Pecot Fabien

BRANDS USING HISTORICAL REFERENCES: A CONSUMERS' PERSPECTIVE

Keywords: Corporate Brand heritage, historical references, Fast-moving consumer goods, Positioning, Past, Band Management

While existing literature on brand heritage focuses on corporate perspectives, this paper investigates the gap between intended and perceived heritage. Two sequential qualitative studies were performed: the preliminary study is based on observation and enables the selection of 27 fast moving consumer brands using historical references that are explicit for consumers; the main study is composed of 25 semi-structured interviews of consumers in order to analyse their interpretations. Results show that consumers know little about parent companies behind brands. However, they imagine that companies are seeking a compromise between an ideal tradition and a necessary modernity. Finally, they also distinguish different strategies in the management of temporality. Results outline the critical role of the consumers and enable to distinguish two types of brandsfamiliar and aristocratic onesand to formulate two distinct sets of recommendations for them based on the use of historical references.

Introduction

Lindt, "maître chocolatier suisse depuis 1845" ("Swiss chocolate master since 1845"), is a chocolate manufacturer using historical references in its marketing mix as an expression of its corporate heritage identity. But what do consumers perceive and remember from this message? Do they relate historical references to corporate identity? At a conceptual level, this question first resonates with recent interrogations about the dynamics between corporate brand heritage and heritage branding orientation, defined as an organisational trait upon which managers build a positioning strategy [START_REF] Santos | Heritage branding orientation: The case of Ach. Brito and the dynamics between corporate and product heritage brands[END_REF].

The second interrogation deals with consumers' interpretation of heritage branding [START_REF] Balmer | Corporate heritage brands in China. Consumer engagement with China's most celebrated corporate heritage brand -Tong Ren Tang: 同仁堂[END_REF][START_REF] Rindell | Two sides of a coin: Connecting corporate brand heritage to consumers' corporate image heritage[END_REF][START_REF] Rose | Emphasizing brand heritage: Does it work? And how[END_REF], and particularly with the use of historical references. Heritage branding orientation aims to facilitate consumers' interpretation of the corporate heritage identity [START_REF] Santos | Heritage branding orientation: The case of Ach. Brito and the dynamics between corporate and product heritage brands[END_REF]. Existing research focuses on detailed case study and only investigate consumers' interpretation of companies for which the implementation of corporate heritage identity has been assessed [START_REF] Balmer | Corporate heritage brands in China. Consumer engagement with China's most celebrated corporate heritage brand -Tong Ren Tang: 同仁堂[END_REF][START_REF] Rindell | Two sides of a coin: Connecting corporate brand heritage to consumers' corporate image heritage[END_REF]. To the best of our knowledge, no research takes what is accessible to consumers as a starting point to investigate their interpretation of the corporate heritage brand.

Building on existing literature on corporate heritage brands [START_REF] Balmer | Corporate heritage identities, corporate heritage brands and the multiple heritage identities of the British Monarchy[END_REF][START_REF] Balmer | Introducing organisational heritage : Linking corporate heritage , organisational identity and organisational memory[END_REF][START_REF] Urde | Corporate brands with a heritage[END_REF], on heritage branding [START_REF] Santos | Heritage branding orientation: The case of Ach. Brito and the dynamics between corporate and product heritage brands[END_REF], and on consumers' interpretation of brand heritage [START_REF] Rindell | Two sides of a coin: Connecting corporate brand heritage to consumers' corporate image heritage[END_REF][START_REF] Santos | Heritage branding orientation: The case of Ach. Brito and the dynamics between corporate and product heritage brands[END_REF], this paper looks at consumers' interpretation of Fast Moving Consumer Goods (FMCG) brands making use of historical references in the marketing mix. A first qualitative study based on observation enables to identify 27 FMCG brands using explicit historical references. A second qualitative study made of 25 semi-structured interviews shows that consumers 1) have little to no knowledge about the organisations behind the product brands, 2) imagine that these companies are managed in a sort of compromise articulating traditional and mainstream production system and ownership structure, 3) perceive different nuances in the management of temporality with implications on the brand's positioning.

Results contribute to the research on corporate heritage brand and on heritage branding orientation by outlining the gap between the corporate and the consumer perspectives on brand heritage. On a theoretical level, they remind that in the absence of a formal corporate brand communication, consumers rely on alternative cues to interpret corporate heritage. They also suggest a dual interpretation of the past which in marketing terms shows that using historical references can be articulated with different strategies combining a brand's adaptability and its stability. Based on these results, we provide brand managers with a guide for strategic decision-making based on the use of brand heritage. We also encourage them to increase corporate communications so as to address consumers' scepticism about the genuineness of their heritage orientation. Consumers' memory and brand relics can serve in this communication strategy.

Related Literature

This paper looks at brand managers' use of the past from a consumer perspective. As such it engages with and builds on two streams of literature. First, it addresses the dynamics between the corporate and the product brand perspectives. Then, it considers the consumer perspective over this marketing phenomenon.

Corporate and product brand heritage

Marketing scholarship distinguishes the foundational concepts of past, history or heritage, and their instrumental counterparts designating the way the past is used as a resource in marketing [START_REF] Burghausen | Repertoires of the corporate past: explanation and framework. Introducing an integrated and dynamic perspective[END_REF]. More specifically, they differentiate seven instrumental modes to referring to the past at a corporate level: past, memory, history, tradition, nostalgia, provenance, and heritage [START_REF] Burghausen | Repertoires of the corporate past: explanation and framework. Introducing an integrated and dynamic perspective[END_REF]. Corporate memory operates as a bridge between the corporate past and the three primary instrumental modes of representing the past (history, heritage, and traditions). Corporate nostalgia and provenance are secondary modes. As for the representations, the concept of heritage is distinct from history [START_REF] Urde | Corporate brands with a heritage[END_REF], and retro [START_REF] Wiedmann | Drivers and Outcomes of Brand Heritage: Consumers' Perception of Heritage Brands in the Automotive Industry[END_REF]. Marketing scholars refer to heritage in a variety of meanings: as the temporality of a construct, as mental associations based on historical references, as a cultural or institutional legacy, as collective memory, as a company's provenance or roots, to denote the longevity, or as a synonym of the past [START_REF] Balmer | Introducing organisational heritage : Linking corporate heritage , organisational identity and organisational memory[END_REF]. In a strict corporate perspective, corporate heritage is defined as "all the traits and aspects of an organisation that link its past, present, and future in a meaningful and relevant way" (Burghausen and Balmer, 2014b, p.394). This link between the different time strata, called omni-temporality, is a cornerstone of corporate heritage [START_REF] Balmer | Corporate heritage identities, corporate heritage brands and the multiple heritage identities of the British Monarchy[END_REF].

There are two internal perspectives on this marketing phenomenon: one looks at the corporate brand level while the other focuses on the product brand level. The former implies a holistic approach of the company. It considers the whole organisation as a brand as well as its multiple stakeholders [START_REF] Balmer | Corporate brands: what are they? What of them?[END_REF]. The latter focuses on the marketing function and mostly consider the interactions between the product brand managers and its consumers.

Most of existing work on heritage and brands falls into the corporate perspective. Scholars define a category of brands called corporate Heritage Brands. They use their corporate heritage as a central aspect of their proposition value [START_REF] Balmer | Corporate heritage identities, corporate heritage brands and the multiple heritage identities of the British Monarchy[END_REF][START_REF] Urde | Corporate brands with a heritage[END_REF]. These corporations share five characteristics: longevity, track records, core values, the use of symbols and an organisational belief that history is important [START_REF] Urde | Corporate brands with a heritage[END_REF]. These traits remain relevant over time to internal and external stakeholders. These corporate brands are different from brands with a heritage which may have a rich past but do not implement it as heritage at an organisational level [START_REF] Urde | Corporate brands with a heritage[END_REF].

As for the management at a corporate level, Urde and colleagues' pioneer article defines the common principles of corporate heritage brands' management [START_REF] Urde | Corporate brands with a heritage[END_REF]. This is later extended by the definition of a corporate heritage identity as the institutional traits remaining meaningful and invariant over time [START_REF] Balmer | Corporate heritage identities, corporate heritage brands and the multiple heritage identities of the British Monarchy[END_REF]. Further work looks at how corporate heritage is constructed and managed over time [START_REF] Burghausen | Corporate heritage identity stewardship: a corporate marketing perspective[END_REF][START_REF] Miller | Brand-building and the elements of success: Discoveries using historical analyses[END_REF], and how top managers communicate it to different internal stakeholders [START_REF] Blombäck | Corporate identity manifested through historical references[END_REF]Burghausen and Balmer, 2014a). For example, the literature clarifies the foundational concepts [START_REF] Balmer | Corporate heritage, corporate heritage marketing, and total corporate heritage communications: What are they? What of them? Corporate Communications[END_REF][START_REF] Burghausen | Repertoires of the corporate past: explanation and framework. Introducing an integrated and dynamic perspective[END_REF], and also look at the specificities of corporate heritage management [START_REF] Burghausen | Corporate heritage identity stewardship: a corporate marketing perspective[END_REF], on the construction of corporate heritage Recent research looks at the phenomenon from a product brand perspective. Unlike prior work at a corporate level, they focus on middle management activities such as marketing mix [START_REF] Balmer | Explicating corporate brands and their management: Reflections and directions from 1995[END_REF]. Some focuses on the role of brand heritage in international expansions [START_REF] Hakala | Operationalising brand heritage and cultural heritage[END_REF][START_REF] Hudson | Brand heritage and the renaissance of Cunard[END_REF], or brand revival [START_REF] Dion | Reviving sleeping beauty brands by rearticulating brand heritage[END_REF][START_REF] Hudson | Brand heritage and the renaissance of Cunard[END_REF][START_REF] Santos | Heritage branding orientation: The case of Ach. Brito and the dynamics between corporate and product heritage brands[END_REF]. Others consider brand heritage as mental associations based on historical references i.e. as the way managers operationalise brand heritage in the distinct facets of the marketing mix: in retail [START_REF] Dion | Retail Luxury Strategy: Assembling Charisma through Art and Magic[END_REF][START_REF] Dion | Managing heritage brands: A study of the sacralization of heritage stores in the luxury industry[END_REF][START_REF] Joy | M(Art)worlds: Consumer perceptions of how luxury brand stores become art institutions[END_REF], or in public relations [START_REF] Martino | When the past makes news: Cultivating media relations through brand heritage[END_REF].

While most scholars focus on a single level of analysis, [START_REF] Santos | Heritage branding orientation: The case of Ach. Brito and the dynamics between corporate and product heritage brands[END_REF] look at the dynamics between the corporate and the product brand levels. They define heritage branding orientation as the organisational disposition upon which managers build their marketing strategies in order to bridge the gap between the corporate and the product brand emphasis.

The present research follows this direction and adds the perspective of the consumer.

Nascent research on consumers' interpretation of heritage cues

So far, little research engages in a consumer perspective although it appears as a critical point, mostly at a product brand level, but also from an organisational perspective as consumers are important stakeholders. There are two perspectives on this phenomenon. First, researchers look at corporate associations defined as perceptual cognitive constructs [START_REF] Brown | Identity, intended image, construed image, and reputation: An interdisciplinary framework and suggested terminology[END_REF].They have three antecedents: consumers hold a specific understanding about corporate brands based on the corporate communication or their reflection through third parties, the product characteristics, or their beliefs about businesses [START_REF] Brown | Corporate associations in marketing: Antecedents and consequences[END_REF]. Indeed, at a product brand level brand heritage can strengthen the relationship with the consumers, its attachment and trust to the brand [START_REF] Rose | Emphasizing brand heritage: Does it work? And how[END_REF]. Another perspective look at historical references defined as representational use of the past in discursive form that consumers interpret and make sense of [START_REF] Balmer | Introducing organisational heritage : Linking corporate heritage , organisational identity and organisational memory[END_REF][START_REF] Blombäck | Corporate identity manifested through historical references[END_REF]. Building on this view, further research shows that consumers also have their own image of the corporate heritage which potentially differs from the company's perspective [START_REF] Rindell | Two sides of a coin: Connecting corporate brand heritage to consumers' corporate image heritage[END_REF]. Also, given that not all organisations communicate their corporate brand [START_REF] Balmer | Corporate brands: what are they? What of them?[END_REF], symbols are considered the elements that are the most accessible to consumers [START_REF] Hakala | Operationalising brand heritage and cultural heritage[END_REF]. Conceptually, the symbols can be defined as historical references used at a product brand level to induce the existence of a corporate heritage [START_REF] Balmer | Introducing organisational heritage : Linking corporate heritage , organisational identity and organisational memory[END_REF].

Actually, prior experimental research operationalise brand heritage through symbols communicating the other dimensions of the corporate heritage: longevity, values, track records and the importance of history [START_REF] Rose | Emphasizing brand heritage: Does it work? And how[END_REF]. Theoretically, historical references (or symbols) engage with the dynamics between the corporate brand they aim to make accessible, the product brand making them accessible, and the consumers interpreting them. Symbols are therefore the focus of this research.

Focus of the present research

The present research focuses on corporate heritage elements that are made accessible to the consumers through the product brand managers' actions. We acknowledge the fact that some product brands have no direct relation with a corporate brand. While every company has a corporate identity, not all organisations have a corporate brand [START_REF] Balmer | Corporate brands: what are they? What of them?[END_REF].

However, existing research finds that the implementation of a corporate heritage identity almost always induces the presence of historical references in the marketing mix. But is the presence of historical references on a product always to be interpreted as a clue for corporate heritage identity? [START_REF] Blombäck | Corporate identity manifested through historical references[END_REF] suggest that the use of historical references in the communication also affects internal audiences. Nevertheless, the literature also acknowledges the use of "faux heritage" in communication [START_REF] Hudson | Corporate Heritage Brands: Mead's Theory of the Past[END_REF], and of retro associations [START_REF] Brown | Teaching Old Brands New Tricks: Retro Branding and the Revival of Brand Meaning[END_REF] which do not require a particular implementation of heritage identity at a corporate level. There could be differences between the consumers' perceived heritage and the company's deliberated heritage, their qualitative exploration can inform the management of the corporate heritage identity.

Figure 1 is a visual representation of our original approach. Most of the existing literature summarised above focuses on a single level approach (represented by the circles, either at a corporate or at a brand level). Some look at cross-level perspectives (represented by the arrows): from the corporate brand to the product brand level and vice versa (arrow number 1, eg. [START_REF] Hudson | Brand heritage and the renaissance of Cunard[END_REF][START_REF] Santos | Heritage branding orientation: The case of Ach. Brito and the dynamics between corporate and product heritage brands[END_REF], from the product brand to the consumer level (arrow number 2, eg. [START_REF] Rose | Emphasizing brand heritage: Does it work? And how[END_REF][START_REF] Wiedmann | Drivers and Outcomes of Brand Heritage: Consumers' Perception of Heritage Brands in the Automotive Industry[END_REF], or from the corporate brand to consumer level (arrow number 3, eg. [START_REF] Balmer | Corporate heritage brands in China. Consumer engagement with China's most celebrated corporate heritage brand -Tong Ren Tang: 同仁堂[END_REF]. The fourth arrow represents our approach, it starts from the product brand level (what marketing managers do) regardless of the organisation they belong to, then it looks at consumers' interpretations of the organisation.

Figure 1 -Focus of the research

As such, it takes historical references as a starting point for consumers to comment. These historical references are material, textual or visual cues that managers make deliberately available for the consumers to interpret and to make sense of. These cues can be in some cases a partial reflection of the corporate heritage identity that marketing managers communicate to the consumers via the marketing mix. It other cases, they can be mere marketing instruments reflecting a product manager's own strategy with little to no relation with the corporate brand strategy [START_REF] Balmer | Corporate brands: what are they? What of them?[END_REF]. We acknowledge this possibility and we come back to it in the discussion section but we do not want to impose our views on the consumers a priori as we seek to study their interpretation.

Methodology

In order to gain a detailed understanding of the interpretation of brands using historical references from a consumers' perspective, a qualitative approach in two steps was chosen. As it is consumer centric, it focuses on what consumers see and know. The selection of brands is based on cues consumers have access to on the pack or on the internet. Contrary to existing corporate centric approaches, we do not use internal data consumers would not have access to.

This research has two sequential qualitative studies. The first study aims to identify FMCG brands using historical references explicitly on their brands' packs or site. The second study is a series of semi-structured interviews aiming to collect consumers' interpretation of these brands and the organisations they belong to, and particularly of their management (Figure 2).

Figure 2 -Design of the research

Preliminary study: Selection of Brands using historical references

Existing research provides methods to identify corporate heritage brands based on in-depth case study (Burghausen and Balmer, 2014a) which is not adapted to our objective and focus.

In manner consistent with [START_REF] Hakala | Operationalising brand heritage and cultural heritage[END_REF] and with experiments inducing heritage for fake brands [START_REF] Rose | Emphasizing brand heritage: Does it work? And how[END_REF], we focus on symbols and more particularly on historical references. The objective of the preliminary study is to select brands using historical references that will be later used as stimuli for the main study. Brand heritage is intuitively associated with luxury, spirits, and to product categories with a rather high implication [START_REF] Hudson | Brand heritage and the renaissance of Cunard[END_REF][START_REF] Hudson | Managing temporality to enhance luxury: Brand heritage at Dom Perignon[END_REF][START_REF] Wiedmann | Drivers and Outcomes of Brand Heritage: Consumers' Perception of Heritage Brands in the Automotive Industry[END_REF]. However, this research takes a slightly different approach and looks across a wide range of FMCG. This approach focusing on FMCG which seeks to make the most of their heritage [START_REF] Alexander | Brand authentication: creating and maintaining brand auras[END_REF] reduces the biases related to a particular product category. Observations aim to identify brands that clearly use historical references in their marketing mix. We used two cues for the marketing mix: the packaging and the websites, both available to consumers. These two cues are not exhaustive but are suitable for our focus. All FMCG use packaging which expresses the brand identity [START_REF] Underwood | The communicative power of product packaging: creating brand identity via lived and mediated experience[END_REF] and serve to mythologise the brand [START_REF] Kniazeva | Packaging as Vehicle for Mythologizing the Brand[END_REF]. We wanted to add a second cue to only select brands with a consistent use of historical references.

An interesting alternative cue would have been advertising, particularly because it tends to have a strong impact on consumers. However, many FMCG brands do not have recent adverts if any. It would have been very restrictive. In contrast, all brands have a website accessible to all consumers and where adverts can also be found. We therefore selected packaging and website as the two cues.

Packaging observations took place in two supermarkets of approximately 1500m², belonging to different corporate groups (Monoprix and Carrefour) located in the centre of a major French city.

The first step of the preliminary study consisted of the observation of all packaged goods sold in these supermarkets by the two experts. Only spirits were excluded from the study as almost all spirit brands use historical references unlike all other categories. Experts adapted Urde et al.'s five criteria for corporate brand heritage (2007) (mention of track records, longevity, core values, symbols and importance of the firm's history) to code historical references on the packaging. Table 1 and Figure 3 show an example of how these criteria were adapted to code De Cecco's pasta brand. Historical references do not directly mention the current corporate brand which is not surprising for FMCG. However, they sometimes reflect the history of the company beyond the product (see Table 1 for De Cecco) and this is even stronger for smaller companies (e.g. La Mère Poulard, De Cecco, Gillot, Briochin…) when the product brand represents most of the company's activity. This observation led to the selection of fifty-seven brands.

Figure 3 -Visual Examples From De Cecco Packaging

The second step of the preliminary study consisted of the reduction of the selected brands to those with a consistent strategy on the packaging and online on the brand's site. The authors analysed all 57 brands' websites. As an example of how the websites were analysed, Monsavon website (A Unilever-owned beauty care brand) displays the founding date is reminded repeatedly throughout the site in different sections, the website has a company history or background section and a "values and commitments" section ("Histoire" and "Valeurs et engagements" in French), the history of the brand is told with emphasis on the track records and use of old black and white posters. As for the packaging, the websites showcase historical references in relation with the product brands and to a smaller extent to the corporate brands. Again, this is not the case for product brands belonging to large conglomerates such as Unilever (e.g. Alsa, Monsavon…).

In total, the preliminary study led to the selection of 27 brands with consistent use of historical references on both the packaging and the website (15 in food, 5 in beverages, 5 in health & beauty, and 2 in home care). For each of [START_REF] Urde | Corporate brands with a heritage[END_REF] criteria, we propose an adaptation of what could be used by an external consumer to assess the existence of brand heritage at a corporate level. We acknowledge all of these 27 brands do not qualify as corporate heritage brands defined by [START_REF] Balmer | Introducing organisational heritage : Linking corporate heritage , organisational identity and organisational memory[END_REF] but they all use historical references which is consistent with the objectives of the research.

The main study: Semi-structured interviews

One of the authors conducted semi-structured interviews with individuals in charge of grocery shopping in their household. Nine male and sixteen female with diverse occupations were interviewed, ranging from 24 to 73 years old, thirteen living in a major French city, nine in suburbs, and three in rural areas so as to capture a wide range of views (Table 2). Theoretical saturation was achieved after 25 interviews [START_REF] Glaser | The discovery of grounded theory: Strategies for qualitative research[END_REF]. On average, interviews lasted for 44 minutes; they were recorded and fully transcribed. The interview guide aims to generate detailed descriptions of the heritage brands each informant knew the best, as well as perceptual elements about the brands' temporality. In practice, it has four phases.

1) Selection. Informants were first introduced with the 27 brands and sequentially asked to eliminate all unknown brands from the set, to eliminate those they never buy, and finally to pick, within the remaining brands, the one, two or three brands they consider to be the most familiar with and loyal to.

2) Description. Consumers were asked to describe the first brand they had selected.

Follow-up questions included memories, places, people, and images associated with the brand, with particular attention to any unexpected information brought by the informants.

3) Personification. Consumers were asked to imagine the brand as a person and describe his or her direct environment.

If the informants had selected a second or a third brand, the second and third phases were repeated.

4) When informants had not already raised and detailed their interpretation of the brands' temporality in the second phase of the interview, we introduced it the following question: "Would you say this brand emphasises its past?", follow-up questions included their justification for this strategy, the cues supporting their interpretation, their position towards this strategy and served to expand the interpretation of heritage branding to other product categories.

The analysis of the transcript focuses on the inferences consumers make about the management of the brands they perceive to use historical references. After a first impressionistic reading of the transcripts, a second reading focused on the descriptions of the brand management. As a result, a series of 21 keywords were identified so as to carry out a more systematic analysis based on the unity of meaning [START_REF] Bardin | L'analyse de contenu[END_REF]. These 21 keywords cover the management, the production, and the marketing of the product.

Findings

The analysis of the transcripts provides three main findings. First, consumers have limited knowledge of the corporations behind the FMCG they buy. Then, results show that consumers imagine brands have to build a compromise between tradition and modernity. Finally, it reveals that consumers perceive different degrees in the management of temporality.

A corporate heritage implementation is hard to perceive

Four main themes emerge from the interviews: uncertainty, little interest, personal experience, and brand relics. The first important finding is that consumers have little knowledge and interest about FMCG brands and their parent companies. When they describe the companies behind the brands, they use expressions such as "I don't know," "perhaps," or "I have no idea." For instance, they are not sure about the production system, or the ownership. They assume more than they know and some justify this lack of knowledge by the little interest they have in finding out.

Two of the informants describe different tactics to assess their interpretation: one is based on personal memories, and the other on the existence of relics related to the brand. "First, there are tons of adverts from the 60s, people even buy them to decorate their home. And all the goodies you find in the bars, the parasols, these kinds of things, the marketing in France! Like Coke's

Christmas special, all these old stuff! [Question: These old stuff?]

They sort of build the brand. We have been around for a long time: look!" (Eric)

A perceived compromise between tradition and modernity

Despite their lack of knowledge and interest, they still imagine how these brands are managed while remaining suspicious. Four main themes emerge: sense of memory, transmission, modern-day production systems, and critical role of supermarkets. These themes reveal a tension between two extremes: the ideal of a family business based on artisanal productions, and the likeliness of a large industrial multinational able to supply large retailers. Most of them imagine that these brands belong to companies seeking a compromise: companies building on a sense of memory and a willingness to perpetuate quality, but still adapting to modern-day production systems and supplying huge quantities to supermarkets. Some of their descriptions resemble criteria listed in the literature such as the unremitting managerial tenacity and the institutional trait consistency. "Now, do they still make it in the same way? I would be surprised ! But either way, they want to project this image of traditional fabrication.

Question: You would be surprised?

It is not possible! The costs are so… there is such a fierce competition that they modified their processes to be profitable. Nobody makes ketchup like they used to 50 years ago, it is not possible". (Eric)

The critical role of supermarkets "For me it still is a big company, even if it reminds me of small farmers and all that, and it makes me smile but actually I also think it must be a production process looking like any other industrial cheese. So…

At worst it was a little farmer who once sold its recipe to a big corporation, which kept the name but did whatever they wanted to do. But I have a hard time thinking it remains… The fact that it is sold in a supermarket (she shakes her head to say no)". (Estelle)

"But there is something wrong with the mass retail and the respect of a manufacture tradition… I mean, in 2015, it is no secrecy that every item sold in supermarkets are made in factories producing tons of things and that… the hand made thing is only for TV adverts! There is something wrong, it's like this date would be a label of legitimacy. It says OK we are now in an era of mass production but we have been here for a long time so there is still an exceptional recipe, something that makes us special." (Lisa)

The use of historical references leads to two distinct perceived positioning strategies However, consumers perceive different degrees in the management of temporality with implications for brands' perceived positioning. Indeed, some brands are perceived to be truly omni-temporal and to be consumer-oriented, while others are perceived as past and more product-oriented.

For instance, Olivier (29) describes differently Lindt (chocolate) and La Mère Poulard (biscuits). Lindt ( 1845 Badoit seems to be rooted in the 19 th century, although it might not be true."

This difference in terms of interpretation does not mean that temporality is actually managed differently at a corporate level. It may outline the difference between a genuine corporate heritage brand and a brand with a heritage. It could also illustrate a degree of heritage implementation in the marketing mix.

One perceived management of temporality is characterised by more flexibility and adaptation.

When consumers understand a brand as such, they describe a brand belonging to the present or future as much as to the past, committed to meet customers' new needs, sometimes creating new trends. Informants relate their longevity to the ability to take risks by launching new products; they also acknowledge their adaptation to modern days' production systems which does not seem to be a problem (Table 6).

These brands are considered as familiar brands. Three main themes characterise these familiar brands: 1) Consumer orientation: They are aware of and adapt to consumers' new needs; 2)

Pioneer spirit: Longevity allow them to take risks, launch new trends; 3) Flexibility:

Adaptation to Modern Production System. "Every two or three years we can see the little "new recipe" label, so there's always a renewed recipe […] I think they must have cooks, or they must adapt, I mean the raw material they use for their powders must change so they need to switch to new providers" (Ludovic, 24)

Here, the historical references mainly bring values to the brand through the track records.

Consumers have a strong relationship with the brand, based on its ability to answer their changing needs continuously. This echoes to the phenomenon of relative invariance: identities seem to remain the same but the meanings attached may change [START_REF] Balmer | Corporate heritage identities, corporate heritage brands and the multiple heritage identities of the British Monarchy[END_REF]; and also to previous results found in the luxury sector [START_REF] Veg-Sala | A semiotic analysis of the extendibility of luxury brands[END_REF]. As such, it represents a case of perceived corporate heritage. This articulation of innovation and tradition seems particularly suitable for brands competing on relatively highly innovative product categories.

In this sample, for shampoo or stain remover brands that must cope with brands launching many innovative products, brand heritage is a distinctive asset [START_REF] Urde | Corporate brands with a heritage[END_REF] as long as an updated version of the past is proposed.

In contrast with the familiar brands, consumers perceive the use of historical references as a sign of worshipping the past. Five characteristics build on this interpretation: safeguards, product orientation, passion, year on year improvement and special occasion. They describe brands being strongly rooted in the past and sometimes opposed to present times. Informants report little to no customer orientation: the brand pushes the same product they have always produced on the market but is not making any effort to understand if consumers' needs have changed. They are said to let passion rather than profit drive the business, and they are associated with special occasions (Table 7). We call them aristocratic brands. Here, the historical references add value to the brand through the core values associated with it. One value is authenticity, influenced by perception of passion driving the business rather than profit [START_REF] Cova | Les particules expérientielles de la quête d'authenticité du consommateur[END_REF]. Another value is the maintenance in a changing world, the promise that no matter what the brand will remain the same. To a certain extent, these brands also appear as supermarkets' luxury brands (see the comparison with Ferrari): prestigious in their rather utilitarian product categories (biscuits, cheese, olive oil, pasta, sardine cans…). As opposed to the first register generating interpretations of familiarity, that one makes the brand appear rather aristocratic: desirable, prestigious and distant at the same time. This positioning appears relevant for brands in categories in which stability and traditional know-how is associated with added-value such as food.

Discussion

These findings interrogate existing knowledge about corporate heritage brands and heritage branding orientation. More specifically, they inform consumers' interpretation of heritage organisations, of the specificities of corporate heritage management, and of the management of temporality.

Perceived corporate heritage orientation

Our results address the dynamic between the organisational level, the brand management level, and the consumer level. We find that consumers have little knowledge of the companies standing behind the product brands. They cannot go beyond speculations and even claim to have very little interest in finding out. It is of particularly interest as all interviews were conducted with brands consumers declare to buy on a regular basis, so potentially those they are the most likely to be interested in. This lack of interest could be a particularity of FMCG, or it could be related to consumers' implication consumers with these categories. As stated above, existing research tend to focus on products with a rather high implication for which consumers have arguably more interest in having information about the company. More importantly, these results outline the relative weakness or even absence of corporate brands in FMCG. The organisations remain discrete although prior research shows that corporate associations influence the beliefs and attitudes towards product brands [START_REF] Brown | The company and the product: Corporate associations and consumer product responses[END_REF]. Consumers generally seek to reduce the informational asymmetry with the producers [START_REF] Erdem | Brand Equity as a Signaling Phenomenon[END_REF]. Their stated lack of interest could be interpreted as fatalism or habits on a market where they are used to receive very scarce information about the organisations. For those product brands belonging to genuine corporate heritage brands, our findings support [START_REF] Santos | Heritage branding orientation: The case of Ach. Brito and the dynamics between corporate and product heritage brands[END_REF] claim for making the use of their heritage as it could be an answer to consumers' scepticism. In absence of corporate communication, suspicious consumers report to assess brand longevity referring to alternative sources. One possibility is their own memory. It relates to and confirms the role of track records [START_REF] Urde | Corporate brands with a heritage[END_REF], ceaseless multigenerational utility [START_REF] Balmer | Corporate heritage identities, corporate heritage brands and the multiple heritage identities of the British Monarchy[END_REF], and image heritage [START_REF] Rindell | Time in corporate images: introducing image heritage and image-in-use[END_REF]. One informant also raises the role of brand relics: branded artefacts from prior times which has remained on the market (e.g. a poster from the 1960s). Prior research suggests the importance of materiality to embody the corporate heritage in a product [START_REF] Santos | Heritage branding orientation: The case of Ach. Brito and the dynamics between corporate and product heritage brands[END_REF]. For our respondent, the relics objectify the heritage as they make it more tangible. They also provide evidence for the company's claims of longevity. The use of such relics is complex as it usually involves various stakeholders such as former suppliers (e.g. advertising agency), in addition, it cannot prove the organisation is currently concerned with its heritage. However, it brings tangible elements in a world of intangible values and can be of particular efficiency for managers engaging in a rebranding based on the corporate heritage [START_REF] Hudson | Brand heritage and the renaissance of Cunard[END_REF] to emphasise on their new intentions.

The management of tradition and modernity

Despite their little knowledge of the companies behind the product, consumers still hold corporate associations. As suggested by the literature, we find that consumers deduce corporate associations from the characteristics of the products or using beliefs they hold about businesses in general [START_REF] Brown | Corporate associations in marketing: Antecedents and consequences[END_REF]. Our results contribute to the existing work reporting how corporate heritage brands are managed internally. Burghausen and Balmer (2014a) show that corporate heritage identities are implemented internally through three interrelated patterns: "the conflation of past and present, the conflation of old and new, and the conflation of traditional and modern" (p.2318). One year later, the same authors find that the management of corporate heritage brands is related to a particular mindset whose characteristics are: continuance, belongingness, self, heritage, responsibility and potency [START_REF] Burghausen | Corporate heritage identity stewardship: a corporate marketing perspective[END_REF]. Our results offer an external stakeholders' perspective on the matter. In the interviews, consumers report about how they imagine the companies to be managed and it clearly goes beyond the product. Indeed, they share their views on the culture of the organisations, the ownership, their production system and their values or covenant. The result of their imagination is very much aligned with the triple conflation found by Burghausen and Balmer inside corporate heritage brands. In other words, consumers fail to differentiate the product brands which could be related to a genuine corporate heritage brand from the others.

The lack of information proactively shared by the organisations themselves reinforces the importance of the alternative cues such as the presence of historical references. This marketing "trick" can easily be disconnected from a corporate heritage identity. The little engagement on corporate branding from part of the FMCG companies certainly plays in favour of those who do not have any corporate heritage but it also maintains consumers' suspicion over the whole categories. From our perspective, genuine corporate heritage brands operating on FMCG markets have underexploited assets they could use to differentiate themselves from the others. Their corporate heritage and their specific management style should help them to be more efficient and to increase their credibility or legitimacy to use historical references [START_REF] Burghausen | Corporate heritage identity stewardship: a corporate marketing perspective[END_REF]. It raises the question of the corporate communication towards consumers which is discussed later in the managerial recommendations.

research on heritage should also consider the possibility that some individuals are reluctant to change and will be attracted to brands looking past-oriented.

Conclusion

Theoretical implications

This research contributes to the existing work on the management of the corporate brand identity [START_REF] Balmer | Corporate brands: what are they? What of them?[END_REF][START_REF] Balmer | Introducing organisational heritage : Linking corporate heritage , organisational identity and organisational memory[END_REF]. In the context of FMCG, our results show that consumer imagine how the company is managed in the absence of formal corporate communication. To feed their imagination, they rely on alternative cues such as corporate image heritage [START_REF] Rindell | Two sides of a coin: Connecting corporate brand heritage to consumers' corporate image heritage[END_REF]. In addition, this original approach based on consumers' interpretation of product brands outlines the role of historical references in shaping the corporate identity in the absence of corporate communication. It refines existing knowledge on the interstice between product and corporate brands. While [START_REF] Santos | Heritage branding orientation: The case of Ach. Brito and the dynamics between corporate and product heritage brands[END_REF] show how corporate brand heritage can shape a product brand positioning; our research shows that consumers understand how a company manages its heritage through their product brands' positioning. Altogether, our results encourage corporate heritage brands to engage in corporate communication towards their consumers to actively take part in the management of their corporate image.

We contribute to the research on the status of the omni-temporal trait by introducing different degrees of perception. Our results show that external stakeholder perceive a brand's omnitemporality in gradual terms. From a conceptual perspective, it implies to think about this trait as a continuum ranging from a strong anchoring on one time period (past, present or future) to a strong conflation between the three periods. From a methodological perspective, studies surveying stakeholders could operationalise the omni-temporality trait as a continuous variable rather than a dichotomous one to render this gradual aspect in the perception.

Managerial recommendations

We can formulate three recommendations to brand managers: on the importance of corporate communications, on the use of consumers' memory and of brand relics, and on the distinct positioning they can achieve while using historical references.

Managers in charge of corporate heritage brands operating on FMCG markets should not assume that consumers are aware of their originality. As many brand managers use similar historical references, consumers become suspicious. There is a risk for genuine corporate heritage brands to be under evaluated while being considered as any other brand claiming to have a heritage. Given the little spontaneous interest consumers have in getting to know the companies, managers should increase their corporate heritage communication to reach to their consumers. [START_REF] Balmer | Corporate heritage, corporate heritage marketing, and total corporate heritage communications: What are they? What of them? Corporate Communications[END_REF] introduces and details the concept of total corporate heritage communication and provides examples of actions that managers could use as starting points.

In their corporate communication strategies, managers can use consumers' memory and brand relics to strengthen their case. Asking consumers about their memories with the brand as we did in the interviews help connect the brand with the self-narrative and could strengthen the emotional bond between the brand and its consumers [START_REF] Ardelet | Self-referencing narratives to predict consumers' preferences in the luxury industry: A longitudinal study[END_REF]. Social media can be an interesting tool to generate brand content based on consumers' memory and to refresh track records. Working on a temporary exhibition or the opening of a brand museum is an opportunity to identify, collect, and promote brand relics while involving former and current stakeholders, including consumers. For instance, one can imagine asking consumers to lend branded artefacts for a collaborative exhibition.

Finally, in addition to the management of corporate heritage, this paper also engages with the mere use of historical references. Based on our results, we can distinguish two positioning strategies. One strategy uses historical references to construct a familiar brand while the other leads to the construction of an aristocratic brand.

In the first positioning, historical references are associated with an updated version of the past and cue familiarity based on the brand's track records. In the second positioning, historical references are associated with a worshipped version of the past, consumer perceive the brand as aristocratic through values of authenticity, exclusivity, permanence and distance. Table 8 presents a guide for brand management and decision-making. Both strategies are compatible with the use of historical references, however, they differ on the "how" these references are used.

Further research

We see three avenues for further research building on this work. First, in addition to our focus on discursive materials (historical references), it would be interested to look at the phenomenon from a psychological perspective. Indeed, research on corporate association engages with CSR and corporate ability (Brown and Dacin, 2007) but overlooks corporate heritage. Further empirical research could replicate our approach within this framework.

Another promising avenue could investigate consumers' perception of historical references in a quantitative approach. Comparing corporate heritage brands to corporate brands with a heritage, both using historical references, could extend our results using a larger sample of brands and product categories. The informational asymmetry tends to increase the importance of signals [START_REF] Erdem | Brand Equity as a Signaling Phenomenon[END_REF] as the multiple historical references and as a consequence reduce the effect of corporate heritage.

Finally, marketing academics could focus on managers' ability to stimulate consumers' memory in a way that is favourable to the brand. There is here potential to bridge the gap between the research on brand heritage and on nostalgia.

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Firm

  summary of the company's history (e.g. "From father to son. Since 1886 we have been carrying on an important responsibility: our tradition of making pasta, without compromise, that we refine each single day and that allows us to bring the authentic pleasure of Italian cuisine all over the world").

Table 1 -Coding: Operationalisation of existing criteria Criteria

 1

	Use of symbols	Use of a symbol or image of times gone by (e.g.: De Cecco is
		written in a vintage font; and below De Cecco's logo is a picture
		of a peasant woman carrying two wheat bundles in a wheat field).

Operationalisation taking De Cecco as an example Track records Mention of achievements in order to recall track records to the consumer (e.g. "we have been…", "based on a 130-year-old recipe"). Longevity Mention of the "established" date on the packaging: either in the logo, or in an explicative text (e.g. De Cecco's logo is associated with the mention "Dal 1886": "Since 1886", the same date is reminded in a short text).

Core values

Mention one or more values the brand has stood for historically, or is committed standing for in the future (e.g. a short text entitled "From father to son" uses the following expressions: "important responsibility", "making pasta without compromise").

Table 2 -Structure of the sample

 2

	Name	Gender Age	Occupation	Selected brands
	Laurent	Male	26	Urban planner	Lindt
	Estelle	Female	30	Librerian	Lepetit
	Justine	Female	28	Journalist	Badoit, Saint-Michel
	Bob	Male	27	Student	La Mère Poulard
	Grace	Female	33	Body-Designer	Twinnings
	Nadia	Female	34	Social worker	Carapelli
	Elodie	Female	38	Translator	De Cecco, Jordans, Lindt
	Olivier	Male	29	Translator	Lindt, Connétable, La Mère Poulard

Table 3 -Key words used in the systematic analysis

 3

	Advertising	Family	Know-how
	Artisanal	Founder	Manager
	Company	Goodies	Offices
	Employee	Group	Price
	Entrepreneur	Hand-made	Production
	Fabrication	Industrial	Retailer
	Factory	Job	Supermarket

Table 4 -Quotes illustrating limited corporate knowledge Themes

 4 , he thinks about its own image, maybe more than others… Now, maybe they were bought, it used to be a family business back in the days but maybe now it's not anymore, I don't know"(Eric)

	Little interest	"I do not think this is a question we ask ourselves when we are in a
		supermarket [if a brand has a heritage], however, this is a question we ask
		ourselves if we go to a smaller shop" (Lisa),
		"Maybe all these products belong to the same company… I don't know,
		this is just my view but… maybe the same company has many products…
		there are not a lot of companies on the detergent sector you know.

Quote

Uncertainty "I think this is a brand which may have existed for a long time, this is a product we imagine to be more traditional, based on traditional recipes, at least in my own perception… A product which may use fewer chemicals, which may be better for our health in the long run. Maybe it is more artisanal, or at least it gives this impression, that it's less industrial.

By the way, maybe it's all fake, but that's the impression I have" (Elodie). "It is a family business do I guess the boss must be a little bit like IKEA'sQuestion: so you don't know if Eau Ecarlate has remained in the same company? No, I have not been interested in the matter"(Sylvie) Personal experience [Question: do you think some brands cheat about their past?] "I don't know, I don't really watch adverts, I have no idea, it's possible… See, I'm

kind of an old lady now so if they exaggerate too much about the past, I do remember

. If a brand claims to have existed for a long time and I have never seen it, it raises questions in my mind.

Maybe a younger person could be fooled but with me it's more difficult.

		There are brands
		my mother used, my grandmother used, so I know it's old" (Annie)
	Brand relics	[Question: how do you know they are older brands?]

Table 5 -Quotes illustrating the compromise

 5

	Themes		Quotes
	Sense	of	"First do what you know and then export it, adapt it to marketing, to
	memory		globalisation, no problem, we need to live in our times but… still have a
			sense of memory. […] Even if it were a new company opening today,
			they would have investigated about what we used to know, and how
			we used to do" (Alexandre)

Transmission

"I think it makes sense to know that the company had been founded in whatever, because there's a real tradition having been perpetuated, know-how… even if it's

not from father to son, but from one worker to another, we

  imagine that the founder did not transmit the company to

			whoever." (Alexandre)
	Modern	days	"Before, I would have imagined a sort of rustic producer; I mean in a
	production		rustic artisanal way. But now, this
	system

producer would have adapted to its epoch, he would produce in a more automated way but still keeping this spirit of authenticity

."

(Guillaume)

Table 6 -Characteristics of familiar heritage brands

 6

	Characteristics	Quotes
	Consumer		"I bought it because it was an organic muesli […] they had many different
	orientation:		varieties and it was organic. Now I don't know if everything is organic but I
	They	are	keep buying it and I still have the feeling it's a rather better quality" (Elodie, 38)
	aware of and	Briochin: "they have updated themselves, now you have the bathroom special,
	adapt	to	you have… originally there was only one product! I know because my cousin
	consumers'		told me all about Briochin" (Veronique, 49)

someone who has automated the production but still sticking to its authentic spirit

[…]

you can see this in the different sorts of products, the normal mustard, the mustard with granules…" (Guillaume, 28)

Table 7 -Characteristics of aristocratic heritage brands

 7

	Characteristics	Quotes
	Safeguard:	"the problem with novelties is that you always need 5 or 10 years to
	Opposed to	acknowledge all negative impacts of a product, so right now you don't know.
	current times

It's a kind of crash-test, when they release a new product, we feel like we're kind of doing the crash tests"

(Ludovic, 24)

"It has to be related to my grandparents' generation

[…]

that epoch before the generalised industrialisation of food, back

		passion of their job" (Bob, 27)
		"These brands do less special offers, buy 3 get 4 kind of thing. It might be silly
		but this sort of thing doesn't help on the brand image […] Ferrari would never
		do this, say, we buy your old car €1000, no they would never do this because if
		you're buying a Ferrari you're not supposed to wonder how you're going to
		pay" (Alexandre, 26)
	Passion Over	"I imagine someone in a non… I'm going to say something stupid, but someone
	Profit	who's not looking for profit, someone who does that for his passion for olives,
		for love" (Nadia, 34)
	Year on year
		when we were still cooking at
		home…" (Amelie, 39)
	Product	"we propose something: if you like it, good because we won't change if you
	orientation	don't. Because our objective is not to make money, it's to propose a certain
		know-how […] Yeah, they're selfish! It relates to the fact they are not really
		interested in what people may expect, they're focused, when I think about this
		brand, I have the feeling they're concentrated on what they can get from the

improvement "This is typically the product that is very simple and has been improved in Italy for generations where they have developed this very traditional and simple thing" (Elodie, 38) For special occasions "I think it's related to rather festive occasions, exceptional occasions. If you bring Badoit… It isn't daily water, it's a water bottle for special events" (Sandrine, 39)

Table 8 -Guide for strategic decision-making based upon brand heritage Target positioning Familiar Brand Aristocratic Brand

 8

	Orientation	Consumer orientation	Product orientation
	Personality	Brand as a partner	Brand as a landmark
	Advert	Pioneer spirit	Vicarious and collective nostalgia
	creative	Adaptability of the brand	Continuity of the brand
	themes	Founder's creativity and inventions	Tribute to the founder
			Passion over profit
			Special occasions
	Innovations	Breakthrough	Incremental improvement of the
		Launch new trends and usages	original products

Degrees of omni-temporality

The literature on corporate heritage shows that corporate heritage brands are not stuck in the past but that they carefully articulate the past, the present and the future [START_REF] Balmer | Corporate heritage identities, corporate heritage brands and the multiple heritage identities of the British Monarchy[END_REF].

Assessing this careful articulation requires access to internal data and often observation of the managerial practices (Burghausen and Balmer, 2014a). Most consumers are not aware of this and our results show they deduce a certain degree of omni-temporality based on the information they have access to. We find that using historical references does not always lead to a interpretation of omni-temporality. Our informants describe two distinct positions: familiar brands with an emphasis on adaptability (i.e. the present and future), aristocratic brands with an emphasis on longevity (i.e. the past). Both strategies are implemented at a product brand level and lead to different outcomes although they all relate to existing research on the concept of brand authenticity, and particularly to the distinction between indexicality and iconicity [START_REF] Grayson | Consumer perceptions of iconicity and indexicality and their influence on assessments of authentic market offerings[END_REF][START_REF] Napoli | Measuring consumer-based brand authenticity[END_REF]. This duality is not surprising given that western societies have two competing visions of a reference to the past. [START_REF] Lowenthal | The Past is a Foreign Country -Revisited[END_REF] summarises different philosophical developments on time and suggest dialectic between ancient and modern: between those who think the past is a source of unbeatable models; and others who see it as a source of inspiration only gaining value if updated. In a marketing context, this echoes with the distinction between "repro" and "retro" [START_REF] Brown | Retro-marketing : yesterday's tomorrows[END_REF]. "Repro" stands for reproduction and designates products representing the past more or less as it was, while "Retro" (retrospection) designates products combining an old-style form and updated content. A dominant idea in marketing is that consumers always seek updated versions [START_REF] Brown | Teaching Old Brands New Tricks: Retro Branding and the Revival of Brand Meaning[END_REF]Weindruch, 2016), however, our results tend to nuance this idea.

Consistently with the literature in history [START_REF] Lowenthal | The Past is a Foreign Country -Revisited[END_REF] and in politics about the conservative ideology [START_REF] Femia | The Antinomies of Conservative Thought[END_REF][START_REF] Hawley | Against Capitalism, Christianity, and America: The European New Right[END_REF][START_REF] Huntington | Conservatism as an Ideology[END_REF], the marketing


Yingyu Yang

Maxime Sermesant

Unsupervised Polyaffine Transformation Learning for Echocardiography Motion Estimation

Keywords: Motion Estimation, Echocardiography, Polyaffine Transformation

Echocardiography plays an important role in the diagnosis of cardiac dysfunction. In particular, motion estimation in echocardiography is a challenging task since ultrasound images suffer largely from low signal-to-noise ratio and out-of-view problems. Current deep learningbased models for cardiac motion estimation in the literature estimate the dense motion field with spatial regularization. However, the underlying spatial regularization can only cover a very small region in the neighborhood, which is not enough for a smooth and realistic motion field for the myocardium in echocardiography. In order to improve the performance and quality with deep learning networks, we propose applying polyaffine transformation for motion estimation, which intrinsically regularizes the myocardium motion to be polyaffine. Our thorough experiments demonstrate that the proposed method not only presents better evaluation metrics on the registration of cardiac structures but also shows great potential in abnormal wall motion detection.

Introduction

Echocardiography is one of the most widely used modalities for cardiac dysfunction diagnosis. It's radiation-free, non-invasive, and real-time, making echocardiography very suitable for portable analysis, such as myocardial motion evaluation. However, ultrasound images generally have poorer quality than other modalities, such as MRI and CT, due to their low signal-to-noise ratio. Additionally, limitations in acquisitions and patient variability may cause the myocardium to occasionally be outside the imaging field-of-view. These burdens make motion estimation of the myocardium in echocardiography a very challenging task.

Traditional methods for motion estimation in echocardiography, such as block matching [START_REF] Alessandrini | Detailed evaluation of five 3d speckle tracking algorithms using synthetic echocardiographic recordings[END_REF][START_REF] Azarmehr | An optimisation-based iterative approach for speckle tracking echocardiography[END_REF] or optical flow [START_REF] Alessandrini | Detailed evaluation of five 3d speckle tracking algorithms using synthetic echocardiographic recordings[END_REF][START_REF] Barbosa | Fast Left Ventricle Tracking in 3D Echocardiographic Data Using Anatomical Affine Optical Flow[END_REF][START_REF] Farneb | Two-Frame Motion Estimation Based on Polynomial Expansion[END_REF], are typically time-consuming and not suitable for real-time or portable analysis. However, recent advances in deep learning (DL) have improved both the time efficiency and tracking performance of motion estimation algorithms. DL-based models can generally be classified into two types: optical flow-based models and registration-based models. Optical flowbased DL models estimate dense displacement fields between consecutive image frames and typically require ground truth displacement for supervised training [START_REF] Evain | Motion estimation by deep learning in 2d echocardiography: synthetic dataset and validation[END_REF][START_REF] Østvik | Myocardial function imaging in echocardiography using deep learning[END_REF]. Since obtaining ground truth displacement from real-world echocardiography images can be difficult, synthetic echocardiography datasets are often used for supervised training of these models [START_REF] Alessandrini | Realistic vendor-specific synthetic ultrasound data for quality assurance of 2-d speckle tracking echocardiography: simulation pipeline and open access database[END_REF][START_REF] Evain | Motion estimation by deep learning in 2d echocardiography: synthetic dataset and validation[END_REF]. Registration-based DL models typically register all other frames to end-diastole either in an unsupervised manner or with weak supervision using segmentation masks, enabling them to work on real-world datasets [START_REF] Ahn | Unsupervised motion tracking of left ventricle in echocardiography[END_REF][START_REF] Ta | A semisupervised joint learning approach to left ventricular segmentation and motion tracking in echocardiography[END_REF]. U-net-like architectures are often used as the core design of such methods [START_REF] Ahn | Unsupervised motion tracking of left ventricle in echocardiography[END_REF][START_REF] Ta | A semisupervised joint learning approach to left ventricular segmentation and motion tracking in echocardiography[END_REF]. Many other studies on cardiac MRI motion estimation have also utilized the registration approach with different temporal smoothness strategies [START_REF] Krebs | Probabilistic motion modeling from medical image sequences: application to cardiac cine-mri[END_REF][START_REF] Qin | Joint learning of motion estimation and segmentation for cardiac mr image sequences[END_REF]. Recently, researchers have also incorporated biomechanical modeling knowledge into deep learning networks with the aim of improving the generalizability of motion estimation performance [START_REF] Qin | Biomechanics-informed neural networks for myocardial motion tracking in mri[END_REF][START_REF] Zhang | Learning correspondences of cardiac motion from images using biomechanics-informed modeling[END_REF].

The motion of the myocardium is not arbitrary, and various spatial regularization techniques have been explored in the literature, such as the divergence penalty [START_REF] Mansi | ilogdemons: A demons-based registration algorithm for tracking incompressible elastic biological tissues[END_REF] for enforcing incompressibility, the rigidity penalty for smoothness [START_REF] Staring | A rigidity penalty term for nonrigid registration[END_REF], and the elastic strain energy for mechanical correctness [START_REF] Papademetris | Estimation of 3d left ventricular deformation from echocardiography[END_REF], among others. Many deep learning models have incorporated these regularization techniques into their work [START_REF] Ahn | Unsupervised motion tracking of left ventricle in echocardiography[END_REF][START_REF] De Vos | A deep learning framework for unsupervised affine and deformable image registration[END_REF][START_REF] Zhang | Learning correspondences of cardiac motion from images using biomechanics-informed modeling[END_REF]. However, these regularization techniques are usually based on first-or second-order derivatives of the displacement vector field, which are applied at the pixel level in discrete implementation and are insufficient for studying the myocardium in echocardiography. The high noiseto-signal ratio in echocardiography degrades the quality of the estimated motion field, despite the pixel-wise constraints in deep learning methods. Other methods tackle the smoothness issue at the transformation level, for instance using regionally affine deformations [START_REF] Mcleod | Spatio-temporal tensor decomposition of a polyaffine motion model for a better analysis of pathological left ventricular dynamics[END_REF].

In this work, we introduce a deep learning-based motion model leveraging such approach and tailored for 2D echocardiography motion estimation, called the PolyAffine Motion model (PAM). It incorporates global-level smoothness regularization for the myocardium through polyaffine motion fusion. Our contributions include:

-Proposing a comprehensive pipeline for using PAM in a weakly-supervised manner on a large public echocardiography dataset, demonstrating the effectiveness of our approach for unsupervised learning of myocardial motion. -Conducting extensive experiments on various real-world datasets to show that PAM outperforms other popular deep learning-based motion estimation methods, thereby highlighting its potential for clinical applications.

Methodology

Polyaffine motion model

Given source image I S and target image I T , we would like to estimate a dense motion field T S←T : R 2 → R 2 from target image I T to source image I S such that

I S (T S←T (•)) = I T (•). (1)
Inspired by the polyaffine motion fusion framework proposed by Arsigny et al. [START_REF] Arsigny | A fast and log-euclidean polyaffine framework for locally linear registration[END_REF], we adapted the motion estimation module from [START_REF] Siarohin | First order motion model for image animation[END_REF] to develop our proposed method for cardiac motion estimation in echocardiography.

The Polyaffine motion model consists of two steps. Firstly, the motion of the left ventricle is approximated through the sparse motion of several key points. An encoder-decoder network is used to output the location of key points and their local affine mapping for both I S and I T separately. Secondly, from the sparse motion, we obtain the final dense motion field through polyaffine motion fusion. The proposed method is illustrated in Fig. 1.

… ED ES ED + 1 ES -1 … …
K key points

Key point and affine transformation estimation

We adopt the encoderdecoder architecture for key point extraction as presented in [START_REF] Siarohin | First order motion model for image animation[END_REF] and provide a brief review of the method from the point of view of affine transformation. In order to process each image separately, we assume there exists an abstract reference frame R. Given an image X, the encoder-decoder network outputs the estimated key points p k X , k = 1, 2, ...K as well as the corresponding linear mappings

A k X←R ∈ R 2×2 , k = 1, 2, ...K.
The local affine transformation from target image I T to source image I S is then computed using the following equation

T k S←T (z) = Āk S←T • z Linear mapping + (p k S -Āk S←T • p k T ) Translation , (2)
where z ∈ R 2 represents the coordinate in the target image, and

Āk S←T = A k S←R (A k T ←R ) -1 .
In order to capture motion around the myocardium, we in-troduce a myocardium-related key-point prior (Section 3.2) and associated loss functions (Section 2.2). This encourages the network to output key points close to the myocardium, in contrast to [START_REF] Siarohin | First order motion model for image animation[END_REF], which employed a self-supervised approach for learning key-point positions.

Polyaffine motion fusion Once we obtain the local affine transformation, the dense motion field is computed through direct polyaffine motion fusion. For each local affine motion, a spatial weight W k (p k T , σ 2 ) controls its influenced region. It is a 2D isotropic Gaussian distribution centered at key point p k T with variance σ 2 . W 0 represents the weight for the background region and the left ventricle cavity area. It is computed as follows:

W 0 = RELU(1 - K k=1 W k (p k T , σ 2 )). (3)
We normalise all weights into Wk =

W k K k=0 W k
, where k = 0, 1, 2...K. An example is shown in Fig. 1. We apply them to compute the polyaffine dense motion

T S←T (z) = W0 z + K k=1 Wk (p k T )T k S←T (z). (4)
The original first-order motion model (FOMM) [START_REF] Siarohin | First order motion model for image animation[END_REF] utilised a second encoderdecoder network to estimate the normalised weights for each local affine transformation, which can not guarantee the center of weights close to the corresponding key point, thereby unstable for myocardial motion estimation.

Sequence motion estimation Considering a sequence of image frames I 1 , I 2 , ...I N , the assumption of abstract reference frame enables a fast way to obtain the dense motion field between any arbitrary pair of frames in the sequence. Without loss of generality, we assume I ED is the frame at end-diastole and I ES is the frame at end-systole and that I ED is ahead of I ES in time. The local affine transformation from I ED to I ES can be calculated by composition:

T k ES←ED (z) = T k ED+1←ED • T k ED+2←ED+1 • • • T k ES←ES-1 = Āk ES←ED • z + (p k ES -Āk ES←ED • p k ED ), (5)
where

Āk ES←ED = A k ES←R (A k ED←R ) -1 .
The final dense motion is computed by combining the local motion, as described in Equation 4.

Loss functions

The model is trained end-to-end using a combination of loss functions, which can be grouped into the following subsets for sequence motion estimation.

Keypoint myocardium losses

We propose two loss functions to enforce the position of key points near the myocardium region. The first loss, denoted by L kp_prior , penalizes the L 2 norm between the estimated key-point position and a prior position. We obtain the prior key-point position from the available training masks, as described in Section 3.2. The second loss, denoted by L kp_myo_ED , constrains key points at end-diastole (ED) to reside within the myocardium region by penalizing the distance between each key point and the myocardium.

L kp_myo_ED = - K k=1 H(p k , σ 2 H ) * (Mask myo_ED -0.5), (6)
where

H(p k , σ 2
H ) is the isotropic Gaussian heatmap centered at p k with variance σ 2 H and Mask myo_ED the binary mask of myocardium at ED.

Keypoint equivalence losses

Another two losses L equi_kp and L equi_affine impose an equivalence constraint to the detected key points [START_REF] Siarohin | First order motion model for image animation[END_REF]. They force the model to predict consistent key points and local linear mappings when applying a known transformation to the input image.

Registration losses

The last four losses regularize the final dense motion field through image similarity and key-point similarity. First, for each pair of consecutive frames in the sequence, we constrain

L seq_im = seq N CC(I T , I S (T I S ←I T )), (7)
L seq_kp = seq 1 K K k=1 |H(p k T , σ 2 H ) -H(p k S , σ 2 H )(T I S ←I T )|, (8)
where N CC represents the normalised cross correlation. Second, in order to force the model to learn temporal motion, we apply a second pair of similarity loss between the image at end-diastole and all frames after the end-diastole frame, denoted as L ED2any_im and L ED2any_kp for image similarity and keypoint similarity respectively. The total loss for the PAM model becomes

L total =λ 1 L kp_prior + λ 2 L kp_myo_ED + λ 3 L equi_kp + λ 4 L equi_affine + λ 5 L seq_im + λ 6 L seq_kp + λ 7 L ED2any_im + λ 8 L ED2any_kp . (9)
3 Experiments

Datasets

Three public datasets of echocardiography are included in our study. EchoNet

Dataset preprocessing

Pseudo myocardium mask There is no ground truth of myocardium mask in EchoNet dataset. To provide guidance for key points, we generate a pseudo myocardium mask for ED and ES by applying a dilation operation using 13x13 and 17x17 structure element to the left ventricle mask at ED and ES frame respectively. The difference between the dilated mask and the original one is regarded as the pseudo myocardium mask (see Fig. 2(b)). Key-point prior at end-diastole A mean myocardium mask is computed using all the pseudo myocardium masks at ED from the training set. Then, all the pixels of the mean mask are clustered into 10 groups using the KMeans function from the scikit-learn package [START_REF] Pedregosa | Scikit-learn: Machine learning in Python[END_REF], where the center of each group is considered as one key-point prior (see Fig. 2(c)).

Implementation

We compare our proposed model with the conditional variational autoencoder (CVAE) method proposed in [START_REF] Krebs | Probabilistic motion modeling from medical image sequences: application to cardiac cine-mri[END_REF], which has demonstrated effectiveness in sequential motion modelling of cardiac images. Its former registration version [START_REF] Krebs | Learning a probabilistic model for diffeomorphic registration[END_REF] has shown more regular motion field than other deep learning methods, including VoxelMorph [START_REF] Dalca | Unsupervised learning for fast probabilistic diffeomorphic registration[END_REF]. We implemented the CVAE method following its description in [START_REF] Krebs | Probabilistic motion modeling from medical image sequences: application to cardiac cine-mri[END_REF] and used the same training hyper-parameters. However, we added a Dice loss between the transformed end-systolic (ES) mask and end-diastolic (ED) mask during CVAE training to keep it consistent with our PAM model, which used segmentation mask information during training (see Section 2.2).

We trained the PAM model using an Adam optimizer with a learning rate of 1e-4. To determine the optimal hyperparameters, we conducted experiments on a randomly selected subset of 1000 training examples from the EchoNet dataset. The hyperparameters for the loss function were set to λ 1 = 20, λ 2 = 0.1, λ 3 = 50, λ 4 = 50, λ 5 = λ 6 = λ 7 = λ 8 = 100. The variance of the Gaussian heatmap was set to σ 2 = 0.05 for affine transformation weights (see Equation 3), and σ 2 H = 0.005 for all other scenarios. We trained the model for a maximum of 100 epochs, and applied early stopping if the validation loss did not improve over 10 epochs. We first evaluated the motion estimation accuracy by assessing the registration performance using the available segmentation masks from all the test datasets. For the EchoNet test split, we compared the ground truth left ventricle mask of end-diastole (ED) with that transformed from end-systole (ES). For the CAMUS dataset, the same evaluation was applied to the myocardium mask for ED/ES. For the HMC-QU dataset, the myocardium masks of one cardiac cycle were all transformed to ED using the estimated motion field. To enable group-level statistical analysis along the cardiac cycle, the temporal metric was interpolated to the same length. Our proposed PAM model demonstrated significant out-performance compared to the CVAE model on the test sets of EchoNet and CAMUS datasets. However, it showed slightly lower Dice scores on the HMC-QU dataset, which may be due to the fact that the pseudo-labelling process for generating the ground truth segmentation of the myocardium on the HMC-QU dataset [START_REF] Degerli | Early detection of myocardial infarction in low-quality echocardiography[END_REF] may be not very accurate. Furthermore, the PAM model exhibited more regular deformation fields compared to the baseline model (as shown in Fig. 4) when evaluating the gradient of Jacobian determinant. This smooth displacement field is advantageous for computing dense strain tensor, which is typically constructed using the second-order derivative of the displacement field. Additionally, as listed in Table 1, we demonstrated that our proposition of using myocardium prior and the polyaffine fusion mechanism greatly improved the registration performance, when compared with the original firstorder motion model (FOMM) [START_REF] Siarohin | First order motion model for image animation[END_REF]. In particular, our explicit design of fusion weights helps the network to efficiently learn affine transformation locally. [START_REF] Siarohin | First order motion model for image animation[END_REF], without prior of any key points (Prior), without explicit design of polyaffine weights (Polyaffine), without registration penalty between ED and any other frames (Sequence). All = FOMM+Prior+Polyaffine+Sequence.

Results

CVAE

In addition to the good performance from various evaluation metrics, the proposed PAM model has the potential for abnormal wall motion detection. We provide examples of myocardial infarction (MI) from the HMC-QU dataset (see Supplementary video material) and show the abnormal strain values in different segments, highlighting the consistency of our findings with the ground truth diagnosis.

Discussion and conclusion

In this paper, we proposed a polyaffine motion model (PAM) for echocardiography motion estimation. The PAM model demonstrated excellent motion esti-mation performance on real-world echocardiography datasets and showed good generalization to unseen datasets from other centers. Our explicit design of fusion weights enabled efficient learning of local affine transformation, and the intrinsic polyaffine structure improved the smoothness of the motion field, showing potential for abnormal wall motion detection. In the future, we will focus on integrating temporal regularization for the PAM model and conducting evaluations on synthetic datasets with known ground-truth displacement.

Fig. 1 :

 1 Fig. 1: Method overview.

1 [ 18 ]Fig. 2 :

 1182 Fig. 2: Dataset overview. (a) EchoNet example and the given annotations of left ventricle tracing. (b) Left ventricle cropping with the generated pseudo myocardium contour (blue). (c) The mean mask from the EchoNet training set and the 10 prior key points. (d) HMC-QU example and the given annotation of the myocardium. (e) CAMUS example and the given annotation of different cardiac structures. (MYO: myocardium, LV: left ventricle, LA: left atrium) image sequences are cropped around the left ventricle center according to the provided segmentation/tracings (see Fig. 2(b)). In this study, we follow the given data division of EchoNet dataset, with 7465 samples for training, 1288 samples for validation and 1277 samples for testing. CAMUS and HMC-QU datasets are used for evaluation during test phase.

Fig. 3 :Fig. 4 :

 34 Fig. 3: Evaluation results on test datasets. (a-c) On EchoNet test split using available left ventricle masks of ED/ES. (d-f) On HMC-QU dataset using frame-wise myocardium masks. The original line represents the comparison between the ground truth ED frame and the ground truth mask of each frame. (g-i) On CAMUS 4-chamber view dataset using myocardium masks of ED/ES. (HD: Hausdorff distance, MSD: main surface distance)

Table 1 :

 1 Performance comparison of different methods on EchoNet and CA-MUS datasets. FOMM: the original model in

	Method	EchoNet-LV Dice HD(pixels) MSD(pixels) Dice HD(mm) MSD(mm) CAMUS-MYO
	All = PAM (ours)	0.92	7.33	2.23	0.81 7.43	1.99
	FOMM+Prior+Polyaffine 0.91	7.53	2.36	0.80	7.95	2.08
	FOMM+Prior	0.77	18.36	5.46	0.57 13.85	3.89
	FOMM [23]	0.75	22.99	6.07	0.48 17.27	4.41
	CVAE [13]	0.91	7.97	2.30	0.77	9.91	2.67

https://echonet.github.io/dynamic/

https://www.creatis.insa-lyon.fr/Challenge/camus/

https://www.kaggle.com/datasets/aysendegerli/hmcqu-dataset

Acknowledgements This work has been supported by the French government through the National Research Agency (ANR) Investments in the Future with 3IA Côte d'Azur (ANR-19-P3IA-0002) and by Inria PhD funding. The authors are grateful to the OPAL infrastructure from Université Côte d'Azur for providing resources and support.