Luc Bousset
email: luc.bousset@cnrs.fr

Ronald Melki
email: ronald.melki@cnrs.frbeat

Anja Böckmann
email: a.bockmann@ibcp.fr

Nina Luckgei

Mehdi Kabani

Carole Gardiennet

Anne K Schütz

Beat H Meier

Prion Amyloid Polymorphs -The Tag Might Change It All

Keywords: prion, fibrils, Sup35pNM, NMR, affinity tags, polymorphs

Sup35p is a protein from Saccharomyces cerevisiae. It can propagate using a prion-like mechanism, which means that it can recruit non-prion soluble Sup35p into insoluble fibrils. Sup35p is a large protein showing three distinct domains, N, M and an extended globular domain. We have previously studied the conformations of the full-length and truncated NM versions carrying poly-histidine tags on the N-terminus. Comparison with structural data from C-terminally poly-histidine tagged NM from the literature surprisingly revealed discrepancies. Here we investigated fibrils from the untagged, as well as a C-terminally poly-histidine tagged NM construct, using solid-state NMR. We find that the conformation of untagged NM is very close to the N-terminally tagged NM and confirms our previous findings. The C-terminal poly-histidine tag, in contrast, drastically changes the NM fibril structure, and yields data consistent with results obtained previously on this construct. We conclude that the C-terminally located Sup35p globular domain influences the structure of the fibrillar core at the N domain, as previously shown. We further conclude, based on the present data, that small tags on NM C-terminus have a substantial, despite different, impact. Modifications at this remote localization thus shows an unexpected influence on the fibril structure, and importantly also its propensity to induce [PSI+].

INTRODUCTION

The Sup35p protein is a prion from Saccharomyces cerevisiae. [PSI+], its loss-of-function phenotype, appears after spontaneous assembly of Sup35p and causes a tRNA-mediated suppression of nonsense mutations [START_REF] Cox | A cytoplasmic suppressor of super-suppressor in yeast[END_REF]. [PSI+] was first discovered by genetic screens [START_REF] Cox | A cytoplasmic suppressor of super-suppressor in yeast[END_REF]. It can propagate via a prion-like mechanism. In contrast to the human prion protein, PrP, whose cellular function is not fully understood, Sup35p is known to play a crucial role in translation termination.

[PSI+]-mediated nonsense suppression can result in the synthesis of a functional polypeptide even though a stop-codon has arisen through mutation in an open reading frame, thereby suppressing the mutant phenotype. Sup35p is a GTP-binding protein that interacts with Sup45p to form the release factor that recognizes an in-frame stop codon in an mRNA [START_REF] Stansfield | The products of the SUP45 (eRF1) and SUP35 genes interact to mediate translation termination in Saccharomyces cerevisiae[END_REF][START_REF] Zhouravleva | Termination of translation in eukaryotes is governed by two interacting polypeptide chain release factors, eRF1 and eRF3[END_REF]. In the context of [PSI+], Sup35p is associated within stable high-molecular-weight aggregates, which reduces the efficiency of termination at stop codons. This results in read-through stop codons in up to 20% of the time.

Sup35p counts 685 amino-acid residues and contains three domains [START_REF] Ter-Avanesyan | Deletion analysis of the SUP35 gene of the yeast Saccharomyces cerevisiae reveals two nonoverlapping functional regions in the encoded protein[END_REF]. The N-terminal domain, including residues 1-123, is necessary and sufficient for [PSI+] occurrence and maintenance. Deletion of this domain allows Sup35p to remain soluble even in [PSI+] cells [START_REF] Paushkin | Propagation of the yeast prion-like [psi+] determinant is mediated by oligomerization of the SUP35-encoded polypeptide chain release factor[END_REF]. The M-domain, including residues 124-253, is highly charged and plays a role in the solubility of non-prion Sup35p and modulates [PSI+] propagation [START_REF] Liu | Changes in the middle region of Sup35 profoundly alter the nature of epigenetic inheritance for the yeast prion [PSI+[END_REF]. The C-terminal domain houses the translation termination activity [START_REF] Zhouravleva | Termination of translation in eukaryotes is governed by two interacting polypeptide chain release factors, eRF1 and eRF3[END_REF] and retains a native and active conformation, even in the context of Sup35p fibrils [START_REF] Krzewska | Biochemical and functional analysis of the assembly of full-length Sup35p and its prion-forming domain[END_REF][START_REF] Luckgei | The conformation of the prion domain of Sup35p in isolation and in the full-length protein[END_REF].

The constructs investigated in this study are the truncated versions Sup35pNM (amino acids 1-253), devoid of, or carrying poly-histidine tags. Indeed, the prion properties of Sup35pNM have been extensively documented by various methods of structural and functional biology using versions of the protein bearing N-and C-terminal poly-histidine tags [START_REF] Glover | Self-seeded fibers formed by Sup35, the protein determinant of [PSI+], a heritable prion-like factor of S. cerevisiae[END_REF][START_REF] Tanaka | Conformational variations in an infectious protein determine prion strain differences[END_REF][START_REF] Krishnan | Structural insights into a yeast prion illuminate nucleation and strain diversity[END_REF][START_REF] Shewmaker | Amyloid of the prion domain of Sup35p has an in-register parallel beta-sheet structure[END_REF][START_REF] Shewmaker | Two prion variants of Sup35p have in-register parallel beta-sheet structures, independent of hydration[END_REF][START_REF] Krzewska | Biochemical and functional analysis of the assembly of full-length Sup35p and its prion-forming domain[END_REF][START_REF] Toyama | The structural basis of yeast prion strain variants[END_REF][START_REF] Shorter | Hsp104, Hsp70 and Hsp40 interplay regulates formation, growth and elimination of Sup35 prions[END_REF]. Until now, the influence of the N-or C-terminal poly-histidine tag on the structure of the Sup35pNM fibrils was not investigated at molecular level. We have previously shown that there are significant structural differences between N-terminal poly-histidine tagged full length/authentic Sup35p and Sup35pNM, even if the fibrillar core in both fibrils was found to localize to the first 30 N-terminal residues [START_REF] Luckgei | The conformation of the prion domain of Sup35p in isolation and in the full-length protein[END_REF][START_REF] Luckgei | Solid-state NMR sequential assignments of the amyloid core of Sup35pNM[END_REF][START_REF] Schütz | Solid-state NMR sequential assignments of the amyloid core of full-length Sup35p[END_REF]. Those differences may be due to the C-terminal, compactly folded Sup35p moiety. However, since the assigned residues of the fibril's core are located at the very N-terminus of Sup35p, almost immediately after the N-terminal poly-histidine tag, we decided to evaluate the impact on the structural features of the fibrillar form of the Sup35pNM protein of the two poly-histidine tags MGSSHHHHHHSSGLVPRGSH (on the N-terminus, His-Sup35pNM) or GSHHHHHH (on the C terminus, Sup35pNM-His). This investigation was further motivated by the observation of a strong Met signal, as well as several broad serine signals in the spectra of N-terminally poly-histidine tagged Sup35pNM that could indeed stem from the poly-histidine tag itself [START_REF] Luckgei | The conformation of the prion domain of Sup35p in isolation and in the full-length protein[END_REF][START_REF] Luckgei | Solid-state NMR sequential assignments of the amyloid core of Sup35pNM[END_REF][START_REF] Schütz | Solid-state NMR sequential assignments of the amyloid core of full-length Sup35p[END_REF]. We show here that when it is present on the C-terminal end, the poly-histidine tag significantly affects the folding landscape of Sup35pNM-His, yielding different fibrillar polymorphs. At the same time, we observe that its N-terminal localization does not significantly alter the structure of His-Sup35pNM when compared to untagged Sup35pNM, validating our previous investigations of N-terminally polyhistidine tagged Sup35p.

MATERIALS AND METHODS

Expression, Labeling, Purification and Assembly of Sup35pNM

The Sup35p and Sup35pNM N and C-terminally tagged proteins were overexpressed and 15 N, 13 C labeled as described previously [START_REF] Luckgei | The conformation of the prion domain of Sup35p in isolation and in the full-length protein[END_REF] in Escherichia coli strain BL21-CodonPlus and purified by affinity chromatography as previously described [START_REF] Krzewska | Molecular chaperones and the assembly of the prion Sup35p, an in vitro study[END_REF][START_REF] Krzewska | Biochemical and functional analysis of the assembly of full-length Sup35p and its prion-forming domain[END_REF]. Assembly reactions were performed at a final concentration of 8-16 µM in assembly buffer (50 mM Tris-HCl, pH 8.0, 200 mM NaCl, 5% glycerol, 5 mM beta-mercaptoethanol, 10 mM MgCl 2 , 2 mM EGTA) for 30 days at 6 • C under very mild agitation (<100 rpm) as described previously [START_REF] Krzewska | Molecular chaperones and the assembly of the prion Sup35p, an in vitro study[END_REF][START_REF] Kabani | A mutation within the C-terminal domain of Sup35p that affects [PSI+] prion propagation[END_REF].

Yeast Strains, Growth Media and Monitoring of Prion Phenotypes

The S. cerevisiae strain used in this study is 74-D694 [MATa ade1-14 (UGA) trp1-289 leu2-3,112 his3 -200 ura3-52]. Yeast cells were grown in YPDA medium (1% yeast extract, 2% peptones, 2% glucose, 0.002% adenine). Prion phenotypes were monitored on 1/4-YPD medium (0.25% yeast extract, 2% peptones, 2% glucose, 2% bacto-agar) via a standard color-based phenotype assay, as described before [START_REF] Kabani | A mutation within the C-terminal domain of Sup35p that affects [PSI+] prion propagation[END_REF][START_REF] Kabani | A role for the proteasome in the turnover of Sup35p and in [PSI(+)] prion propagation[END_REF].

Induction of [PSI + ] by Transformation of Yeast Spheroplasts

Yeast 74-D694 [psi -] cells were converted to spheroplasts by lyticase treatment and then transformed with His-Sup35pNM or Sup35pNM-His fibrils (5 µg) in the presence of 100 µg ml -1 of salmon sperm DNA and 20 µg ml -1 of the URA3-based pRS316 plasmid, as described before [START_REF] Kabani | A mutation within the C-terminal domain of Sup35p that affects [PSI+] prion propagation[END_REF][START_REF] Kabani | A role for the proteasome in the turnover of Sup35p and in [PSI(+)] prion propagation[END_REF]. Just before transformation, in vitro assembled fibrils were briefly sonicated on ice 4 times for 5 s with 20 s pauses between each sonication using a Misonix S-4000 sonicator with a microtip at 20% amplitude. Mock transformation reactions lacking spheroplasts and/or pRS316 ensured that no viable cells remained in the cell extracts and the absence of spontaneous [ura + ] revertants.

Semi-Denaturant Detergent Agarose Gel Electrophoresis (SDD-AGE)

Yeast cells (∼20 OD 600nm units) were harvested by centrifugation at 4,000 g for 2 min and resuspended in 500 µl of lysis buffer (100 mM Tris-Cl pH 7.5, 50 mM KCl, 10 mM β-mercaptoethanol, 0.5% Triton X-100, 1 mM PMSF and protease inhibitor cocktail, Roche Diagnostics). Glass beads were added to half the cell suspension volume and cells were broken by six cycles of vortexing for 30 s with 1 min incubation on ice between each vortexing. Debris and unbroken cells were removed by centrifugation for 2 min at 4,000 g and at 4 • C. SDD-AGE analysis was performed as described previously [START_REF] Wang | A prolonged chronological lifespan is an unexpected benefit of the [PSI+] prion in yeast[END_REF]. Immunoblots were developed using enhanced chemiluminescence reagents (Pierce) and a Chemidoc imaging system (Biorad).

NMR Spectra

Solid-state NMR spectra were obtained from uniformly 13 C, 15 Nlabeled protein pelleted at 100,000 g and ultracentrifuged into the NMR rotor [START_REF] Böckmann | Characterization of different water pools in solid-state NMR protein samples[END_REF]. NMR experiments were performed as described in [START_REF] Luckgei | Solid-state NMR sequential assignments of the amyloid core of Sup35pNM[END_REF]. Briefly, they were recorded on Bruker Avance II spectrometers operating at 800 and 850 MHz field strengths equipped with 3.2 mm tripleresonance MAS probe at 17.5 kHz MAS spinning frequencies and a sample temperature around 5 • C. DARR (Takegoshi et al., 2003), NCA [START_REF] Baldus | Cross polarization in the tilted frame: assignment and spectral simplification in heteronuclear spin systems[END_REF], NCACB [START_REF] Schuetz | Protocols for the sequential solid-state NMR spectroscopic assignment of a uniformly labeled 25 kDa protein: HET-s(1-227)[END_REF][START_REF] Habenstein | Extensive de novo solid-state NMR assignments of the 33 kDa C-terminal domain of the Ure2 prion[END_REF], 1 H- 13 C INEPT (Siemer et al., 2006), and T 1 -filtered 13 C - 13 C correlation spectra [START_REF] Luckgei | The conformation of the prion domain of Sup35p in isolation and in the full-length protein[END_REF] were recorded on protein samples filled in the 3.2 mm rotors using ultracentrifugation [START_REF] Böckmann | Characterization of different water pools in solid-state NMR protein samples[END_REF].

RESULTS

We compared in this work the solid-state NMR spectra of the fibrillar forms of His-Sup35pNM, Sup35pNM-His and untagged Sup35pNM. In the primary structure shown in Figure 1, the sequences of Sup35pNM (green, N in bold), the N-terminal poly-histidine tag (blue) and the C-terminal poly-histidine tag (red) are outlined. The previously assigned amino acids, comprising residues 4-14 and 20-28 [START_REF] Luckgei | The conformation of the prion domain of Sup35p in isolation and in the full-length protein[END_REF][START_REF] Luckgei | Solid-state NMR sequential assignments of the amyloid core of Sup35pNM[END_REF], are underlined.

N-Terminally Tagged and Untagged NM Show Very Similar Conformations

We have, in our previous studies [START_REF] Luckgei | The conformation of the prion domain of Sup35p in isolation and in the full-length protein[END_REF][START_REF] Luckgei | Solid-state NMR sequential assignments of the amyloid core of Sup35pNM[END_REF], used His-Sup35pNM. In order to assess whether the tag changes the structural features of the protein, we performed a comparison between untagged and His-Sup35pNM using 2D DARR and 3D NCACB solid-state NMR spectra. An analysis of 20 ms DARR, NCA and NCACB fingerprint spectra reveals that untagged Sup35pNM is indeed very similar to the previously studied His-Sup35pNM with respect to line positions in the NMR fingerprints indicating very similar structures (Figures 2A,B), as well as to signal-to-noise ratio (and thus dynamic behavior). Most of the assigned residues of the Sup35pNM amyloid fibril core have highly similar chemical shifts and comparable peak intensity in the spectra of the two fibrils. 3D NCACB spectra confirm this analysis (Figures 2C,D). Few minor differences can be observed: The serine residue 4S is shifted by 1 ppm in the 15 N-dimension, but shows identical Cα and Cβ chemical shifts. It can be noted that 4S is located at the beginning of the assigned stretch and is the closest residue to the N-terminal poly-histidine tag. Residue 12N shows a slightly different chemical shift for Cα, Cβ, and N.

FIGURE 1 | Primary structure of Sup35pNM with an N-and C-terminal poly-histidine tag. The N-terminal poly-histidine tag is colored in blue, the C-terminal one in red. The assigned residues [START_REF] Luckgei | The conformation of the prion domain of Sup35p in isolation and in the full-length protein[END_REF][START_REF] Luckgei | Solid-state NMR sequential assignments of the amyloid core of Sup35pNM[END_REF] are underlined.

Further, residue 22Q seems to be shifted in the 15 N dimension in NCACB spectra.

The 2D NCA spectra of His-Sup35pNM and untagged Sup35pNM are given in Figures 2E,F. The fingerprints of the spectra are very similar, with slightly broader lines for untagged Sup35pNM. Most resonances can be observed at very similar chemical shifts. The resonance frequencies of 4S, 12N, 17S, 20G and 21N might be shifted slightly. Red arrows indicate possible chemical-shift changes, since new unassigned resonances appear close to the prior, now vanishing, resonance frequencies. Figures 2G,H show 1D traces from 20 ms DARR spectra of His-Sup35pNM (blue) and untagged Sup35pNM (green). The traces are representative for many peaks that show a highly similar signal intensity for most of the assigned peaks in both spectra.

The broad serine signals visible in the DARR spectra around 65/57 ppm of the His-Sup35pNM, which likely belong to residues outside the fibrillar core, are weaker in the spectra of the untagged Sup35pNM. This indicates that these residues are probably more rigid in His-Sup35pNM. Conversely, some peaks in untagged Sup35pNM fibrils that are not observed in His-Sup35pNM can be identified in the 20 ms DARR and NCACB (DREAM) spectra indicating that those are rather more rigid. The signals cannot be assigned unambiguously; however, one signal might belong to residue 17S, which has been assigned in the fibril core and disappears in untagged Sup35pNM. The others might be assigned to D and R/K residues. Since only very few new peaks appear, it cannot be known from which domain they might stem and therefore they were not further investigated.

Figure 2I summarizes the resonances, which are observed either at the same chemical shift (underlined) or very likely at an only slightly changed chemical shift (yellow frame) in His-tagged (blue sequence) and untagged Sup35pNM (green sequence). Surprisingly, several chemical-shift changes occurred within predicted β-strands. Especially residue 22Q seems to have shifted more strongly, or disappeared (orange frame). This residue represents the center of a 3-residues β-strand. However, depending on their role for the structural elements (as for example inside/outside of a steric zipper) the residues might be more or less stabilized.

Taken together, our results show that His-Sup35pNM and untagged Sup35pNM fibril cores are highly similar. This similarity includes the observed residues, their chemical shifts and their signal intensities, which also indicates that both fibril cores have a similar dynamic behavior.

To assess the influence of the N-terminal His-tag on the structure of the M-domain of Sup35pNM, we recorded T 1filtered, directly pulsed 13 C 200 ms DARR and INEPT spectra on untagged Sup35pNM. The waiting time between scans was 4 s favoring more dynamic residues with a faster 13 C-T 1 relaxation. Reminiscent of His-Sup35pNM [START_REF] Luckgei | The conformation of the prion domain of Sup35p in isolation and in the full-length protein[END_REF], the resonances of the M-domain of untagged Sup35pNM appear in both 1 H- 13 C INEPT and T 1 -filtered 200 ms DARR spectra (Figures 3A,B). The resonances appear near the random-coil shifts of the respective residues. A comparison of the peak intensities in the T 1 -filtered 200 ms DARR spectra and the numbers of the corresponding residues in the M-domain reveals that the ratio between signal intensity and the number of FIGURE 2 | Comparison between His-Sup35pNM (blue) and untagged Sup35pNM (green). All spectra from His-Sup35pNM (blue) are from references [START_REF] Luckgei | The conformation of the prion domain of Sup35p in isolation and in the full-length protein[END_REF][START_REF] Luckgei | Solid-state NMR sequential assignments of the amyloid core of Sup35pNM[END_REF], including assignments of the fibril core of His-Sup35pNM are shown as previously established there. (A) 20 ms 13 C- 13 C DARR correlation spectra of His-Sup35pNM and (B) untagged Sup35pNM, as well as representative planes of 3D NCACB spectra of (C) His-Sup35pNM and (D) untagged Sup35pNM. Panels (A,C) were recorded at 850 MHz [START_REF] Luckgei | The conformation of the prion domain of Sup35p in isolation and in the full-length protein[END_REF][START_REF] Luckgei | Solid-state NMR sequential assignments of the amyloid core of Sup35pNM[END_REF]; Panels (B,D) were recorded at 800MHz proton frequency; all with a MAS spinning frequency of 17.5 kHz and 5 • C sample temperature. (E) NCA spectrum of His-Sup35pNM and (F) untagged Sup35pNM. The spectrum in panel (F) was recorded at 850 MHz proton frequency (12 ms acquisition in F2, 8 scans) [START_REF] Luckgei | The conformation of the prion domain of Sup35p in isolation and in the full-length protein[END_REF][START_REF] Luckgei | Solid-state NMR sequential assignments of the amyloid core of Sup35pNM[END_REF] and in panel (E) at 800 MHz proton frequency (6 ms acquisition in F2, 16 scans); both spectra were measured at a MAS spinning frequency of 17.5 kHz and 7 • C sample temperature. Red arrows suggest possible chemical-shift changes from His-Sup35pNM to untagged Sup35pNM. (G,H) 1D traces from 20 ms DARR spectra of His-Sup35pNM (blue) and untagged Sup35pNM (green). The spectra were recorded 850 MHz proton frequency (His-Sup35pNM) [START_REF] Luckgei | The conformation of the prion domain of Sup35p in isolation and in the full-length protein[END_REF][START_REF] Luckgei | Solid-state NMR sequential assignments of the amyloid core of Sup35pNM[END_REF] and 800 MHz proton frequency (untagged Sup35pNM) at 7 • C sample temperature and with a MAS spinning frequency of 17.5 kHz. The assignments of 9N and 5N are indicated. (I) Comparison of His-Sup35pNM (blue) and untagged Sup35pNM (green). Secondary structures derived from secondary chemical shifts of the assigned residues from the Sup35pNM-Ntag fibril core are shown according to [START_REF] Luckgei | The conformation of the prion domain of Sup35p in isolation and in the full-length protein[END_REF]. The assigned residues in the His-Sup35pNM spectra and residues which are visible in the untagged Sup35pNM spectra at the same chemical shift are underlined. Yellow boxes indicate which residues are visible in untagged Sup35pNM with a slight chemical shift change, and in orange the residue which could not be traced. 13 C INEPT and (B) T 1 -filtered 13 C- 13 C correlation spectrum [START_REF] Luckgei | The conformation of the prion domain of Sup35p in isolation and in the full-length protein[END_REF] of untagged Sup35pNM. The spectra were recorded at 800 MHz proton frequency and a MAS spinning frequency of 17.5 kHz. The 13 C- 13 C-correlation spectrum was recorded with a recycle delay of 4 s. The assignments of the random-coil chemical shifts assigned in His-Sup35pNM are indicated. (C) Comparison between the signal intensity in T 1 -filtered 13 C- 13 residues in the M-domain is very similar for untagged Sup35pNM (Figure 3C) and His-Sup35pNM [START_REF] Luckgei | The conformation of the prion domain of Sup35p in isolation and in the full-length protein[END_REF]. We conclude that these signals indeed stem from the M domain in both constructs. Overall, this reveals an analogous T 1 -relaxation property for the M-domain in untagged Sup35pNM and His-Sup35pNM fibrils.

FIGURE 3 | (A) 1 H-

Extensive Polymorphism Is Detected in C-Terminally Tagged Sup35pNM

To analyze the potential effect of a C-terminal His-Tag on the structure of Sup35pNM fibrils, the solid-state NMR spectra of four C-terminally His-tagged Sup35pNM fibrillar preparations, from four independent but supposedly identical Sup35pN-His expressions and purifications, were recorded and compared. The four different spectra exhibited a significant degree of difference, as can be readily observed in 20 ms DARR spectra (Figure 4) from four different samples, prepared following the same protocol and numbered as Sup35pNM-His-#1; (b) Sup35pNM-His-#2; (c) Sup35pNM-His-#3; (d) Sup35pNM-His-#4). Furthermore, Sup35pNM-His-#2 and Sup35pNM-His-#4 exhibited a low signal-to-noise ratio. In contrast to the 20 ms DARR spectrum of His-Sup35pNM, the signals of the fibril core, reported on the spectra, do not contribute to the strongest peaks.

One-dimensional traces from the 20 ms DARR spectra of all four Sup35pNM-His fibrillar samples (orange, purple, red and pink) and previously reported His-Sup35pNM (blue) [START_REF] Luckgei | The conformation of the prion domain of Sup35p in isolation and in the full-length protein[END_REF][START_REF] Luckgei | Solid-state NMR sequential assignments of the amyloid core of Sup35pNM[END_REF] are shown in Figures 4E-J. In order to compare the signal intensity of the assigned peaks, which stem from the fibril core identified in His-Sup35pNM, the spectra were normalized on the 12N resonance that is strong in all spectra (Figure 4E). Many peaks of the assigned residues from the His-Sup35pNM fibrils core seem to disappear in Sup35pNM-His spectra, as for example 4S and 5N (Figures 4F,G). This observation can be due either to dynamical effects (chemicalexchange broadening) or to heterogenous broadening which is difficult to disentangle in the present case. One possibility would be to vary temperature, but it is well known that fibril resonances substantially broaden below the freezing point of water [START_REF] Bauer | Line-broadening in low-temperature solid-state NMR spectra of Fibrils[END_REF], further increasing signal overlap. These effects add to any chemical-exchange broadening, and render temperature-dependent studies of the mechanisms relevant in the physiological temperature range very difficult to interpret.

Since N and Q are the most abundant amino-acid residues within the Sup35p N-domain, which mainly adopts a β-strand conformation, they give rise to strong signals in all spectra. This can be observed in Figure 4F, where a 1D trace not only shows the disappearance of 5N in all Sup35pNM-His fibrils spectra, but also the appearance of a strong new peak at the generic chemical shift of β-strand N residues. A similar phenomenon can be observed in Figure 4I for residue 23Q, which also disappears, and a strong generic chemical shift of β-strand Q residues appearing. Furthermore, Figures 4H,J show that peaks at random-coil resonance positions originating from the M-domain dominate Sup35pNM-His fibril spectra.

Since Sup35pNM-His-#2 and Sup35pNM-His-#4 fibrillar preparations suffered from a lower signal-to-noise-ratio compared to the other samples, despite of the fact that the rotors were filled completely with fibrils, it was not possible to record 3D NCACB spectra in order to investigate these samples in more detail. Sup35pNM-His-#1 and Sup35pNM-His-#3 showed a sufficient signal-to-noise-ratio, so that in each case 3D NCACB spectra could be obtained. The spectra, however, show a poor signal-to-noise ratio compared to His-Sup35pNM. Representative planes of the 3D NCACB spectra for Sup35pNM-His-#1 (Figure 4K) and Sup35pNM-His-#3 (Figure 4L) are shown. Some peaks clearly assigned in His-Sup35pNM spectrum seem to have shifted, some new peaks can be observed and some seem to have disappeared. This indicates that also in 3D NCACB spectra His-Sup35pNM and Sup35pNM-His fingerprints differed.

Altogether, the 2D DARR spectra of Sup35pNM-His fibrils are seemingly dominated by signals corresponding to aminoacid residues in generic random-coil and β-strand conformation but, the latter are not necessarily found the context of a β-sheet (vide infra).

The observations we report here clearly suggest different structures and dynamic behavior between different samples related to the absence or the presence of an N-or C-terminal His-tag. While the spectra of Sup35pNM-His-#1, -His-#2 and -His-#4 appear rather featureless, with large blobs at chemical shifts of the amino-acid residues that are most numerous, new strong peaks appear in the spectrum of Sup35pNM-His-#3. These peaks could be assigned tentatively to L, K, P, G, E, S, N, D and H residues considering typical chemical shifts and spin systems (Figure 5A). Although the assignment of the new peaks is only tentative, we derived their secondary chemical shifts to obtain insight into the possible secondary-structure elements which might embed these residues. Most of the residues have secondary chemical shifts typical for a β-strand conformation (Figure 5B). However, it is only when three or more residues in a row show negative secondary chemical shifts that they are indicative of a β-sheet [START_REF] Wishart | The 13C chemical-shift index: a simple method for the identification of protein secondary structure using 13C chemical-shift data[END_REF].

A possible amino-acid stretch represented in Figure 5B includes residues 118-144 (underlined in Figure 5C), although residues M, F, and A are missing. As the stretches of amino acids between the missing ones are at least 4 amino acids long, they could in principle form three β-strands (Figure 5C).

To probe for the dynamic behavior of Sup35pNM-His-#3, directly pulsed T 1 -filtered DARR and INEPT spectra were recorded (Figures 6A,B). The T 1 -filtered spectra (interscan delay 4 s) show a lower signal-to-noise ratio although they have been recorded 3× as long as for His-Sup35pNM. Since the signals of the T 1 -filtered 100 ms DARR spectra have been assigned exclusively to the M-domain in His-Sup35pNM [START_REF] Luckgei | The conformation of the prion domain of Sup35p in isolation and in the full-length protein[END_REF], this might indicate that the M-domain has a different mobility in Sup35pNM-His-#3. In contrast, several new resonances appear in the INEPT spectra, which cannot be assigned to random-coil chemical shifts. Until now, these peaks remain unexplained.

Altogether, this indicates that in the Sup35pNM-His-#3 sample, parts of the M domain shows different dynamics, with parts of it more rigid, and several residues FIGURE 4 | 20 ms DARR spectra of His-Sup35pNM and Sup35pNM-His samples. The spectra have been recorded at 850 MHz (A) Sup35pNM-His-#1, (B) Sup35pNM-His-#2, (C) Sup35pNM-His-#3, and 800 MHz (D) Sup35pNM-His-#4 proton frequency. The assignments of the fibril core from His-Sup35pNM are indicated in blue. (E-J) 1D traces from 2D 20 ms DARR spectra of His-Sup35pNM (blue) and Sup35pNM-His-#1 (orange), Sup35pNM-His-#2 (purple), Sup35pNM-His-#3 (red) and Sup35pNM-His-#4 (pink). The spectra were scaled manually to achieve a similar peak height for 12N. The assignments of some residues from the fibril core, Asn and Gln β-sheet chemical shifts and random coil (rc) chemical shifts are indicated. (K,L) Representative planes of 3D NCACB spectra of (K) Sup35pNM-His-#1, and (L) Sup35pNM-His-#3 samples. The spectra have been recorded at 850, and 800 MHz proton frequency, respectively. The assignments of the fibril core from His-Sup35pNM are indicated in blue.

in β-strand conformation, corresponding either to β-sheet or aggregated regions.

The Infectious Properties of N-Terminally and C-Terminally His-Tagged Sup35pNM Are Different Next, we asked whether the different fibrillar structures of His-Sup35pNM and Sup35pNM-His affect their prion properties in vivo. To this end, we used protein transformation assays [START_REF] Tanaka | Conformational variations in an infectious protein determine prion strain differences[END_REF] to compare the infectious properties of His-Sup35pNM and Sup35pNM-His fibrils (Figure 7). We found that Sup35pNM-His induced [PSI + ] formation with a much higher efficiency than His-Sup35pNM (Figures 7A,B). In agreement with previous data [START_REF] Tanaka | Conformational variations in an infectious protein determine prion strain differences[END_REF], His-Sup35pNM induced a mixture of strong and weak [PSI + ] clones, as judged by the range of pink to white colors observed on adenine-limiting plates (Figure 7A), and by the differences in the size of SDS-resistant Sup35p aggregates visualized by SDD-AGE (Figure 7C). Strikingly, Sup35pNM-His induced only the formation of strong [PSI + ] clones that were homogenous in color (Figure 7A) and that contained SDS-resistant Sup35p aggregates of comparable sizes (Figure 7C).

DISCUSSION

Prions have the inherent characteristic to form a variety of variants, or strains, de novo or after their re-introduction or propagation into their host cells. This effect seems to be to some extent dependent on the cellular environment and proteostasis. The prion Sup35p yields strong and weak [PSI+] phenotypes that are most likely structurally encoded. Sup35 7-13 , and smaller fragments thereof, are highly polymorphic [START_REF] Sawaya | Atomic structures of amyloid cross-beta spines reveal varied steric zippers[END_REF][START_REF] Lewandowski | Structural complexity of a composite amyloid fibril[END_REF]. We previously demonstrated that even if the fibrillar forms of Sup35p and its NM fragment differ structurally [START_REF] Luckgei | The conformation of the prion domain of Sup35p in isolation and in the full-length protein[END_REF], both show an ordered fibrillar core which is localized within the first 30 residues of the proteins. Thus, although the Sup35pNM domain is critical for [PSI+] formation and maintenance [START_REF] Depace | A critical role for amino-terminal glutamine/asparagine repeats in the formation and propagation of a yeast prion[END_REF][START_REF] Toyama | The structural basis of yeast prion strain variants[END_REF], the driving force for fibril formation and the structural characteristics of the fibrils cannot be confined to the NM domain of Sup35p. The results we report here indicate that fibrils made of Sup35pNM bearing a His tag on the C-terminal end of the protein, a construct that has been used in many studies on Sup35pNM (e.g., [START_REF] Glover | Self-seeded fibers formed by Sup35, the protein determinant of [PSI+], a heritable prion-like factor of S. cerevisiae[END_REF][START_REF] Depace | Origins and kinetic consequences of diversity in Sup35 yeast prion fibers[END_REF]Shorter andLindquist, 2004, 2008;[START_REF] Tanaka | Mechanism of cross-species prion transmission: an infectious conformation compatible with two highly divergent yeast prion proteins[END_REF][START_REF] Tanaka | The physical basis of how prion conformations determine strain phenotypes[END_REF][START_REF] Tessier | Prion recognition elements govern nucleation, strain specificity and species barriers[END_REF][START_REF] Ohhashi | Differences in prion strain conformations result from non-native interactions in a nucleus[END_REF][START_REF] Foo | Radically different amyloid conformations dictate the seeding specificity of a chimeric Sup35 prion[END_REF][START_REF] Verges | Strain conformation, primary structure and the propagation of the yeast prion [PSI+][END_REF][START_REF] Frederick | Sensitivity-enhanced NMR reveals alterations in protein structure by cellular milieus[END_REF][START_REF] Frederick | Combining DNP NMR with segmental and specific labeling to study a yeast prion protein strain that is not parallel in-register[END_REF][START_REF] Keefer | Heterologous prion-forming proteins interact to cross-seed aggregation in Saccharomyces cerevisiae[END_REF][START_REF] Shida | Short disordered protein segment regulates cross-species transmission of a yeast prion[END_REF], and fibrils made of untagged or N-terminally tagged Sup35pNM, are structurally distinct.

Despite the view that fibrils formation is rather driven by the global composition of the prion-forming domain [START_REF] Ross | Primary sequence independence for prion formation[END_REF], it is evident that the very precise interactions that are established between defined amino-acid residues stretches yield the fibril's amyloid core and determine its structure. Indeed, the side chains of Q and N residues can interdigitate and form a "steric zipper"-like conformations [START_REF] Nelson | Structure of the cross-beta spine of amyloid-like fibrils[END_REF], a structure of which has recently been described at high resolution for Orb2 [START_REF] Hervas | Cryo-EM structure of a neuronal functional amyloid implicated in memory persistence in Drosophila[END_REF]. In a more general manner, G and P residues are prone to form turn elements between β-strands, and Y residues might play a role in the initiation of fibril formation through ring stacking. Altogether, the finding that a C-terminal His-tag, at distance from Sup35 N-terminal end, affects the Sup35pNM fibril core structure suggests that changes in the primary structure of the protein even outside the core region can give rise to different fibril core structures.

In addition, major discrepancies are apparent in published structural models for Sup35p fibrils, with models suggesting an overall structural organization in a β-helix [START_REF] Krishnan | Structural insights into a yeast prion illuminate nucleation and strain diversity[END_REF], or supporting parallel in-register β-sheets [START_REF] Shewmaker | Amyloid of the prion domain of Sup35p has an in-register parallel beta-sheet structure[END_REF]. One reason for these differences might be the limited resolution attained so far, that leaves space for individual interpretation of the results. [START_REF] Shewmaker | Amyloid of the prion domain of Sup35p has an in-register parallel beta-sheet structure[END_REF] FIGURE 6 | T 1 -filtered 13 C- 13 C correlation (A) and INEPT (B) spectra of Sup35pNM-His-#3. The spectra have been recorded at 800 MHz proton frequency, the recycle delay for the T 1 -filtered spectra was 4 s, the sample temperature 7 • C and the MAS spinning frequency for all spectra 17.5 kHz.

analyzed selectively Y-, F-and L-labeled fibril samples of C-terminally His-tagged, i.e., Sup35pNM-His, by solid-state NMR spectroscopy. Judging from the relative area underneath the corresponding peaks and the upfield shift compared to the random coil chemical shift in 1D 13 C spectra, they suggested that 18 out of 20 Y residues, six out of eight L residues, three out of four F and five out of 15 A residues have β-strand conformation. A similar number of residues was determined to have nearest neighbor contacts of about 0.5 nm from which it was concluded that the residues are located in in-register parallel β-sheets. Since about seven out of eight Leu residues were found to have a β-strand conformation and seven L residues are located in the M-domain, it was suggested that the M-domain must have partial β-strand conformation. This data on Sup35pNM-His is to some extent consistent with the data we report here on this construct, since we also see L and K residues with chemical shifts which are typical of β-strand conformation; but they are clearly not consistent with the data we show here on untagged Sup35pNM. The above-mentioned resonances, which can only be observed within Sup35pNM-His, not in His-Sup35pNM nor Sup35pNM, are the strongest new resonances we observe in CPbased spectra. This made it possible to identify several peaks of the same spin system and assign them tentatively to amino-acid types. However, further new resonances appear which are weaker and not assignable. Similar results were obtained by Tessier et al. who also observed an interaction site/recognition element of C-terminal tagged Sup35pNM in the region of residues 90-120 [START_REF] Tessier | Prion recognition elements govern nucleation, strain specificity and species barriers[END_REF].

We show here that under identical assembly conditions, the context of Sup35pNM, e.g., whether it is within the full-length protein or harboring a short N-or C-terminal tag, influences the resulting final structure of the fibrils. We previously biochemically and functionally documented the influence of the C-terminal domain on Sup35p assembly into fibrils [START_REF] Krzewska | Biochemical and functional analysis of the assembly of full-length Sup35p and its prion-forming domain[END_REF]. We also showed that the C-terminal domain affects the overall structure of the fibrils amyloid core [START_REF] Luckgei | The conformation of the prion domain of Sup35p in isolation and in the full-length protein[END_REF]. The present results show that as little as a short poly-His tag affects the overall structure of the amyloid form of Sup35pNM domain significantly. Our findings strongly suggest that Sup35pNM conformational landscape is not only affected by the presence of the C-terminal moiety of the protein, but also by smaller additions, even if the C-terminus is distant from the segment forming the amyloid core at the very N-terminal end. Thus, slightly distinct sequences, characteristic of each version of Sup35pNM, can assemble into structurally distinct fibrils. While the poly-His tag affected marginally the structure of Sup35pNM fibrils (untagged protein) when placed on the N-terminal end of the protein, its positioning at the C-terminal end in contrast radically changed the spectra. Also, C-terminally His-tagged Sup35pNM fibrils displayed a strong degree of polymorphism. Several new resonances could be observed in some samples, which led us to hypothesize that a region lying at the end of the N-domain and the beginning of the M-domain (around residues 120-140) is structured in the presence of a C-terminal His-tag. Studies on two prion variants (Sc4 and Sc37) of C-terminally tagged Sup35pNM [START_REF] Toyama | The structural basis of yeast prion strain variants[END_REF] revealed H/D exchange protection for both constructs in the region between 110 and 128, in addition to protection of the residues of the fibril core, which lie between residues 1-40. Our results thus support those reports, however, only for C-terminally His-tagged Sup35pNM.

In vivo analysis of the functional properties of the different polymorphs we describe yielded clear cut and unexpected results. The polymorphic C-terminally His-tagged NM preparations induced [PSI+] formation with a much greater efficiency than their His-Sup35pNM counterparts (Figure 7). Several explanations may account for this observation. As Sup35pNM-His may consist of different polymorphs, it is reasonable to envisage that one or several polymorphs within this mixture have more potent seeding capacity than others, thus, inducing [PSI+] with greater efficiency. In addition, the Sup35pNM folding landscape might be more compatible with the structural heterogeneity in Sup35pNM-His, thus, facilitating Sup35pNM molecules recruitment by fibrillar Sup35pNM-His and [PSI+] induction. Last, it is not unreasonable to consider that the structural heterogeneity of Sup35pNM-His may yield fibrils with greater probability of being remodeled by breakage or severing in yeast cells. This would yield a larger number of short fibrils and therefore to increased [PSI+] induction. The observation that the size of Sup35pNM prion particles induced by the polymorphic Sup35pNM-His is smaller than that induced by His-Sup35pNM (Figure 7C) would be consistent with seeds recruiting endogenous Sup35p with higher efficiency, thus, depleting Sup35p within the cells with greater efficiency and yielding strong [PSI+], as opposed to slowly growing His-Sup35pNM fibrils that yield weak [PSI+] and larger prion particles in agreement with the data presented in Figure 7.

Despite significant consistencies between the results we report here and previously published data, caution is required when comparing different datasets, as some lack residue-specific (molecular) resolution. Most importantly, different preparations of C-terminally tagged NM did not yield reproducible spectra. As sample preparation is as tightly controlled as for the other samples, we suspect that this protein construct does not form a single polymorph consistently. Our results clearly show that in addition to a dependence on the experimental conditions, amyloid fibrils polymorphism strongly depends on the context and additions to the amyloid-forming polypeptide chain. Our observations further bring valuable insights into the building principle of structural elements of prion variants.

  FIGURE 3 | (A)1 H-13 C INEPT and (B) T 1 -filtered13 C-13 C correlation spectrum[START_REF] Luckgei | The conformation of the prion domain of Sup35p in isolation and in the full-length protein[END_REF] of untagged Sup35pNM. The spectra were recorded at 800 MHz proton frequency and a MAS spinning frequency of 17.5 kHz. The 13 C-13 C-correlation spectrum was recorded with a recycle delay of 4 s. The assignments of the random-coil chemical shifts assigned in His-Sup35pNM are indicated.(C) Comparison between the signal intensity in T 1 -filtered13 C-13 C correlation spectra (light bars) and the number of the respective amino acid in the M-domain (dark bars) of untagged Sup35pNM. The signal intensity of Lys residues was arbitrarily set to 1, and scaled accordingly for the remaining residues. The error bars indicate the standard deviation of the noise level of each spectrum.

FIGURE 5 |

 5 FIGURE 5 | (A) 20 ms DARR spectrum of Sup35pNM-His-#3. The spectrum has been recorded at 850 MHz proton frequency, the sample temperature 7 • C and the MAS spinning frequency for all spectra 17.5 kHz. The amino-acid specific assignments of the new peaks in the Sup35pNM-His-#3 sample are indicated in red (only visible in 20 ms DARR spectra) and black (visible in 20 ms DARR spectra and 3D NCACB spectra). (B) Secondary chemical shifts of the newly assigned peaks in Sup35pNM-His-#3. Black bars: amino acids which could be identified in 20 ms DARR spectra and 3D NCACB spectra; red bars: amino acids which only could be observed in the 20 ms DARR spectra. For glycine, the Cα secondary chemical shift was used. (C) Amino-acid sequence of His-Sup35pNM-His, with the C-terminal tag in red. Stretches of amino acids which coincide with the amino acid types that newly appear in the Sup35pNM-His-#3 spectrum are underlined.

FIGURE 7 |

 7 FIGURE 7 | (A) 74D-694 [psi -, pin -] cells were transformed with 5 µg of in vitro assembled His-Sup35pNM (His-NM) or Sup35pNM-His (NM-His) fibrils, or with buffer as a control. Random clones from each transformation reaction were then patched on 1/4-YPD plates to assess their prion phenotype (white: [PSI + ]; pink, weak [PSI + ]; red [psi -]). (B) Quantification of data such as those presented in panel (A). Error bars represent the standard deviation from three independent experiments, each performed in triplicate (**P < 0.001, unpaired two-tailed Student's t-test). The [PSI + ] conversion frequency was null when transforming with buffer. (C) Cell lysates were prepared from random [PSI + ] clones picked from the plates shown in panel (A), and analyzed by SDD-AGE and immunoblotting using an anti-Sup35p antibody. Large (upper solid arrow head) and small (lower solid arrow head) Sup35p aggregates. Monomeric Sup35p (open arrow head).

Frontiers in Molecular Biosciences | www.frontiersin.org

August 2020 | Volume 7 | Article 190

FUNDING

This work was supported by the ANR (ANR-12-BS08-0013-01), the ETH Zürich, the SNF (200020_188711), and the CNRS. Financial support from the IR-RMN-THC Fr3050 CNRS for conducting the research is gratefully acknowledged.

DATA AVAILABILITY STATEMENT

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

AUTHOR CONTRIBUTIONS

LB prepared all NMR samples. CG, AS, and NL recorded spectra. NL, AS, AB, and BM analyzed NMR data. MK performed protein transformation and SDD-AGE assays. RM, BM, NL, LB, and AB designed study and wrote the manuscript. All authors contributed to the article and approved the submitted version.

Conflict of Interest:

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


P Even

P Ngo

LIVE EXTRACTION OF CURVILINEAR STRUCTURES FROM LIDAR RAW DATA

Keywords: Lidar, raw data processing, digital geometry, forested area, mountainous area, road extraction, ridge extraction

In this paper, a general framework is proposed for live extraction of curvilinear structures such as roads or ridges from airborne LiDAR raw data, in the scope of present and past man-environment interaction studies. Unlike most approaches in literature, classified ground points are directly processed here, rather than derived products such as digital terrain models (DTM). This allows to detect possible lacks of ground points due to LiDAR signal occlusions caused by dense coniferous canopies. An efficient and simple solution based on discrete geometry tools is described for supervised context in which the user just indicates where the extraction should take place. Fast response times are required to ensure a good man-system interaction. The framework performance is first evaluated on the example of the extraction of forest roads in a mountainous area, as these objects are well marked in the DTM and hence provide some kind of ground truth. Good execution time and accuracy level are reported. Then this framework is applied to the detection of prominent curvilinear structures, which are much more diffuse objects, but of greater interest than roads in the scope of the present project. Achieved results show high potential of the proposed approach to help archaeologists and geomorphologists in finding areas of interest for future prospection using LiDAR data.

INTRODUCTION

The present work addresses the problem of the supervised extraction of curvilinear structures from LiDAR ground point cloud in the scope of interdisciplinary studies of past and present environment of a forested site located in a mountainous area. Airborne laser scanning, also called LiDAR for Light Detection And Ranging, is a 3D acquisition technique based on the emission of a laser beam swept over the measured scene and on the reception of echoes on hit obstacles. Combined with other data from on-board sensors and differential global navigation satellite systems (GNSS), the measure of the signal travelling time provides a detailed survey of the overflight landscape [START_REF] Wehr | Airborne laser scanning -an introduction and overview[END_REF]. In forest environment, the received signal is composed of multiple echoes that correspond to the successive hit obstacles, from the forest canopy, down to lower vegetation levels and, finally, to the ground itself. Therefore, a point classification is performed to separate ground points from low, medium, or high vegetation, and from other kind of specific features, such as water surfaces, buildings or wire lines. A surface is fit to ground points using optimization techniques to produce a digital terrain model (DTM) [START_REF] Axelsson | DEM generation from laser scanner data using adaptive TIN models[END_REF][START_REF] Evans | A multiscale curvature algorithm for classifying discrete return lidar in forested environments[END_REF], which can then be displayed using different visualization tools [START_REF] Challis | A generic toolkit for the visualisation of archaeological features on airborne LiDAR elevation data[END_REF]. But too sparse data may produce large approximations, that end users are not aware of [START_REF] Jones | High-resolution interpretative geomorphological mapping of river valley environments using airborne LiDAR data[END_REF]. In particular, conifers are still a strong obstacle that impedes the laser beam reaching the soil [START_REF] Popescu | Estimating plot-level tree heights with lidar: local filtering with a canopyheight based variable window size[END_REF][START_REF] Devereux | The potential of airborne lidar for detection of archaeological features under woodland canopies[END_REF], thus producing holes in the ground point distribution. In this exploratory work, classified ground points are processed rather than the DTM, in order to design and test a new approach more aware of points distribution in the raw data. Digital geometry tools are used to efficiently process the sparse point set.

This work takes place in the scope of a multidisciplinary project gathering different specialists to study past and present impacts of man activity on current landscape. Among them, archaeologists are looking for remains of man-made structures and their * Corresponding author geographical organization, while geomorphologists aim at discriminating natural from anthropogenic reliefs. The studied terrain is a forested area rich of past human activities located in the heart of Vosges mountain in Eastern France. On-site spotting is one of the preliminary task to perform.

A LiDAR acquisition is of great help to survey forested areas, where on-site observations are often hindered by the vegetation [START_REF] Sittler | Revealing historical landscapes by using airborne laser scanning. A 3-D model of ridge and furrow in forests near Rastatt (Germany)[END_REF][START_REF] Georges-Leroy | Contribution of lidar data to the study of land-use history in Haye forest[END_REF]. It provides bare soil visualizations allowing the detection of details that may be missed during on-site prospections. Moreover delineation tools are available to extract these geolocalized features and collect them into a geographic information system (GIS). More and more specialized detection tools are provided to help technical teams in this fastiduous task, using supervised or automated techniques [START_REF] Sevara | Pixel versus object -a comparison of strategies for the semi-automated mapping of archaeological features using airborne laser scanning data[END_REF]. But most often, the produced information must be confirmed or even completed by on-site validation. In the present project, a large amount of studied objects have an elongated shape: walls, ditches, ancient tracks, parcel limits, agricultural benches, etc. This work aims at providing simple solutions to extract those curvilinear structures from LiDAR raw data and to display them on DTM views. An illustration is given in Figure 1. After a presentation of available data and a brief survey of existing studies, section 2 exposes our approach and the selected methodology. Digital geometry notions used in this work are introduced in Section 3. Section 4 details the main framework designed for curvilinear structures extraction. Then an instanciation of this framework to the case of forest roads detection is presented and achieved performance on these well-marked objects is given in section 5. Section 6 focuses on the application to prominent curvilinear structures detection, and discusses possible extensions. Finally section 7 gives a conclusion and draws opened perspectives.

CONTEXT

The LiDAR data

The Despite a mean density of 9.89 ground points/m 2 , a point repartition analysis (summarized in Figure 2) showed that the point cover is not homogeneous at all, and revealed many occluded places mostly due to the presence of coniferous canopies. This study points out the required level of robustness to data lacks, that the proposed method should reach.

Limits of existing approaches

Most of automated or semi-automated detection tools rely on the DTM [START_REF] Sevara | Pixel versus object -a comparison of strategies for the semi-automated mapping of archaeological features using airborne laser scanning data[END_REF]; this interpolated map is accurate enough for applications in well controlled environments.

In lack of efficient solutions to process the point cloud, it seems more practicable to use spatially arranged height values than sparse 3D points. In [START_REF] White | Forest roads mapped using LiDAR in steep forested terrain[END_REF], careful manual delineation of haul roads in DTM view show comparable results to accurate field surveys. Unsupervised solutions based on DTM analysis have also been developed, using a morphological classification and stochastic geometry tools to build and assemble a graph structure [START_REF] Ferraz | Large-scale road detection in forested montainous areas using airborne topographic lidar data[END_REF], or convolution neural network architectures [START_REF] Salberg | Largescale mapping of small roads in lidar images using deep convolutional neural networks[END_REF][START_REF] Liu | Road mapping in LiDAR images using a joint-task dense dilated convolutions merging network[END_REF]. But all these tools incorporate the interpolation errors.

Few approaches make direct use of LiDAR raw data. In [START_REF] Clode | Detection and vectorisation of roads from lidar data[END_REF] None of these approaches try to directly exploit the spatial organization of available raw 3D ground points from the beginning of the process, and they strongly depend on local conditions such as surface reflectance or vegetation cover.

These works are not easy to transpose to archaeological or geological structures which are much more diffuse objects with geometrical properties that may largely vary along their layout. Some studies deal with local structures, numerous enough and geometrically distinctive to build or learn a model that can be applied to automatically detect additional instances [START_REF] Toumazet | Automatic detection of complex archaeological grazing structures using airborne laser scanning data[END_REF][START_REF] Trier | Semi-automatic mapping of charcoal kilns from airborne laser scanning data using deep learning[END_REF]. But most often, known artefacts are quite few, so that no learning basis can be used to train convolution neural networks. Moreover, surface data are generally not sufficient to surely discriminate these structures, so that on-site surveys by specialists are still necessary to collect additional information.

Recent advances of discrete geometry techniques [START_REF] Klette | Digital Geometry: Geometric Methods for Digital Picture Analysis[END_REF], Couprie et al., 2019) have reached a break point, that makes them mature to address a lot of concrete problems dealing with discrete data, such as the addressed cloud of 3D points. This research field appeared fifty years ago to set the foundations of a new mathematical theory intended to the processing of numerical data produced by most of today's devices. It aims at providing computationally efficient and well controlled solutions to solve a wide range of problems.

The present work explores the use of recent discrete geometry tools to design a generic framework for extracting curvilinear structures directly from the LiDAR ground point cloud. In order to clearly bring out pros and cons of the approach, no attempt is made to filter the processed data or to exploit the interpolated DTM. A first specialization of the framework to forest roads was achieved. These objects are not really of greatest interest in the scope of the project, but as they are well marked in DTM views, they provide a good basis for the method performance evaluation. In a second stage, we set up another specialization to prominent elongated structures, in order to demonstrate the approach feasibility for detecting objects in better adequation to the project objectives.

DIGITAL GEOMETRY NOTIONS

Digital geometry notions used in this work are recalled here.

A digital straight line L(a, b, c, ν) is the set of points P (x, y) of Z 2 that satisfy :

0 ≤ ax + by -c < ν, with(a, b, c, ν) ∈ Z 4 (1)
In the following, we note V (L) = (a, b) the director vector of digital line L, w(L) = ν its arithmetical width, h(L) = c its shift to origin, and p(L) = max(|a|, |b|) its period (i.e. the length of its periodic pattern). When ν = p(L), then L is the narrowest 8-connected line and is called a naive line (see Figure 3). A digital straight segment is a digital straight line restricted to

[xmin, xmax] interval if |a| < |b|, to [ymin, ymax] otherwise.
A blurred segment B of assigned thickness ε is a set of points in Z 2 that all belong to a covering digital straight line L of thickness µ = ε (see Figure 4). The optimal line of the blurred segment is the covering line with minimal thickness. The thickness of the blurred segment is the thickness of its optimal line. Blurred segments can be detected in linear time by a recognition algorithm [START_REF] Debled-Rennesson | Optimal Blurred Segments Decomposition of Noisy Shapes in Linear Times[END_REF] based on an incremental growth of the convex hull of added points. At each step, the convex hull width is maintained and compared with the blurred segment assigned thickess. A directional scan is an ordered partition restricted to the grid domain G of a thick digital straight line D, called the scan strip, into scans Si, each of them being a segment of a naive line Ni, called a scan line, orthogonal to D. The directional scan is defined as the set:

ε = 1 ε = 3 ε = 7
Si = D ∩ Ni ∩ G V (Ni) • V (D) = 0 h(Ni) = h(Ni-1) + p(D) (2)
In this definition, the clause V (Ni) • V (D) = 0 expresses the orthogonality constraint between the scan lines Ni and the scan strip D. Then the shift of the period p(D) between successive scans guarantees that all points of the scan strip are traversed one and only one time. The scans Si are developed on each side of a start scan S0, and ordered by their distance to the start line N0 with a positive (resp. negative) sign if they are on the left (resp. right) side of N0 (see Figure 5). The directional scan is iteratively parsed from the start scan to both ends. At each iteration i, the scans Si and S-i are successively processed.

An adaptive directional scan [START_REF] Even | Thick line segment detection with fast directional tracking[END_REF] is a dynamical version of the directional scan notion, that allows on-line registration to a moving search direction. Compared to static directional scans where the scan strip remains fixed to the initial line D0, here the scan strip follows a goal curve C while scan lines remain fixed (see Figure 6). An adaptive directional scan is defined by the set:

   Si = Di ∩ Ni ∩ G V (Ni) • V (D0) = 0 h(Ni) = h(Ni-1) + p(D0) Di = L( Ci, w(D0)), i > 0    ( 3
)
where Ci is an estimate at position i of the tangent to the goal curve C. The last clause expresses the scan bounds upate at iteration i.

MAIN EXTRACTION FRAMEWORK

Based on the presented notions, a curvilinear structure extraction framework was designed, according to the following principle: LAZ points classified as "ground" are mapped into a 2D grid; a DTM-based control view is displayed to the user to let him localize potential structures; a stroke is drawn across the selected one and corresponding elements of the ground point grid are analyzed to recognize the structure section; in case of success, the structure is tracked and extended on each sides of this start position as far as possible; after post-processing validation and cleaning, the found structure is displayed over the DTM in the control view. In order to ensure user acceptability, the extraction process is required to hold in a fraction of a second, thus producing a feeling of live extraction.

Before giving thorough details on the extraction framework, we first introduce the DTM-based control view and the associated ground point grid, then the curvilinear structure model used.

The control view

It should be mentioned that the DTM-based control view is used only for two purposes: manual selection of relevant areas, and result display. Assuming that no DTM visualization technique is ideal for every application contexts and that generally several ones should be combined to guarantee a complete visual survey [START_REF] Bennett | A comparison of visualization techniques for models created from airborne laser scanned data[END_REF][START_REF] Štular | Visualization of lidar-derived relief models for detection of archaeological features[END_REF][START_REF] Mayoral | The highest gradient model: a new method for analytical assessment of the efficiency of LiDAR-derived visualization techniques for landform detection and mapping[END_REF], we therefore implemented a simple but sufficient solution able to ensure good test conditions. It relies on a multidirectional hill-shading based on three directional light sources at 120 o from each other, one brighter at high incidence angle (60 o ), the two others at a lower angle (30 o ). The light set azimuth is let under user control to ensure a correct lighting of relevant details.

Here, accurate perception is not required from the user, and such simple visualization technique does not question the relevance of the extraction tool. Moreover, this low demanding user control is the only function ensured by the control view, so that DTM approximations have no impact in this context.

The ground point grid

The LAZ point set is organized in 500 m × 500 m tiles which cover the whole acquisition area. Classified points as "ground" are extracted and projected into a high resolution grid G that covers all the tiles and ensures fast access to the points stored in each cell. The resolution of this grid is set in accordance to the DTM resolution, that provides the input stroke P1P2. An adaptive directional scan in grid G is built from an initial scan S0 that joins the cells containing P1 and P2. The points contained in the cells of S0 are projected on line P1P2 to get an initial profile of the structure.

However this scan structure leads to an irregular point repartition along the profile (see Figure 7). Therefore, the grid resolution is set to a multiple NR of DTM resolution. The profile is then built by the set of points contained in a sequence of NR scans, thus ensuring a fairer repartition. In practice, NR is set to 5, leading to a grid cell size of 0.1 m in the present case.

The curvilinear structure model

In this work, a curvilinear structure S is considered as a surface produced by a spatially consistent extension of a characteristic noisy profile P along a 3D curve C. For example, a break-inslope profile may be seen as a succession of two noisy straight lines that form an angle α at their intersection (see Figure 8).

In that case, the noise tolerance threshold δ should be set large enough to absorb the terrain unevenness.

In order to take into account the spatial evolution of the structure S along the curve C, the profile P is declined in a sequence of adjacent profiles Pi. Each profile is extracted from the point cloud using successive scans Si. Each profile contains a list of 3D points and a geometric template, specific to each kind of structure to extract: roads, ridges, etc. The template embeds several attributes, such as height or position, in order to speed up the structure tracking in the next profile and to enforce spatial consistency. The position attribute is also used to update the scan strip ( Ci in Equation 3). At each profile position, slope and direction values of the curve C are estimated from previous profiles height and position. Null values are assumed at start.

The curvilinear structure detection framework

The curvilinear structure detection framework is depicted in Figure 9. It globally features two main stages: (i) initial detection of the structure from the input stroke P1P2, (ii) extension of the structure on each side of the initial detection.

❄ P1P2 Initial structure detection ❄ P0 ✟ ✟ ✟ ✟ ❍ ❍ ❍ ❍ Succeeds ? ✲ no ∅ ❄ yes Structure extension ❄ Pi ✟ ✟ ✟ ✟ ❍ ❍ ❍ ❍ NF successive failures ? no ❄ ❄ yes ✟ ✟ ✟ ✟ ❍ ❍ ❍ ❍
Both sides processed ? no The initial detection performs the following steps: D1. creates an adaptive directional scan with S0 = P1P2; D2. collects points in NR first scans; D3. sorts points by increasing distance to P 1 along ---→ P1P2; D4. runs a start profile detection (specific to each structure).

Then each extension step operates the following way: E1. centers the adaptive directional scan Di on the template position attribute of previous detected profile; E2. collects points of NR next scans; E3. sorts points by increasing distance to P 1 along ---→ P1P2; E4. runs a next profile tracking (specific to each structure).

The extension loop ends when the grid bound is reached or after a given threshold NF of profile detection failures if they are not due to a lack of ground points. This parameter allows to cross some obstacle, but it also increases the risk of false detections in chaotic areas. A default value of NF = 5 is assumed in this work. In areas with quite few ground points, undetected profile templates are discarded and the detection process may continue until a well covered area is met again.

Algorithms to detect first and next profiles are not necessarily identical. For next profiles, the former profile template is used to check the spatial consistency constraint, and if possible, to speed up the search of the new template. As nearby detected profiles are already validated at this stage, constraints may be released to accept some terrain roughness.

FOREST ROADS EXTRACTION

Forest roads are well marked objects in DTM views. Their delineation could provide some convenient ground truth to test the performance of the curvilinear structure extraction tool. Only main ones are already reported into geographical information systems, and this available knowledge must be updated and completed in prospection areas to get a more accurate position at the price of time consuming surveys on the field. Therefore, although these objects are not central in the scope of the project, their supervised extraction from the LiDAR data would yet be of great help. For all these reasons, their detection was implemented at first as a good basis for the extraction framework development and evaluation.

Forest road model

A forest road cross section, here called plateau, is modelled as a bounded horizontal blurred straight segment, with possible width varying from Dmin = 3 m up to Dmax = 10 m (see Figure 10). This model is quite similar to the one used in [START_REF] Ferraz | Large-scale road detection in forested montainous areas using airborne topographic lidar data[END_REF] for forestry management purposes, and suits rather well to mountain roads. In the few flat areas found, bounds are often marked by surrounding ditches or by the hollowness due to terrain compaction. The blurred segment width is restricted to ∆H = 0.1 m, that is enough to cope with most road surface irregularities. Then, at least Nmin = 6 points are required to consider a plateau as being reliably detected. The horizontal area materializes the road plateau (see Figure 10). Because of the discrete nature of the point cloud, the can not be detected exactly, but just estimated within an interval between the last point of the blurred segment and the next point. Bounds are considered as detected if this interval is less than ∆B = 0.5 m. By default, the estimated bound is this interval center. When both bounds are detected, the road width can be estimated and the profile position is set at the middle. But very often, only one bound is detected, for instance, due to the presence of an occluding tree besides the road. In that case, the profile position is defined by the detected border shifted by half the last estimated width when this information is available.

When it occurs at the first detection, new trials are made using next scans and the detection is aborted after NF failures.

First plateau detection

In initial structure detection stage of the framework (see Figure 9), the specialization of start profile detection (step D4 of Section 4.4) to forest roads proceeds the following way:

1. sorts collected points by increasing height value; 2. finds the ∆H-wide height interval containing the greatest number of points; 3. finds the longest sequence of consecutive points at this height interval in sorted points by distance to P1: it forms a horizontal blurred segment of assigned thickness ∆H; 4. checks the sequence size (≥ Nmin) and length (≥ Dmin); 5. checks if at least one of this horizontal sequence ends is correctly bounded: the distance of each end point to the next point out of the sequence should be less than ∆B.

In this algorithm, horizontal road sides at nearly the same height can be interpreted as a road plateau, thus leading to a false detection (see Figure 11). This may happen many times. Also, the proportion of those points at optimal height effectively inserted in the blurred segment is a good test to detect such situations. If the obtained blurred segment does not contain a large majority (70%) of these points, they are discarded from the height sequence and a new height interval is searched. The new blurred segment is compared to the former one and the longest one is kept. This strategy is certainly not perfect, but it succeeds in most encountered cases.

Next plateaux tracking

Optimizations based on a blurred segment detection are made for the detection of next plateaux, in a specialization of next profile tracking (step E4 of Section 4.4). Followed steps are:

1. test of available scan points count; 2. selection of scan point PC nearer to template center; 3. test of PC height wrt template height; 4. initialization of a blurred segment of assigned thickness ε = ∆H on point PC; 5. metrically balanced extension of the blurred segment on each side of PC with a tolerance of 3 successive points out of the blurred segment; 6. as soon as the blurred segment length reaches Lexp, assigned thickness pinching to the observed blurred segment thickness augmented with a security margin ∆ε, then extension continuation; 7. when the extension is stopped, test of obtained blurred segment size and length; 8. withdraw of extremal points if they belong to the bounds of the enclosing digital straight segment; 9. test of the blurred segment tilt angle ∆β; 10. if the detection failed, restart from step 3 with PC shifted 1 meter on the right, then 1 meter on the left.

Steps 6 and 8 are necessary to avoid the inclusion of points on road sides, that could possibly tilt the blurred segment. Therefore, Lexp is set to 2 m to incorporate most of the road irregularities before reaching the edges, and ∆ε to 0.1 m to tolerate additional roughness after the pinching. The maximal tilt angle is set to ∆β = 9.5 o to differentiate possibly slanted roads from local terrain trend. Constants were arbitrarily set, but small changes do not affect the detection process behavior. Steps 9 and 10 help to detect again the true road plateau after crossing a large flat area with wide plateaux or a pointless sector.

Achieved results

The set of plateaux which constitutes the forest road structure are displayed over the DTM view. Typically, hundred meters long road sections such as the one displayed in Figure 12

Performance evaluation

To evaluate the detector, a set of forest roads was selected in three distinct 1500 m × 1500 m large areas (see Figure 14 (a-b-c)): St-Mont (10 points/m 2 mean density), Fossard1 (7 points/m 2 ) and Fossard2 (6.5 points/m 2 ). In order to get a reference to compare detection results with, their central line was manually delineated on the DTM view. In accordance to on-site estimations, a fixed width of 3 m was assigned to most forest tracks, 5 m to larger mountain roads. As roads are not central objects for the project, no attempt was made to filter the detection outputs or even to estimate their width. Detected roads were drawn with successive plateaux connected together to fill the detection failure gaps, so that they could be compared to delineated roads on a pixel count basis (see Figure 13). Because the tool was not designed to detect road ends and forks, we artificially removed the plateaux beyond these limits in order to ensure a comparison on the basis of delineated roads, excluding possible derivations or extensions. All parameters were set beforehands and kept fixed during all the tests, including the profile detection failures threshold NF . Detected roads are displayed in Figure 14 (d-e-f). Figure 15 shows their detailed overlay on delineated roads in St-Mont area.

Let call L the cumulated length of selected roads, N the number of input strokes used for the detection, G (resp. D) the set of displayed pixels of delineated (resp. detected) roads, and S the count of pixels of set S. Achieved results are listed in Table 1, where the detection precision P , recall R and global performance F-measure F are given by Equation 4.

P = D ∩ G D , R = D ∩ G G , F = 2 * P * R P + R (4) Sector L (m) N P (%) R (%) F (%) St-

Discussion about technical performance

Time performance is about 220 ± 20 ms per 1000 m of delineated road, that suits quite well to interaction context requirements. Precision and recall results are quite satisfying if we consider the absence of any filtering. In particular, horizontal places nearby the road are largely integrated into the detection thus producing many side shifts that penalize the precision measure. In a road vectorization application, some filters could be added at post-processing stage and interpolated height from the DTM could also be used. In some sectors of the Fossard, the density is particularly low, and the structure extension often stops when no adequate profile is found after crossing long places with not enough points. This problem mostly affects the recall measure.

By definition, the directional scan is sensitive to large direction changes. The adaption ability only deals with side shifts. Therefore tight curves cause detection stops. If they could be detected, it would be possible to start a new directional scan. But no filter is applied and the implemented method does not handle rapid changes of the direction. More strokes are thus necessary. Moreover, the performed delineation is certainly far from perfect. The fixed width assumption for forest roads is not always true, and the width estimation is just approximated. It may also affect both precision and recall measures.

The assumed road model for mountainous areas suits apparently well in most tested places, but it is no longer valid in flat places where the detection may often be attracted by a nearby terrace for instance. It is observed that some recent cutoffs are also undetected, the old laying-out being rather tracked. This drawback could probably be avoided by a verification of points classified as "low vegetation" in the raw data, but at the price of much longer execution time.

Using the proposed framework, such verifiable objects as mountain roads are efficiently extracted despite of the occurance of many areas with no ground points. In the following section, we show how it can be adapted to the case of other morphological structures more relevant to the project goals.

PROMINENT CURVILINEAR STRUCTURES

A prominent curvilinear structure is defined by the displacement of a convex profile in orthogonal direction along a 3D curve. This rather large definition covers a wide range of shapes at different scales, from small communal delimitation walls less than one meter high, up to cliffs or crests which may reach more than fifty meters high in the studied sector. In the present project, archaeologists are studying the remains of an undated decayed wall surrounding the Saint-Mont summit while geomorphologists pay a particular attention to breaks in slope which might delimit some spaces potentially arranged by men.

Our purpose here is certainly not to try to interpret these shapes, but rather to provide specialists with geometric tools aiming at easily extracting them from the LiDAR. Therefore, quite a neutral terminology, such as ridge, is intentionally used for these shapes. Here again, exploiting the spatial consistency of the profile along the curve is the key idea to detect these structures.

Ridge model

The ridge structure is defined by a set of cross sections, called bumps. The bump has a straight basis over which a volume can be determined through its center of mass and its height based on the given sequence of points.

The construction (see Figure 16) is as follows: let L be the baseline of the convexhull of the point set, A and B its bearing points, S the polyline joining all the points of the sequence, and S (resp. E) the nearest polyline vertex to A (resp. B) at distance HB from the baseline. We compute the area between the line (SE) and the polyline S, and determine an orthogonal line M to B that splits the polygon in two parts with same area. The bump center of mass belongs to M. We finally compute the bump position C at the intersection of M and S, and the bump height H as the distance between C and the line (SE). Note that point C does not necessarily coincide with the bump top T , defined as the highest polyline vertex to the baseline. A volume property such as the center of mass is much more a stable measure than the top, a surface feature submitted to large shift caused by terrain irregularities. C is thus better suited than T to ensure a stabilized tracking of the ridge structure. Initially intended for ridge characterizations, the base height parameter HB is not yet used, and is set to 10% of the bump maximal height, just to cope with global terrain roughness.

Bumps detection and tracking

The size of the ridge structure to detect is determined by the length of input stroke P1P2. The bump detection algorithm realizes the previous construction from the sequence of sorted points by distance to P1. It produces a template that contains the point C, the bump height H and the base points S and E. The baseline construction is optimized using Algorithm 1, where the function pointsOver(S,L) builds the set of points over the line L in set S. The other operations of the detection method are trivial.

Algorithm 1: getBaseLine: provides base line bearing points. input : A sequence P of sorted points by horizontal distance with at least one point over the line between first and last points. output: (D1, D2) → Bearing points of the baseline B ← line (first (P), last (P)); S ← highestPoint (P); P1 ← subSequence (P, first (P), S); P2 ← subSequence (P, last (P), S); D1 ← lowestPoint (P1);

D2 ← lowestPoint (P2); while D1 / ∈ B or D2 / ∈ B do B ← line (D1, D2); for i ← 1 to 2 do Pi ← removePoints (Pi, pointsOver (Pi, B)); Di ← lowestPoint (Pi); i ← i + 1; end end
Next bump tracking realizes the same operations than the first detection. No particular optimization based on previous detection was found with this very simple and multi-purpose model. Therefore the template is only used for spatial consistency checking through the use of rather large tolerance values: the tolerance to point C shifts is set to ∆C = 0.5 m, and the tolerance to height variations to ∆H = 0.25 m.

Achieved results

As no real ground truth is yet available to evaluate the ridge detection, mostly visual tests were performed on well marked salient features in the DTM. The analysis of obtained bump profiles indicates a good consistency between successive scans. Moreover, the structure sinuosity is correctly surveyed, as long as direction changes are not too strong (around 45 o limit). But of course, this is not more than a visual subjective appreciation.

To corroborate these observations, we performed a detection of the edge of Saint-Mont summit platform, which position is well identified. Because it features sharp angles, four input strokes were necessary to extract the whole circumference, but a correct delineation could quickly be obtained (see Figure 17).

Discussion about suitability to project needs

These results show good potential of the proposed framework to help specialists in finding areas of interest for future prospection using LiDAR data. Beyond simple structure localization, some volume quantification may also be delivered for ridge shapes whose baseline matches the local terrain trend. Notice also that the proposed framework could be easily extended to the detection of hollow structures by applying a symmetry around the baseline to the ridge model. However no such structure has been surveyed by archaeologists in the studied area untill now.

The last test shows the present limits of the ridge model used. In this case, a more complete specification of the wall profile may help to better discriminate the structure from nearby ridges. All these results must now be confirmed through detailed evaluations on concrete tasks in close cooperation with the archaeologists and geomorphologists involved in the project.

CONCLUSION AND FUTURE WORKS

This paper introduced a new framework based on recent discrete geometry tools for live extraction of curvilinear structures from raw LiDAR data as an alternative to standard DTM processing. In particular, ground point density disparities are taken into account with the new approach. To evaluate the framework performance, it was first instanciated for the detection of forest roads, whose position can easily be identified on DTM views. In regards of the simple road model used and in absence of any filtering of the extracted data, precision and recall performance achieved are quite satisfying. A long section may be extracted from a single user input and the response is immediate so that good interaction is ensured to fulfill given task requirements. A remaining challenge is the detection of tight changes of direction, that could help to reduce the amount of necessary user inputs.

This exploratory work was realized in the scope of an interdisciplinary project on past and present environment studies. Therefore, the framework was also applied to the detection of curvilinear prominent structures, and tested on the edges of a large flat area and on parts of decayed wall remains. Visually consistent detections are obtained, inciting us to develop more thoroughly this approach for effective needs related to the project goals.

Future works consist in experimental validations where detected structures will be compared to on-site surveys for finer validations in close cooperation with field specialist teams. In parallel, we intend to design a fully unsupervised detection tool based on this approach. For this purpose, visual indices could be extracted from the DTM view to automatically select relevant input strokes for the detection algorithm. Another development deals with the detection of tight direction changes using a finer estimation of the structure orientation.

  50m

Figure 1 .

 1 Figure 1. Extraction of a huge ancient stone structure (on left) from a section in the cloud of ground points (on right).

Figure 2 .

 2 Figure 2. Ground points repartition: percentage of 1 m 2 cells with at most N ground points.

Figure 3 .

 3 Figure 3. Naive digital straight line L(2, -7, 13, 7).

Figure 4 .

 4 Figure 4. Blurred segment with different assigned thicknesses.

Figure 5 .

 5 Figure 5. A directional scan: start scan S0 in red, odd scans in green, even scans in blue, bounds of scan lines Ni with dashed lines and bounds of scan strip D with bold dashed lines.

Figure 6 .

 6 Figure 6. An adaptive directional scan. The scan strip is dynamically fit to the curve position, so that scans are shifted to continuously cover the goal curve C.

Figure 7 .

 7 Figure 7. Profile extraction in a point grid with DTM resolution (top) and in an oversampled point grid (bottom).

Figure 8 .

 8 Figure 8. Example of model: break-in-slope profile.

Figure 9 .

 9 Figure 9. The main detection framework.

Figure 10 .

 10 Figure 10. Forest road section model: the road plateau lies between the displayed blurred segment and next points highlighted by the vertical strokes.

Figure 11 .

 11 Figure 11. Risk of false detection due to horizontal road sides at the same height: the dashed height interval may contain more points than the plateau but it is split in two disconnected sets.

Figure 12 .

 12 Figure 12. Example of road extraction displayed in white color; (a) input stroke in black; (b) section with no ground point.

Figure 13 .

 13 Figure 13. Detail of St-Mont sector : (a) delineation of road central line, (b) 3m-wide delineated road, (c) detected plateaux, (d) connected plateaux for comparison to wide delineation.

Figure 14 .Figure 15 .

 1415 Figure 14. Tested sectors : (a-d) St-Mont, (b-e) Fossard1, (c-f) Fossard2, (a-b-c) delineated roads, (d-e-f) detection result.

Figure 16 .

 16 Figure 16. Ridge section (or bump) model.

Figure 17 .Figure 18 .

 1718 Figure 17. Ridge detection: edge of Saint-Mont platform. We also tested the detection of a more diffuse structure: decayed remains of an ancient wall that forms a long detectable relief ranging up to 1 m high. Parts of this structure were surveyed by archaeologists and the achieved detection conforms well to the wall laying-out. The lower part of this wall (see Figure 18 bottom left) was rather easily extracted as it stands out distinctly in this area. Only one stroke was used here. The upper part extraction was more tedious because the structure lies few meters back from a terrace edge. Unfortunately much less ground points are available in this area. The wall extraction could only be ensured by some trials before finding a correct length for the input stroke to avoid the extraction being captured by the sharper terrace border.

  LiDAR acquisition campaign took place in December 2018. It covered a large part of the Fossard mountain, in an area delimited by Remiremont, Eloyes and Bémont (Vosges, France), A Titan DW device was used, with 300 kHz pulse frequency and 37 Hz scan frequency. Flight speed was 58 m/s, at 1150 m height for a slope ranging from 400 m in Moselle valley up to 800 m at Fossard top. The scan angle was set to ±21 o to ensure a 50% swath overlap. Obtained data are composed of 162 tiles with 500 m × 500 m size: 92 tiles (about 23 km 2 ) cover the mountainous sector, and the rest corresponds to surrounding urbanized plains. A set of classified points stored in LAZ format (compressed version of ASPRS laser file format) and a 1000 × 1000 pixels resolution DTM are provided with each tile.

Table 1 .

 1 Forest road performance evaluation results.

	Mont	6322	71	75.10	84.50	79.52
	Fossard1	11001 128	75.17	80.88	77.92
	Fossard2	5995	52	75.50	79.25	77.33

ACKNOWLEDGEMENTS

This work was realized in the scope of the SolHoM project (Interactions hommes-milieux et évolution des sols au cours des deux derniers millénaires dans le massif du Fossard, dir. Anne Poszwa), an interdisciplinary project of Université de Lorraine. The LiDAR acquisition, realized in the scope of PCR AGER project (Projet collectif de recherche Archéologie et GEoarchéologie du premier Remiremont et de ses abords, dir. Charles Kraemer), was made available for the present work. The authors would also like to thank Anne Gebhardt, Axelle Grzesznik, Thomas Chenal and the anonymous reviewers for their help and precious comments.