river junctions. Unfortunately, we found it impossible to achieve alignment with the base terrain, while balancing control and ease-of-use. We also attempted to incorporate elevation-to-satellite translation, as a means of texture synthesis. Although the generated textures exhibited well-defined feature lines and shadows, present in the satellite imagery, they were particularly noisy and lacked a coherent global structure.

Diffusion models have shown marked success in text-to-image generation tasks [RDN * 22, SCS * 22]. This prompted us to experiment with terrain synthesis conditioned on free-form textual descriptions. Unfortunately, the results were deeply disappointing: our crowdsourced labeling resulted in generic landform descriptions and vaguely specified placement leading to poor quality inference. Our conclusion is that non-expert language is insufficiently precise in this context, especially when compared to a combination of stylization and sketching.

Finally, the performance of our framework approaches but does not cross the threshold of real-time response (20Hz) and indistin- guishability from real terrains across all landform classes. Another issue, common in the use of diffusion models for iterative authoring, is flickering and inconsistent outputs after minor adjustments to the canvas. Although increasing the detail of the input sketch and fixing the random seed during authoring may improve consistency, further research and experimentation is required. This may include, for example, conditioning on previous frames to provide a more coherent authoring experience. It is also worth noting that this is a highly active area of research and the inevitable improvements to come can be carried over to our system.

Conclusion

We have shown that diffusion models form a sound basis for authoring terrains, with an appropriate balance of interactive response and both perceptual and structural realism. Our diffusion-based authoring framework enables artists to select terrain styles from a palette and also sketch features that include cliffs, ridges, drainage, and flat areas. This provides expressivity in terms of the achievable terrain diversity, economy in the extent to which terse input leads to rich output, and precision in that the combination of a style and detailed feature sketch effectively represents an accurate terrain signature.

Nevertheless, there is an opportunity to take diffusion-based terrains further in future work. We would like to extend authoring to encompass accurately registered surface detail derived from satellite imagery and elevation controls at feature points, such as river junctions and mountain peaks. In this regard, recent advances in latent diffusion [RBL * 22] offer a promising avenue.

CGAN Ours Real

Figure 13: A side-by-side comparison of cGAN, ours, and real terrain based on the same canyon signature. All three of these terrains appeared by chance in the perceptual experiment due to a lack of diversity in the cliff category. Within its category the cGAN canyon scored worst, ours performed best, and the real was intermediate (see Figure 11). as opposed to raw height values. Mathematically, a terrain's slope is defined as a two-dimensional vector field, whose components are the first-order partial derivatives of the elevation function, h, given by g = ∇h = (∂h/∂x, ∂h/∂y). These gradient/derivative images can also be stored as images with two channels being used (one for each component of the vector field), where the pixel value represents the angle of the slope at a point.

In practice, elevation images are stored at a bit-depth of 16 (values between 0 and 65535), while derivative images use 8 bits for each channel (values between 0 and 255). These approaches to structuring height data play an important role in transferring geographical knowledge to computer-processable information [HWL * 22] and have found many uses in texture synthesis and machine learning methods [GGP * 19].

Appendix B: Diffusion Models

The forward diffusion process, q, is modelled as a Markov chain, where Gaussian noise is added to a data point y 0 ≡ y over T timesteps: q(y t+1 | y t ) = N (y t-1 ;

√ αt y t-1 , (1αt )I)

(1)

q(y 1:T | y 0 ) = T ∏ t=1 q(y t | y t-1 ) (2)
The hyper-parameters αt determine the variance of the noise added at timestep t and are chosen such that by timestep t = T , y T is virtually indistinguishable from Gaussian noise.

A useful property of this process is that we can sample y t at an arbitrary time step t in a closed form by reparameterising the forward process. Let γt = ∏ t i=1 α i , then q(y t | y 0 ) = N (y t ;

√ γt y 0 , (1γt )I)

The posterior distribution of y t-1 given (y 0 , yt ) can be derived as q(y t-1 | y 0 , yt ) = N (y t-1 | µ, σ 2 I)

where µ = √ γt-1(1-αt ) 1-γt y 0 + √ αt (1-γt-1) 1-γt y t and σ 2 =

(1-γt-1)(1-αt ) 1-γt .

Learning

The goal of the reverse process, p, is to recover the target image y 0 from a noisy image y, y = √ γy 0 + 1γε, ε ∼ N (0, I)

To this end, the neural network f θ (x, y, γ) is parameterised to condition on an input image x (e.g., a user sketch), a noisy image y, and the current noise level γ. The network is then trained to predict the noise vector ε by optimising the objective function:

E (x,
This estimate, ŷ0 , is then substituted into the posterior distribution of q(y t-1 | y 0 , yt ) in equation 4 to parameterise the mean of p θ (y t-1 | yt , x) as

µ θ (x, yt , γt ) = 1 √ αt yt - 1 -αt √ 1 -γt f θ (x, yt , γt ) (8)
The variance of p θ (y t-1 | yt , x) is set to (1αt ), a default given by the variance of the forward process [HJA20].

Finally, with this parameterisation, each iteration of the reverse process can be computed as

y t-1 ← 1 √ αt yt - 1 -αt √ 1 -γt f θ (x, yt , γt ) + √ 1 -αt εt (9)
where εt ∼ N (0, I). Table 2: Demographics in our perceptual study pertaining to regularity of experiencing nature (hiking) and playing games in outdoor environments (gaming). Possible responses: A) never or rarely (less than once a year), B) occasionally (a few times a year), C) often (every month), or D) usually (every week or almost).

Figure 2 :

 2 Figure 2: An overview of diffusion-based terrain authoring. During pre-processing and training, a database of real-world terrains is constructed by filtering and downsampling. Then signatures, consisting of a feature sketch and style vector, are derived for these terrains (1) and used to train an ensemble of diffusion models (2). During iterative authoring, the trained models are used to synthesize terrains based on styles and sketches provided by an artist (3). Once the artist is satisfied, the terrain can be upsampled (4) to create a final high-resolution version.

Figure 3 :

 3 Figure 3: Inverse terrain modeling: a structural replica of a terrain can be generated from the extracted signature and subsequently edited by the user to introduce or remove features.

Figure 4 :

 4 Figure 4: Super-resolution upsampling from a coarse resolution of 153m per pixel to the limits of the original source data at 2.39m per pixel.

Figure 5 :

 5 Figure 5: Categories of excluded source data: [top] recording errors -pixelation, patching, and line-artifacts; [bottom] artificial elements -buildings, roads, and farmland.

Figure 6 :

 6 Figure 6: Our diffusion model architecture supports stylization using a terrain encoder and cross-attention, and feature sketching through concatenation with the input noise image. The denoising process applies a U-Net to iteratively reduce noise and introduce structure.

Figure 7 :

 7 Figure 7: As part of an authoring sequence an artist sketches drainage (green), ridges (red), cliffs (blue), and a flat area (outlined in white) to produce a landscape reminiscent of the Yosemite National Park.

  Figure 8 provides a visual comparison of the drainage of our method against reference procedural, image-based synthesis and erosion simulations, obtained from the online repository of Galin et al. [GGP * 19].

Figure 8 :

 8 Figure 8: A comparison of drainage areas for different synthetic terrains: our method produces fewer endorheic pits and greater hydrological consistency (as measured by average breaching volume b) than previous data-driven approaches. Instances of procedural (ridged noise) and simulation [CCB * 18] outputs are included for a basis of comparison. A lower breaching volume, b, is better.

Figure 9 :Figure 10 :

 910 Figure 9: Cascaded application of our upscaling models U 1 (153 → 19.1 m/pixel) and U 2 (19.1 → 2.39 m/pixel), allowing for 64× superresolution.

Figure 11 :

 11 Figure 11: Terrains selected as most and least realistic in our perceptual study, by category (mountains, cliffs, hills, and plains) and method (CGAN, ours, and real).

Figure 12 :

 12 Figure 12: Sketch-to-terrain generation at different sampling timesteps.

Figure 15 :

 15 Figure 15: Examples of terrains authored by non-expert users in under a minute. From left to right:(1) a canyon with a narrow river flowing through it, (2) a snow-capped mountain range with a fjord, (3) a large island and surrounding lake, and (4) a cliff-dominated coastline with rocks protruding from the sea.

Figure 16 :

 16 Figure 16: Sketch-to-terrain sample diversity, showing progressively less diversity as sketches become more detailed.

,Algorithm 1

 1 y) Eε,γ f θ (x, √ γy 0 + 1γε y Training a denoising model f θ 1: repeat 2: (x, y 0 ) ∼ p(x, y) ▷ Sample conditional and target images 3: γ ∼ p(γ) ▷ Select amount of noise to add 4: ε ∼ N (0, I) ▷ Sample Gaussian noise 5:Take a gradient descent step on∇ θ ∥ f θ (x, √ γy 0 + √ 1γε, γ) -ε∥ p p 6: until convergedInferenceSince f θ is trained to estimate ε given a noisy image y and yt , y 0 is approximated by rearranging the terms in equation 5 to get ŷ0 = 1 √ γt yt -1γt f θ (x, yt , γt )

Algorithm 2

 2 Inference in T timesteps 1: y T ∼ N (0, I) ▷ Start with pure Gaussian noise 2: for t = T, . . . , 1 do ▷ Perform iterative refinement 3:z ∼ N (0, I) if t > 1, else z = 0 4:y t-1 = 1 √ αt y t -1-αt √ 1-γt f θ (x,y t , γt ) + √ 1αt z 5: end for 6: return y 0 ▷ The denoised image Appendix C: User study demographics

Table 1 :

 1 Hyperparameter tuning, including options considered (column 2) and finally selected (column 3).

	ResNet blocks	2, 3, 4

  Posterior beta distributions for θours, θ CGAN and θ real from our perceptual study, grouped by terrain category. Dashed lines indicate the mean with a higher score meaning that the treatment in question is selected more frequently. The shaded portions show the 95% credible interval, with no overlap implying a statistically-significant difference in distributions.

					Ours						Ours
	10						10
					Real						Real
	8				CGAN	8				CGAN
	6						6
	4						4
	2						2
	0						0
	0.0	0.2	0.4	0.6	0.8	1.0	0.0	0.2	0.4	0.6	0.8	1.0
			Plains					Cliffs
	12
					Ours						Ours
							10
	10				Real						Real
					CGAN	8				CGAN
	8
							6
	6
							4
	4
	2						2
	0						0
	0.0	0.2	0.4	0.6	0.8	1.0	0.0	0.2	0.4	0.6	0.8	1.0
			Hills						Mountains
	Figure 14:

© 2023 Eurographics -The European Association for Computer Graphics and John Wiley & Sons Ltd.

Acknowledgments

We are grateful to Oscar Argudo for providing advice and code for Bayesian analysis and Daniel Lochner for his input on the use of text labelling for terrain generation. This work is funded by the National Research Foundation of South Africa (Grant Number: 129257) and the project AMPLI ANR-20-CE23-0001, supported by Agence Nationale de la Recherche. Computations were performed using facilities provided by the University of Cape Town ICTS High-Performance Computing team.

Style Generated

Appendix A: Terrain Representation A terrain's elevation can be defined by a continuous function h : R 2 → R, where the height/altitude of the terrain at a point (x, y) is given by h(x, y). The primary limitation of such a definition is its inability to represent terrains that contain overhangs, arches, or caves, since only one height value can be associated with each point in the function's domain [GGP * 19]. However, due to its simplicity, terrain is most often represented in this manner.

A Digital Elevation Model (DEM) is a 3D representation of a terrain's surface, created from elevation data. DEMs are most commonly defined as heightmaps, where altitudes are arranged on a regular 2D grid. As a result, they can be stored as grayscale images, where the pixel value represents the altitude at a point.

While heightmaps remain the predominant form of terrain surface representation, in many cases, such as landslide detection algorithms [START_REF] Barlow | High spatial resolution satellite imagery, DEM derivatives, and image segmentation for the detection of mass wasting processes[END_REF]Paw19], it is advantageous to store terrain slope