André Lapidus
email: andre.lapidus@univ-paris1.fr.

Bringing Them Alive

Introduction

It might seem impertinent to begin a presidential address to a society of historians of economic thought by raising the question of why weas historians of economic thoughtexist, and whether our existence is in any sense justified. 1 And this sense of impertinence betrays the fact that neither our core intellectual goals, nor the efforts we make to satisfy a certain social demand, are as able as we would have liked to justify the kind of work we are doing. This is rather uncomfortable; and might even at times have led some of us to cast envious glances towards our colleagues specialized in, say, fractional calculus or biochemistry, not to mention banking and finance. This is an enduring discomfort, which can be traced back to the birth of economics as an autonomous discipline. And Jean-Baptiste Say proposed a sweeping remedy in the "Abridged history of the progresses of political economy" which concludes his Cours complet d'économie politique pratique: let us get rid of our history, he enjoined, as other disciplines are wont to do once they are sufficiently mature (Say 1828, vol. 2, pp. 540-41). Yet it seems that the remedy, though still advocated today by a number of doctors, has been incompletely adhered to: thus the same discomfort remains, the history of economic thought still exists, and self-searching questions are still raised about its future, often focusing on how we do the history of economic thought, as if this could provide the answer to the question of why we do it (see the contributions gathered in Weintraub (ed.) 2002). Most of the previously published Presidential Addresses to the ESHET conferences (that is, from the 2006 edition onward), for instance, assigned a prominent place to the justification of the history of economic thought through an investigation of the ways in which we practice it (Heinz Kurz 2007[START_REF] Maria | Is History of Economic Thought a "serious" subject?[END_REF][START_REF] Rosselli | Economic History and History of Economics: In Praise of an Old Relationship[END_REF][START_REF] Hans-Michael | The Last Generalists[END_REF]; and for the others [START_REF] Harald | European émigrés and the 'Americanization' of economics[END_REF], José Luis Cardoso 2015) it was at least implicit in their discussions of tradition and of its possible transmission.

Despite having persisted since the beginning of the 19 th century, about three decades ago the need for a justification took on a new character as a result of Mark Blaug's pioneering introduction of a typology of approaches to the history of economic thought [START_REF] Mark | On the Historiography of Economics[END_REF]. His typology spread throughout our community, quickly becoming canonicalthe kind of thing with which you agree or disagree, but which you can hardly bypass. And its influence was all the more pervasive in that the typology gave birth to conflicting positions that firmly distinguished two opposing ways of doing the history of economics, typically referred to as Historical Reconstruction and Rational Reconstruction, to which were added two subsidiary approaches, Geistesgeschichte and Doxography (section 2).

This canonical typology was presented as borrowed from an important paper by Richard [START_REF] Richard | On the Historiography of Philosophy: Four Genres[END_REF], whose concern was the historiography of philosophy. But it was a special interpretation, resting on Blaug's own reading of Rorty, which set aside the possibility of a fifth genre introduced by Rorty, Intellectual History. Yet taking into account the possibility of this fifth genre opens the path to a non-canonical typology, blurring the border between Historical Reconstruction and Rational Reconstruction and lessening the divide between them, while also promising to challenge contemporary knowledge and enrich it with statements which do not belong to it (section 3).

The idea that the history of economic thought also has something to do with present-day changes in economic theory obviously preceded the birth of Blaug's canonical typology. It could easily be traced back to [START_REF] Joseph | History of Economic Analysis[END_REF] and, since the mid-twentieth century, has been a recurrent preoccupation among historians of economics, as typified by several presidential addresses to the ESHET. As such, that idea has shaped the long story of the way we have done history of economic thought in recent decades, leaving room for the progressive systematization of non-canonical typologies of approaches (section 4).

Drawing on this evolution, I have proposed a typology comprising three alternative approaches, distinguished on the basis of the way they conceive of the link between statements,2 old and contemporary [START_REF] André | Introduction à une Histoire de la Pensée Economique qui ne Verra Jamais le Jour[END_REF][START_REF] André | Почему история экономической мысли отличается от других историй? [Why is History of Economic Thought Different from all other Histories?[END_REF]: these approaches are extensive, retrospective, and intensive. The extensive approach, quite general in its scope, refers to any account of old statements in terms of other old statements, whatever their nature. The retrospective approach accounts for old statements in terms of the present-day economic statements which they prefigure. Finally, the intensive approach addresses old statements insofar as they can produce new statements, thus renewing our present knowledge (section 5).

Unlike the extensive and retrospective approaches, however, the very possibility of an intensive approach seems at odds with its relatively thin outcomeswitness, for instance, the paucity of handbooks in the history of economic thought which provide a firm and longlasting expression of their authors' methodological perspective. Taking the works of Sraffa [START_REF] Piero | Introduction[END_REF][START_REF] Piero | Production of Commodities by Means of Commodities[END_REF][START_REF] Amartya | Open and Closed Impartiality[END_REF] as examples, I will argue that this is a consequence of the intensive approach being heuristic, and hence its results being by nature transient, such that it is destined to remain poised between the extensive and retrospective approaches. As a result, among the three approaches available to historians of economic thoughtthe extensive, retrospective, and intensive approachesit is the latter which appears as a privileged route by which the history of economic thought can begin to engage with economic theory (section 6).

The canonical typology

The story of the canonical typology of approaches in the history of economics begins in 1962, when Blaug published the first edition of his well-known Economic Theory in Retrospect. In the introduction, he drew a sharp distinction between two approaches: relativist and absolutist (Blaug 1962, pp. 1-2). This today is quite familiar to us: according to the relativist approach, each theory is to be consideredand justifiedin its own context. The absolutist approach, on the contrary, allows a ranking of earlier theories according to the present state of knowledge.

Blaug's position at this time is also well known: while not dismissing the relativist approach, he clearly expressed sympathy with the absolutist viewpoint. And the later editions of Economic Theory in Retrospect reiterated the same position, at least until his influential 1990 paper on the historiography of economics. This paper had the notable aim of introducing the community of historians of economic thought to a typology designed by a major philosopher, Richard Rorty, who had posited a distinction between four "genres" in the history of philosophy [START_REF] Richard | On the Historiography of Philosophy: Four Genres[END_REF].

The result of Blaug's reading of Rorty's paper was a kind of compounding of two typologies.

The first was Blaug's old typology, in which he contrasted the absolutist and the relativist views. The second was his own interpretation of the four genres identified by Rorty:

Geistesgeschichte, Historical Reconstruction, Rational Reconstruction, and Doxography. This gave birth to a refinement of the initial relativist-absolutist typology which we today acknowledge as a canonical, that is, as a familiar gateway for taking up methodological issues in the history of economic thought. This refinement, relying on Rorty's four genres, was produced as follows. Firstly, Blaug showed rather little interest in Geistesgeschichte [history of the spirit], which aims at showing how such-and-such a question became important in the work of a past author: typically, it might concern whether the Napoleonic wars bear any responsibility for Ricardo's concern with a decrease of the profit rate. He then considered Historical Reconstruction as equivalent to his own conception of relativism, which he split between moderate and strict relativism, the latter being dismissed on the grounds that it is untenable. As regards absolutism, meanwhile, he asserted the equivalence between, on the one hand, Rational Reconstruction and Doxography and, on the other hand, strict and degenerate absolutism, before also dismissing Doxography, which he regarded as an ill-founded approach in the history of economic thought (Blaug 1990, pp. 27-28). What remains are the two well-known approaches Historical Reconstruction and Rational Reconstruction, which strive towards different kinds of rephrasing of what a past author said: the first one rephrases, or accounts for, past authors' answers in their own terms, or in the terms of their time; the second rephrases, or accounts for, past authors' answers in our own terms. Blaug at the time unequivocally favored Rational Reconstruction at the expense of Historical Reconstruction, thus upholding his preference for absolutist rather than relativist approaches. 1). First of all, obviously, it was influential on Blaug himself: he supplemented his introduction to the 5 th edition of Economic Theory in Retrospect by "sharpening" his position, as he put it, through adding the distinction between Historical Reconstruction and Rational Reconstruction, which he explicitly viewed as "almost the same" as his prior distinction between relativism and absolutism (Blaug 1997, p. 7).

Blaug

Geistesgeschichte and Doxography were no longer discussed in the subsequent reeditions. But the 1990 paper also exerted a palpable and long-lasting influence upon historians of economic thought, who turned to it each time questions arose about the legitimacy of their methodology (see, for instance, in the years which followed its publication, [START_REF] Paul | On the Historiography of Economics: a Correspondence[END_REF][START_REF] Roger | How Should We Approach the History of Economic Thought, Fact, Fiction, or Moral Tale?[END_REF][START_REF] Pierre | Les Lecteurs de l'Armée Morte -Note sur les Méthodes en Histoire de la Pensée Economique[END_REF][START_REF] Elias | Has Economics Progressed? Rectilinear, Historicist, Universalist, and Evolutionary Historiographies[END_REF][START_REF] André | Introduction à une Histoire de la Pensée Economique qui ne Verra Jamais le Jour[END_REF].

As we know, of course, this is not the end of the story: for, some years later, Blaug changed

Back to Rorty

For instance, when Rorty discussed the issue of Historical Reconstruction versus Rational Reconstruction, he didn't view it in terms of the relativist-absolutist opposition. Rather, he borrowed it from a paper by Quentin Skinner published in 1969, and he followed Skinner in defining Historical Reconstruction as an approach in which no one "can eventually be said to have meant or done something which he could never be brought to accept as a correct description of what he had meant or done" (Skinner, 1969, p. 28).

In contrast, Rational Reconstruction is an approach in which we are not searching for what an author meant, but rather for what is meant by him or her. That is, we are seeking the outcome of a forced conversation, in alternative contexts, between the past author and us today. Rorty proposed to adopt a restricted use of "meaning", so as to reserve the words "meaning" and "significance" for Historical Reconstruction and Rational Reconstruction respectively (Rorty 1984, pp. 54-55).

The opposition between Historical Reconstruction and Rational Reconstruction, understood as an opposition between what an author meant (the meaning) and what is meant by his or her works (the significance), seems rather powerful. For instance, it clearly leads us to conclude that asking what Adam Smith would have said about digital economics is not at all nonsensical: we would only say that this is something that falls under Rational Reconstruction, not Historical Reconstruction.

Here I would like to draw the reader's attention to another aspect of the Skinnerian origins of Rorty's distinction between Historical Reconstruction and Rational Reconstruction: in arguing that it rests on the possibility of bringing past authors to accept an interpretation of what they said, we blur the border between the two types of reconstruction. Just think, for instance, of a simple statement which might pertain to Christopher Columbus:3 "he discovered America".

At first sight it's a Rational Reconstruction, since nothing like the American continent was part of Columbus's knowledge. But assuming we adopt Skinner's criterion, do we really believe that "he could never be brought to accept it as a correct description of what he had meant or done"that is, that he could not accept the kind of information provided to him? On the one hand, this can be viewed as introducing an alternative context, and hence justifying such a claim would be regarded as Rational Reconstruction; but, on the other hand, how could we be so presumptuous as to imagine that we could in no way bring Christopher Columbus to accept this enlarged, rather than new, context? In which case, "Christopher Columbus discovered America" would be a Historical, not a Rational, Reconstruction. This illustrates the fact that when a statement falls within the sphere of Intellectual History, it might well be a Rational Reconstruction, but it might equally be a Historical Reconstruction.

This non-canonical typology, which includes Intellectual History as a fifth genre, could be derived from Rorty's paper; yet it is rather different fromand far less conflictual thanthe canonical typology we are used to, which was nonetheless also derived from Rorty's paper.

Towards a non-canonical typology

Independently of Rorty's development of the idea of Intellectual History, there is a longstanding and familiar intuition that what we can learn from the past might, at least, be meaningful for economists today. More than thirty years before the publication of Rorty's paper, in his History of Economic Analysis Schumpeter noted that in economics "much more than in physics have results been lost on the way or remained in abeyance for centuries" (Schumpeter 1954, p. 5), such that it was the task of historians of economics to revive them.

And a similar position is evinced by more recent authors, albeit stated from different points of view or in different terms. Illustrating his claim by reference to monetary theory, Cesarano (1983) argued that economic knowledge was increasing in the long run, whereas in the short run its trend showed oscillatory movements, and thus there was room for smoothing them by means of the history of economic thought. In the same way, Hollander (1987) noted that the replacement of one theory by another often appeared as the result of a change in what he called the "focus of attention", and that it was one of the tasks of historians of economic thought to move the focus back to the theory that had been abandoned. This point, he claimed, was illustrated by the revival of the Smithian distinction between productive and unproductive labour in order to explain the weakness of the British rate of growth (Hollander 1987, p. 1).

Drawing on Lakatos, Negishi argued that research programs in economics at times enter periods of hibernation, and that it was the role of historians of economic thought to bring them out of hibernation, as Keynes or Sraffa were supposed to have done when reading respectively Malthus or Ricardo (Negishi 1989).

Even Blaug's paper from 2001 might be regarded in this way. At first sight it relies on the same canonical typology, but the approach he favoured had changed: he gave up on Rational Reconstruction, and turned to Historical Reconstruction on the basis of an efficiency argument according to which new propositions, which didn't belong to present economic knowledge, might be found in the works of past authors. The idea had clearly been in the air for a long timelong enough that it was unnecessary to make reference to Rorty's contribution on this point. Blaug, then, could view it as part of a Historical Reconstruction, enlarged to encompass Geistesgeschichteyet without noting that for Rorty, the approach involved in the efficiency argument fell under Intellectual History, not Historical Reconstruction.

In much the same way, previous Presidential Addresses to the ESHET Conferences have expressed concern about the possibility that the history of economic thought might be able to renew contemporary economic knowledge. These addresses were opportunities to recall the identity of the discipline and its distinctiveness, even when its relation with other disciplines was also praised (like, for instance, economic history for Annalisa Rosselli in 2012; see [START_REF] Rosselli | Economic History and History of Economics: In Praise of an Old Relationship[END_REF]). Among them, some were directly concerned with the kind of approaches which prevail in the history of economic thought. This was the case for Heinz I would like to call our attention not to the differences between these perspectivesfor of course there are differencesbut rather to what they have in common. They have in common a special ambition of scouring the works of past authors in order to find ideas, propositions, or, as we might more generally put it, statements, which do not belong to present economic knowledge, and which potentially challenge it, and which might even contribute to its transformation.

When compared with the canonical typology, they make its limitations obvious. All of them, in their own ways, promote a special vocabulary to support various typologies of approaches in the history of economic thought which might be related to the canonical typology; but they also all make room for approaches which search the works of past authors for issues which do not belong to our present knowledge, thus also opening the path to a non-canonical typology.

This allows us to link them to Rorty's five genres of historiography (see Table 2). 1991). And, of course, they also correspond to Rorty's Intellectual History, his fifth genre which fitted so badly into Blaug's absolutist-relativist perspective that it found no place in the canonical typology.

Rorty

This, then, is the outline of the story of how we have done the history of economic thought in recent decades. It is the story of the birth of a canonical typology of approaches in the history of economic thought, and the story of its dissolution, which opened room for an alternative approach.

A proposed typology

We can put this point differently by focusing on the opposition between old and contemporary statements (see [START_REF] André | Introduction à une Histoire de la Pensée Economique qui ne Verra Jamais le Jour[END_REF][START_REF] André | Почему история экономической мысли отличается от других историй? [Why is History of Economic Thought Different from all other Histories?[END_REF]. I have used the term "extensive approach" for any account of old statements in terms of other old statements, irrespective their nature, or the discipline in which they are located. This corresponds to what Blaug, after Rorty, called

Geistesgeschichte or Historical Reconstruction. An obvious example of an extensive approach is Karl Pribram's attempt, in his book published posthumously in 1983, to promote what he called a history of economic reasoning. Such an approach amounts to viewing economics as an application of principles of reasoning elaborated elsewhere. By "elsewhere", he means the discipline which aims precisely at building principles of reasoningthat is, philosophy.

Hence, in Pribram's book one finds chapters on Thomist economics, Cartesian economics, and Kantian economics, respectively appealing to Thomas Aquinas, Descartes, and Kant. The intervention of philosophy in a historical account is only one example of an extensive approach: in fact the term covers a range of possibilities which are not usually considered together. For instance, a link might be established between a political situation and economic propositions: such could be the case if we follow Cannan (1892) in interpreting the contributions of Malthus, Ricardo, and West in February 1815, which led to a novel explanation of rent, as an impact in the field of economic theory of debates within the political field about the Corn Laws. Or, in the same way, we might be concerned with such a link if, following Mitchell (1967-69), we paid special attention to technological and organizational change in accounting for changes in economic theory.

In Figure 1, I have drawn up on the left a set of old statements, irrespective of whether they are by nature economic or not. Areas shaded in medium or strong grey represent the subset of what we consider to be theoretical statements in economics. Areas in light grey represent what we consider to be other kinds of statements. This reference to "we" is the irreducible mark of present knowledge, of which Rorty said that it could never be cancelled out, in any genre of historiography. Consequently, the extensive approach is simply a way to pass from old statements in economics to other old statements.

I have used the term "retrospective approach" for any attempt to account for old statements in terms of the present-day economic statements which they prefigure. obviously corresponds to Rorty's categories of Rational Reconstruction and Doxography. An exemplary instance was given by Blaug himself when, with a certain sense of humour, he dedicated his famous handbook Economic Theory in Retrospect "to David Ricardo, my son". This shows more clearly than any more sophisticated comment what adopting a retrospective approach involves: Blaug's naming his own son after the famous economist reflects the manner in which we, like Blaug, view David Ricardo or any other past author much as if they were our childrenthat is, as people full of promise, who might yet be what we have already succeeded in becoming, and who reflect our current knowledge imperfectly, naïvely, and with less mastery than we now have.

Again in Figure 1, I have set out on the right hand side, in medium grey, modern economic statements belonging to contemporary knowledge. The retrospective approach therefore amounts to linking an appropriate subset of old statements marked in medium grey with the set of modern statements. Now, it should be clear from Figure 1 that something structural is missing. Specifically, whereas the extensive approach potentially concerns all old statements, the retrospective approach concerns only those old statements which might be viewed as more or less accurate prefigurations of what today is known. Thus there is room to introduce a missing approach, which I have called the "intensive approach". In Figure 1, this would be another way to relate old to contemporary statements. Old statements (in dark grey) are retained only insofar as they do not prefigure modern statements, but can still produce new statements (also in dark grey), thus renewing present knowledge.

Like the retrospective approach, the intensive approach is concerned with contemporary economic theory; but, like the extensive approach, it is not concerned with what we already know. And unlike either of these approaches, it is concerned with the challenges faced by our knowledge in its present state. My contention is that the intensive approach covers Kurz's (2006) building of "heterodoxies", Marcuzzo's ( 2008) "quest for alternatives", and

Trautwein's (2017) identification of "blindspots".

Figure 1. A non-canonical typology

The intensive approach as a heuristic

The intensive approach therefore supports the intuitive view that the history of economic thought is not simply self-sufficientas it surely is on an extensive or retrospective approach, much like any academic practice in the history of ideas which doesn't require further justificationbut is also a way to contribute to advances in economics. But if so, this means that the history of economic thought should be counted among the possible means to feed into

The answer seems to be that, unlike the extensive or retrospective approaches, the intensive approach is by nature a transient approach. 1960, p. 93), and particularly to his understanding of the role of corn in Ricardo's system, which he has generalized into the idea of the basic commodity, his approach appears as intensive: it was clear to the reader in 1960 that the subtitle of Sraffa's book ("Prelude to a critique of economic theory") was an understatement. He had gone far beyond a simple prelude to a critique, and instead supplied a positive alternative to the standard theories of prices. And he did this through his reading of a text nearly 150 years old, 4 and by giving a solution to a problem he found therein. and what he claims to be his legacy within contemporary academia. Hence the whole discussion can be viewed methodologically as engaged in a retrospective approach.

For both Sraffa and Sen, what I have called the "intensive approach" therefore proves to be a transient approach in the history of economic thought, poised between the extensive and the retrospective paradigms. And it is because of this transient nature that the intensive approach is too fleeting, too short-lived, to give birth to an object as long-lasting as anything like a handbook in the history of economic thought. Yet the transient nature of the intensive approach is the consequence of its being a heuristic, whose potential effect is a transformation of present economic knowledge by means of historical investigation. No less, yet no more.

The intensive approach is born from the extensive; and from the moment it is implemented, it is destined to vanish into the purely retrospective.

On the one hand, for a historian of economic thought whose concern is to contribute, no matter how modestly, to the economic knowledge of her or his time, the transient nature of the intensive approach might seem unappealing: no handbooks; no firm construction upholding the memory of one's work; a visibility restricted only to major results like Sraffa's, Morishima's, or Sen's. While, at the same time, one's everyday results, all these minute potential changes to economic knowledge induced by close historical investigation, add up to barely any steps away from the field of history of economic thought towards that of economics. From this point of view, the history of economic thought may well appear to be a superfluous and excessively complicated detour, at least to the extent that it aims at the concrete transformation of economic knowledge on a par with empirical or experimental approaches to economics.

But, on the other hand, the history of economic thought also effects an incredible extension of the number of past authors with whom today's historians of economic thought may talk, share ideas, and jointly enter into new projectsat least in so far as they themselves are engaged in an intensive approach. In the introduction to the volume in which Rorty's 1984 paper was published, the editors asked the reader to imagine a thousand-volume edition of a giant

Intellectual History of Europe. To imagine also that all the authors whose works were discussed therein should be restored to life, and would all then read all of each others' books, engaging in discussion, dialogue, dispute, and common projects [START_REF] Richard | Introduction[END_REF].

Transposing this to economics and to what I've called the intensive approach, the present implication is that we may consider works which we normally view as belonging to the early history of our discipline, like Jevons's Theory of Political Economy or Marx's Capital, as having just been written. Moreover, this would also mean that they were written very shortly after Smith's Wealth of Nations, which was itself published almost simultaneously with Quesnay's Tableau économique, etc.: as if time were being compressed, though leaving history intact. And then we invite the authors to engage in dialogue with each other as well as with ourselvesnot only for the purposes of presentation, as if we wanted to enhance the impact of these authors' works, for this is the least we can hope to do as historians of economic thought. No: it is above all a way to take what they wrote and thought seriously; so Keynes, Jevons, Marx, Smith, Quesnay, and so many others: they are still with us. As historians of economic thought, we have often been charged with speaking with the dead. Yet this is precisely not what we do: we bring the dead alive, all of them. And we may be proud of it.

  his mind, his preferences shifting from Rational to Historical Reconstruction (Blaug 2001). His 2001 paper, in turn, fueled the ongoing and at times schismatic debate on the methodology of the history of economic thought (in the special issue of the Erasmus Journal for Philosophy and Economics devoted to Mark Blaug in 2013, see for instance the papers by John Davis and by Harro Maas). But although Blaug did change his mind about the kind of approach he favored, he nonetheless remained faithful to the canonical typology inherited from Rorty. Yet what such persistent faithfulness concealed was that in passing from Rorty's hands to Blaug's, and thus transiting from the history of philosophy to the history of economics, the initial typology had evolved. Rorty's original typology had faded into Blaug's: yet, as had already been shown (see Shionoya 2009), Rorty's original paper was also open to alternative interpretations, and was not committed to the relativist-absolutist interpretation, as Mark Blaug's interpretation was.

  Kurz's contribution in 2006[START_REF] Maria | Is History of Economic Thought a "serious" subject?[END_REF], and Hans-Michael Trautwein's in 2016[START_REF] Hans-Michael | The Last Generalists[END_REF].

  seriously that we are willing to confront it with what we as economists now know. Through what we write about them, they continue to challenge our knowledge, in continuum with what they did in their own periods.

(1962) Blaug (1990) Blaug (1997) Blaug's Rorty (1984) Blaug's Blaug (1962)

		Geistesgeschichte
	Relativism	Historical Reconstruction	Strict Relativism Moderate Relativism	Historical Reconstruction
	Absolutism	Rational Reconstruction	Strict Absolutism	Rational Reconstruction
		Doxography	Degenerate Absolutism

Table 1 .

 1 The canonical typology

	Subsequent to Blaug's 1990 paper, what I have called the "canonical typology" became
	influential (see Table

  surplus-value is a necessary and sufficient condition for a positive rate of profit(Morishima 1974, pp. 621-22). One might discuss at length the question of how we can know whether this kind of relation between the rate of surplus-value and the rate of profit was something which Marx actually meant. Let us assume it was.In 1973, however, despite

	certain pioneering contributions like that of Okishio (1963), this didn't really belong to the
	economic knowledge of the time when Morishima published his book. Thus:
	1. You could argue that the so-called fundamental Marxian theorem belonged to
	Intellectual History, being an issue which didn't belong to our present knowledge as
	economists.
	2. Nonetheless, you could also say that it is a Rational Reconstruction, since Morishima
	used the properties of non-negative square matrices and linear programming, which
	Marx clearly could not have known about.
	Intellectual History is obviously a way to challenge the fuzzy border between Historical
	Reconstruction and Rational Reconstruction. It yields an enlargement of the interpretations of
	a past author which -again in Skinner's words -he "could be brought to accept […] as a
	correct description of what he had meant or done". Take as an example one of the main
	messages which Morishima found in Marx. What he called the "fundamental Marxian

The existence of a fuzzy, and thus debatable, border between Historical Reconstruction and Rational Reconstruction led Rorty to view his three relevant genres (Geistesgeschichte, Historical Reconstruction, Rational Reconstruction) not as independent approaches which might be mixed contingently in the work of such-and-such historians of ideas, but rather as an example of what he regarded as a "Hegelian triad"

(Rorty 1984, p. 68)

, whose working opens the path to a fourth genreor, better, a fifth, if Doxography is taken into account, despite its exclusion by Rorty, much like Blaug would also do. In the canonical typology this fifth genre is set aside: yet the entire final section of Rorty's paper is devoted to it. He called it "Intellectual History".

Intellectual History is presented by Rorty as raising issues which do not belong to our present knowledge. This is obviously the case with marginal or forgotten figures: taking them into account might result in a revision in the headings of the chapters of canonical histories of economic thought (in the history of philosophy, for instance, he mentions the relatively minor place of Diderot; Rorty 1984, p. 69). But it is also a way of saying that what an author meant, in the Skinnerian sense, some centuries ago, might also become meaningful for us today.

theorem" was published in its basic version in his book on Marx in 1973 and in its generalized version one year later. Broadly speaking, this theorem states (in its 1974 version) that in a quite general linear model of production, with alternative techniques and joint production, a positive rate of 3. But if the equivalence between the signs of the rate of surplus value and of the rate of profit was really something which Marx meant, there is no reason to view these formal developments as an unsurmountable obstacle, according to the Skinnerian criterion. (I mean, there are no reasons other than Marx's possible intellectual limitationswhich would be a rather odd argument.) Thus Morishima's fundamental theorem could be viewed as an alternative account, meeting the requirements of a Historical Reconstruction, of what Marx had said in some passages from Capital, Book 3.

Table 2 .

 2 ESHET Presidential Addresses: towards a non-canonical typology economic thought and are of the highest general interest. Clearly, the categories of heterodoxy, textual exegesis, quest for alternatives, blind spots identification, and innovation by backtracking, correspond to the search for new results[START_REF] Joseph | History of Economic Analysis[END_REF], the historical smoothing of oscillations in economic theories[START_REF] Filippo | On the Role of the History of Economic Analysis[END_REF], the change in the focus of attention(Hollander 1987), and the awakening of hibernating research programs (Negishi

	(1984)	Kurz (2006)	Marcuzzo (2008)	Trautwein (2017)
	Geistesgeschichte		Historical reconstruction =	Exploration of the past
	Historical		{Contextual analysis,	Exploration of the
	reconstruction		Historical narrative}	past / Correction
	Intellectual history	Heterodoxy	Textual exegesis / Quest for alternatives	Exploration of the past / Blindspots & backtracking
	Rational reconstruction Doxography	Whiggism	Textual exegesis / Quest for ascendency	Decoration Abbreviation
	Heinz Kurz (2006) pointed to heterodoxy as an alternative to "Whiggist" interpretations
	(according to terminology drawn from a 1931 book by H. Butterfield), which I relate to the
	canonical typology's category of Rational Reconstruction. Cristina Marcuzzo (2008) noted
	the role of textual exegesis in the search for new ideas, and also of the quest for alternatives,
	though she viewed this as a kind of Rational Reconstruction. And, drawing on the idea that

today's increasing specialization in economics also increases the risk of neglecting the history of economic thought,

[START_REF] Hans-Michael | The Last Generalists[END_REF]

found support in what he called blind spots identification and innovation by backtracking, which both require the highest skill in the history of

  I'll give two examples, drawn from those mentioned above. The first is Sraffa's interpretation of Ricardo's Essay on Profit in 1951. Let's engage in the following thought experiment: we are transported back to 1951 and, despite this backward transportation, we remember everything of our lives except what is connected to Sraffa's works from 1951 onwards. What would we think of Sraffa's newly published introduction tohis long-awaited first volume of the new edition of Ricardo's works? Some of us would agree with Sraffa's interpretation of the Essay, accepting the idea of the structural specificity of agriculture (corn made with corn), so that the profit rate might be viewed independently of prices, and rather as a ratio of homogeneous quantities. Others would not: but this is not my point. I want to draw our attention to the fact that at this time, in 1951, we would regard Sraffa's introduction as a typical instance of what I've called an extensive approach. That is, an approach which accounts for what Ricardo did on the basis of his works, his correspondence and discussions, and on the basis of which we might draw inferences, rightly or wrongly, about what he meant.

	Now we are transported forward to 1960, and Sraffa publishes his Production of Commodities
	by Means of Commodities, in which he introduces the concept of a "basic commodity",
	standing for a composite commodity produced by itself and labour. At this very moment, but
	only then, when reading and according credit to Sraffa's appendix D on his sources (Sraffa

  And after this? Continuing our journey through time, let us return to the present. Whatever our interest in the theory of prices of production and in its capacity to challenge other theories of prices, we must agree that it is now a part of contemporary knowledge (see, among others, Kurz and Salvadori 1995)to such an extent that if we should try to explain, today, that what Ricardo wrote in 1815 was an intuition about a theory of prices of production where corn is the only basic commodity, this would be an example of a retrospective approach. That is, it would be an account of what Ricardo meant by what he said in 1815: a prefiguration of what we now know so well, and so much better than he did, two centuries later.My second example from Amartya Sen's unwavering interest in Adam Smith, especially on matters related to individual behavior, justice, and moral philosophy. Some of his works focus directly on Smith: they were written either alone[START_REF] Amartya | Adam Smith's Prudence[END_REF] 2010a; 2010b;[START_REF] Harald | European émigrés and the 'Americanization' of economics[END_REF] or in collaboration with his wife Emma Rothschild (Rothschild, Sen 2006), whose book on Smith and Condorcet (Rothschild 2001) seems to have had great influence on him. Others, although they deal with other issues, deliberately leave room for reminders of the link between what Sen is now doing as an economist and what Smith wrote some two centuries earlier (for instance,[START_REF] Amartya | On Ethics and Economics[END_REF] 2002; 2009). As with Sraffa's relationship with Ricardo, from the mid-1980s onwards Sen was giving an interpretation of Adam Smith which contrasted the idea that public reasoning on justice should include not only people directly concerned by the deliberation itself (the "focal group"), but also people from outside this group(Sen 2002, pp. 449-51). Again, such an interpretation, which Sen set in opposition to the Rawlsian one(Sen 2002, pp. 451-53), might be disputed (Ege, Igersheim, Le Chapelain 2016; Bréban, Gilardone 2018); however, it remains an outcome of an extensive approach directed at reappraising some features of a major contribution by Adam Smith.On the other hand, however, and as confirmed in further works (Sen 2009), Sen explicitly drew on his interpretation of Smith's impartial spectator in order to introduce the idea of "open impartiality" in his theory of justice (Sen 2002)a theory of comparative justice which he views as rooted within a tradition that includes Smith and Condorcet, and which had been overshadowed by the transcendental tradition rooted in Hobbes or Rousseau, and now exemplified by Rawls's theory of justice[START_REF] John | A Theory of Justice[END_REF]. This, in turn, is an example of an intensive approach which aims at challenging the Rawlsian theory of justice through reference to writings that are more than two centuries old.

	with some major interpretations then extant, exemplified for Sen by Stigler's (1971) account,
	to which he systematically referred (see, for example, Sen 1986, p. 31; 1987, pp. 17-22),
	notably in order to call into question the "self-interest" line of reading of Adam Smith which
	was used, Sen said, to support a "cramped and simplistic theory of human rationality" (Sen
	2010a, p. 54). All of this falls within an extensive approach whose conclusions might have
	been (and obviously were) debated.
	Yet although until 2002 Sen's emphasis in his contributions on Smith seems mainly to have
	been on issues related to individual behavior, rules of conduct, and individual rationality,
	something different appeared after 2002, where his interest now seems to be morality and
	justice (see Bréban, Gilardone 2018). In his 2002 paper, he continued his re-interpretation of
	Smith, extending it now to the impartial spectator which Smith had introduced in the Theory
	of Moral Sentiments (1759). He understood Smith's account of the impartial spectator as

between basics and non-basics had emerged in the course of the present investigation that the above interpretation of Ricardo's theory suggested itself as a natural consequence"

(Sraffa 1960, p. 93)

. supporting Sen refined his previous argument in 2009, when he published The Idea of Justice (dedicated to the memory of John Rawls). But things had changed since 2002: when discussing the link between Smith's impartial spectator and open impartiality within a theory of comparative justice, he is now dealing with the relation between an account of the work of an old author

I employ the underspecific word "statement" precisely for its wide meaning, intending thereby to encompass judgements, propositions, beliefs, and so on.

The example continues Rorty's discussion. SeeRorty 1984, p. 53.

Strictly speaking, when Sraffa reviewed the circumstances in which he made his finding of the idea of a basic commodity, he himself cast doubt on the idea that he might have been led from his historical investigation to his analytical discovery: "It should perhaps be stated that it was only when the Standard system and the distinction

Acknowledgements

I have greatly benefitted from comments and suggestions provided by Laurie Bréban on an earlier draft of this paper. I also wish to thank Ben Young for his patient and efficient reading, and two anonymous referees of this Journal for their valuable recommendations.

economic theory. Thus besides the direct access to economic theory enjoyed by economists, and the indirect access which also belongs to economists trained in empirical or experimental economics, we should also add the access made available through the history of economic thought, which is no less real for being less commonplace. And access in this instance requires an intensive approach.

Nonetheless, it turns out to be unexpectedly difficult to find evidence not only of the efficacy of the intensive approach, but even of its very existence: as if it was the missing piece of a puzzle which we can only imagine and in no sense hold in our hands. The extensive and the retrospective approaches were illustrated above by the handbooks of Karl Pribram (1982) and[START_REF] Mark | Economic Theory in Retrospect[END_REF] respectively. Is there any handbook which might also illustrate the intensive approach? At the beginning of his History of Economic Analysis, Schumpeter argued that the history of economic thought was a proper means to find lost or idle ideas (Schumpeter 1954, p. 5). But in spite of its scholarly achievements, and of its enduring originality, Schumpeter's book falls far from providing a significant example of an intensive approach, and rather provides its readers with numerous illustrations of the extensive or the retrospective approaches. It is all the more puzzling that, setting handbooks aside, we have to wrack our brains to find convincing instances of the intensive approach actually being employed. I can give only a few examples.

For many of us, Sraffa's introduction to the works of David Ricardo in 1951, and especially his interpretation of Ricardo's so-called Essay on Profits (1815), in relation to his 1960 theory of the prices of production, might be viewed as an impressive illustration of what an intensive approach can do (see also [START_REF] André | Introduction à une Histoire de la Pensée Economique qui ne Verra Jamais le Jour[END_REF][START_REF] André | Почему история экономической мысли отличается от других историй? [Why is History of Economic Thought Different from all other Histories?[END_REF]. And as already mentioned, Morishima's interpretation of Marx through his Marxian fundamental theorem might be another example [START_REF] Michio | Marx's economics[END_REF][START_REF] Michio | Marx in the Light of Modern Economic Theory[END_REF], alongside Leijonhufvud's reading of Keynes's theory of unemployment (Leijonhufvud 1968), or Sen's reading of Smith's conception of poverty in relation to the capabilities approach, or of the impartial spectator in relation to open impartiality [START_REF] Amartya | Open and Closed Impartiality[END_REF]. We could also add to this rather meager list some "if only" examples, suggesting that, with a few tweaks, history might have been different and have left more room for the intensive approach: if only Paul Romer had read Smith before his 1987 paper; if only Daniel Kahneman had read Bentham before his joint paper with Amos Tversky from 1979. I could go on wracking my brain, but I guess that what I intend to ask is already obvious: why, considering its potential importance, are there so few examples of the intensive approach in action?


Helena R Torres

Bruno Oliveira

Jaime Fonseca

Sandro Queirós

João Borges

Nélson Rodrigues

Victor Coelho

Johannes Pallauf

José Brito

José Mendes

Real-Time Human Body Pose Estimation for in-Car Depth Images

Keywords: Autonomous driving, deep-learning, depth images, pose estimation

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

In recent years, the concept of autonomous driving vehicles is emerging owing to an increment on the development of advanced driver-assistance systems [START_REF] Levinson | Towards Fully Autonomous Driving: Systems and Algorithms[END_REF]. In fact, it is expected that fully automated driving will be the next goal for the automobile industry, which will extinguish the role of the driver. Thus, without the necessity of driving the car, the passengers can spend their time doing other types of activities [START_REF] Banks | Analysis of driver roles : Modelling the changing role of the driver in automated driving systems using EAST Analysis of driver roles : modelling the changing role of the driver in automated driving systems using EAST[END_REF]. In this sense, the need for monitoring all occupants in the car becomes crucial to analyze the passengers' behavior and, therefore, to ensure their safety.

There are different types of visual sensors that can be used for monitoring purposes, including monitoring persons through the detection of their pose. The most common sensor consists of RGB cameras that allow to retrieve visual information of the interior of the car and its occupants. However, these sensors only produce 2D images which hampers the interpretation of the human activity that is enrolled in the 3D world and is susceptible to brightness variations [START_REF] Regazzoni | RGB cams vs RGB-D sensors : Low cost motion capture technologies performances and limitations[END_REF]. A depth sensor, which is robust to light variations, can be used to solve this problem, as it also provides information about the distance between an object and the camera, giving a 3D information about the scene. However, they not give textural information, which is useful to detect different parts of the body. Recently, several works have focused on the integration of RGB and Depth sensors (RGB-D), which allow merging the advantages of both sensors [START_REF] Shao | Computer Vision for RGB-D Sensors : Kinect and Its Applications[END_REF], which could potentially increase the robustness of human pose detection. However, these sensors are more expensive in comparison with RGB and depth sensors.

To detect the human body pose in images acquired with camera sensors and, thus, the activity of the car's occupants, a robust method for human body pose estimation is needed. Specifically for the in-car environment, few strategies were previously proposed. Indeed, the images acquired inside a car have several occlusions, making some joints undetectable. This problem hampers the direct usage of traditional human pose estimation algorithms and makes this task more challenging than open space pose estimation scenes. The focus of the present work was to develop a method for human body pose estimation in depth images acquired inside a car. For it, a state-of-the-art method developed for open space human pose estimation in RGB images, Part Affinity Fields (PAF), was extended for an accurate and robust detection of human body pose inside a car using depth images [START_REF] Cao | Realtime Multi-Person 2D Pose Estimation using Part Affinity Fields[END_REF]. The main requirements of the method were its accuracy in detecting the pose along with its robustness to deal with large variability between different people (i.e. regarding body shape or size). Moreover, to deal with fast human movements, it was also important to guarantee the real-time capability of the pose detection. Overall, the current work introduces three main contributions: (1) extension of the PAF method for the detection of the presence/absence of a specific joint in the image; (2) a data augmentation strategy for depth datasets; and (3) a dataset for human body pose detection inside a car with depth images.

The rest of the paper is organized as follows. In section 2, the relationship of the present work with industrial and services systems is presented. In section 3, the stateof-the-art for human body pose estimation is detailed. The proposed framework for the human body pose estimation is described in section 4. In section 5, some implementation details related to the proposed method are outlined, being the results presented in section 6. In section 7, the method's performance is discussed, with the main conclusions of this paper presented in section 8.

Relationship to Industrial and Service Systems

With the progress in technology, it is expected that autonomous cars will become part of our life, and so, this new paradigm has high influence in industrial and service systems. In fact, partial and fully autonomous driving can bring social-economic advantages [START_REF] Casner | The Challenges of Partially Automated Driving[END_REF]. One of the advantages will be an improvement in road safety, since most of current accidents is caused by errors committed by the driver. Moreover, it is also expected that the traffic flow and the mobility could be improved in the autonomous driving scenario. Another advantage of these systems is related to the increase of the driver's comfort, which by not being focused on driving will have time to do other types of tasks [START_REF] Fagnant | Preparing a nation for autonomous vehicles : opportunities , barriers and policy recommendations[END_REF]. However, this technological evolution not only concerns personal aspects but also affects public services. In fact, it is expected that shared autonomous vehicles (SAV) will be the next revolution in public transportation. Similarly to personal autonomous vehicles, the SAV also brings several advantages, such as the improvement of passengers' mobility in an easy and economical way [START_REF] Krueger | Preferences for shared autonomous vehicles[END_REF]. Despite all the above mentioned advantages in autonomous driving, removing the responsibility of the driver/passengers in the driving activity may not be straightforward as it may seem. Indeed, the safety of both car's occupants and vehicle must always be ensured. Regarding personal vehicles, the driver should have the capability to take control of the car when the autonomous driving option is not safe. Concerning the SAVs, the monitoring of the car environment is crucial to maintain the integrity of the vehicle and to ensure the safety of all passengers. This is intrinsically related to the concept of resilient systems, where a system has the capability to recover from perturbations that may affect its normal functioning, allowing the reduction of the vulnerability of the system. A higher capability of maintaining a good performance of the autonomous vehicles can be achieved by monitoring the occupants of the car, being the proposed method of high interest for industrial and services systems.

Related Work

To recognize human body pose in images acquired by camera sensors, and, therefore, the activity of the car's occupants, a robust method for human body pose estimation is required. There are two main classes of algorithms for human body pose detection: generative approaches and discriminative approaches. Generative approaches are designed to fit and deform a model to match the image and detect the pose [START_REF] Demirdjian | Driver pose estimation with 3D Time-of-Flight sensor[END_REF]- [START_REF] Sigalas | Full-Body Pose Tracking?The Top View Reprojection Approach[END_REF]. Discriminative approaches are designed to learn a mapping from image features to a body pose, using only the information of the image [START_REF] Shotton | Real-Time Human Pose Recognition in Parts from Single Depth Images[END_REF]- [START_REF] Haque | Towards Viewpoint Invariant 3D Human Pose Estimation[END_REF]. Regarding generative ones, the main advantage is the robustness, once these methods fit one or more previous models to the image, allowing to introduce shape prior information to the method. However, this class of methods uses error minimization functions, being susceptible to be trapped in local minima and requiring high computational cost. In opposition, discriminative methods are fast during inference, allowing to more easily achieve realtime detection. Moreover, these methods are capable to deal with large body shape variations. However, they are inherently limited by the amount and quality of the training data. Nevertheless, discriminative approaches, namely deep learning strategies, have shown to be more robust and accurate for human body pose detection than other type of algorithms [START_REF] Belagiannis | Recurrent Human Pose Estimation[END_REF]- [START_REF] R-Cnn | Mask R-CNN[END_REF].

Owing to the success of discriminative approaches for human body pose estimation, several methods have been developed using these type of strategies, specifically deep learning methods. In [START_REF] Chen | Articulated Pose Estimation by a Graphical Model with Image Dependent Pairwise Relations[END_REF], a graphical model for human pose estimation was used where convolutional neural networks (CNN) were used to learn the different body parts and their spatial relationships (represented by a mixture model over several possible relations). In [START_REF] Tompson | Joint Training of a Convolutional Network and a Graphical Model for Human Pose Estimation[END_REF], the graphic model for the human body pose was obtained using the Markov Random Fields approach. Despite its accuracy in human body pose estimation, the previous methods rely on graphic models which can fail to model complex human poses. To overcome this issue, in [START_REF] Fan | Combining Local Appearance and Holistic View : Dual-Source Deep Neural Networks for Human Pose Estimation[END_REF], a dual source CNN was used to detect both full body and local body parts to achieve the final body pose estimation. In [START_REF] Bulat | Human pose estimation via Convolutional Part Heatmap Regression[END_REF], another method for human pose estimation using CNNs was proposed. In this method, a detection followed by a regression cascade strategy was used, where in a first stage heatmaps are inferred to detect the human body parts and then a regression of these heatmaps is performed to learn body relationships. In this work, heatmaps are confidence maps that represent the belief that a particular body part occurs at each pixel of the image. In [START_REF] Cao | Realtime Multi-Person 2D Pose Estimation using Part Affinity Fields[END_REF], this heatmaps concept was also used, where a network with two branches was designed to learn both part locations (heatmaps learning) and their associations (Part Affinity Fields -PAF). In this sense, instead of using regression of the heatmaps to learn body relations, the association of the different body parts are simultaneous learned with the heatmap inference.

Although several methods have been proposed for human body pose detection, these methods were applied mostly for pose estimation in open spaces, with the in-car scenario having received little attention in the research world [START_REF] Demirdjian | Driver pose estimation with 3D Time-of-Flight sensor[END_REF], [START_REF] Borghi | POSEidon : Face-from-Depth for Driver Pose Estimation[END_REF], [START_REF] Murthy | 3D Human Pose Tracking inside Car using Single RGB Spherical Camera[END_REF].

Methods

The main goal of the proposed method was to accurately detect the human body pose of passengers inside a car in depth images. Fig. 1 presents an overview of the proposed method, which is based on the deep learning-based body pose estimation method presented in [START_REF] Cao | Realtime Multi-Person 2D Pose Estimation using Part Affinity Fields[END_REF]. The proposed method uses as input a depth image of the driver acquired from a time-of-flight camera (Fig. 1A) and as output the location of each joint of the different human body parts (Fig. 1D). To obtain the joint positions, a CNN is used to simultaneous predict a set of heatmaps (one for each body part joint, Fig. 1B) and a set of part affinity field vectors that represent the association between the different parts (Fig. 1C). Since the in-car environment produces occlusions of some body parts and the Field-of-View (FoV) of commercial depth sensors may not be enough to visualize all joints once the driver stands near the camera, some joints may not be detectable in the images. Thus, the proposed network also predicts if a joint is presented in the image or not (henceforward called as label detection branch), which may boost the method's robustness.

In Fig. 2, the architecture used for the convolutional neural network is presented. As shown in the figure, the first part of the convolutional network consists in the first ten layers of the VGG-19 [START_REF] Simonyan | Very Deep Convolutional Networks for Large-Scale Image Recognition[END_REF], which are used to perform a first analysis of the image, generating a set of feature maps 𝑭. Next, the network is split in three branches for the simultaneous learning of the heat maps, the part affinity fields, and the label detection. 2 Architecture of the convolutional network used in the proposed method. The coral branch concerns the learning of the heat maps for body parts' detection and the blue branch concerns the part affinity fields for body part associations. Finally, the green branch is related to the label detection for joint categorization. Adapted from [START_REF] Cao | Realtime Multi-Person 2D Pose Estimation using Part Affinity Fields[END_REF].

Heat Maps for Body Parts' Detection

One of the branches of the convolutional network is used to predict confidence maps of each human body part (coral branch showed in Fig. 2). As previously stated, a confidence map represents the belief that a body joint occurs in a given image pixel, being assigned to each pixel a probability of being a body joint. In this sense, a confidence map can be seen as a 2D gaussian-like function, where the maximum of the gaussian map represents the ideal joint position.

To train the method to predict heat maps, a loss function 𝑓 ℎ𝑒𝑎𝑡 was applied in the end of this branch to calculate the difference between predictions and ground truth. In this case, the ground truth for the confidence maps was generated using a manual labeling of the joint positions and constructing a gaussian map around the joint locations. The loss function for this branch is given by:

𝑓 1 = ∑ ||𝑆 𝑗 -𝑆 𝑗 * || 𝐽 𝑗=1 , (1)
where 𝐽 represents the number of joints, and 𝑆 𝑗 and 𝑆 𝑗 * are the prediction and ground truth maps for part 𝑗, respectively. In the test phase, the joint position for each body part is given by the maximum of the respective confidence map, i.e. its peak, after a non-maximum suppression.

Part Affinity Fields for Body Part Association

To increase the accuracy of the body part detection, a second branch that measures the association between each pair of body parts was added to the convolutional network (blue branch in Fig. 2). This association is given by part affinity fields, which consists in a vector field between two body joints that encodes the direction between one body joint to another (see Fig. 1). To better understand how the part affinity fields are generated, the reader is kindly directed to [START_REF] Cao | Realtime Multi-Person 2D Pose Estimation using Part Affinity Fields[END_REF].

The loss function associated to this branch is given by:

𝑓 2 = ∑ ||𝑃 𝑐 -𝑃 𝑐 * || 𝐶 𝑐=1 , (2)
where 𝐶 represents the number of connections between the different body parts, 𝑃 𝑐 is the prediction of a part affinity field and 𝑃 𝑐 * is the ground truth for the association. Besides refining the inference of the confidence maps during training, owing to the backpropagation scheme used during it, the part affinity fields are useful when there is more than one person in the image. Indeed, in this scenario, a confidence map by itself may not be enough for an accurate detection because several peaks for the same joint may be detected (one for each person in the image). In this sense, the association between body parts are crucial to understand which joints belong to the same person. However, in this work, and given the FoV of the camera used, we only focused in the detection of one person, and therefore, we only used the part affinity fields to refine the heat map prediction.

Label Detection for Joint Categorization

Owing to the limited size of an in-car environment and to the reduced FoV of the cameras used for monitoring in this environment, there is a higher probability of certain body joints being outside of the image, specially the extremity limbs (e.g. the driver can have its arm outside of the lateral window and the associated joint is therefore not present in the image). It is thus important to understand if the joint is present or not in the image to increase the accuracy of the human body pose estimation. To deal with this problem, we added a third branch to our network. This third branch allow us to categorize the joint with a different label according to its existence in the image, i.e. the joint has the label 0 if it is outside of the image and label 1 if it is inside.

This label detection was achieved by using a set of fully-connected layers to learn non-linear combinations of the features 𝐹 𝐿 extracted by the convolutional layers (green branch in Fig. 2). Afterwards, a softmax layer was used to assign a probability for the label detection, by taking the output of the fully-connected layers and transforming it into a vector with two prediction scores (one for each class 𝑖: presented in the image or not). Each prediction score is given by:

𝑝 𝑖,𝑗 = 𝑒 𝑎 𝑖,𝑗 ∑ 𝑒 𝑎 𝑘,𝑗 𝐾 𝑘=1 , 𝑖 = 1, … , 𝐾 (3)
where 𝑎 𝑖 represents the output of the last fully-connected layer for class i, 𝐾 corresponds to the number of classes (in this case 𝐾 = 2), and J represents the number of joints. Please note that the sum of the probabilities is equal to 1 and, therefore, the joint's presence label is given by selecting the class with higher score. The loss function for this branch is given by equation ( 4), where 𝑡 𝑘 is the ground truth for the probability of each class (0 or 1).

𝑓 3 = ∑ - 1 𝐾 ∑ log(𝑝 𝑘 , 𝑡 𝑘 ) 𝐾 𝑘=1 𝐽 𝑗=1 . (4)
At test time, the prediction of this third branch is used to verify which heat maps predicted in the first branch should be evaluated. If the label detection branch predicts that the joint is not present in the image, it is considered not detected and the respective heap map is not evaluated. Otherwise, it is assumed that the joint is presented in the image and its position is given by the maximum of the respective heat map, as stated in section 4.1.

The final human body pose estimation is obtained by combining the output of the three branches. Thus, the overall objective function is given by summing the loss of each branch:

𝑓 = 𝑓 1 + 𝑓 2 + 𝑓 3 .
(5)

Experiments

Dataset Creation

Due to the inexistence of public datasets of depth images in an in-car scenario, it was needed to create our own dataset. Owing to the deep learning nature of the method, a massive amount of data is needed as training data, and therefore, it was needed to create a large dataset. Moreover, besides the high number of training images, the training dataset must also be variable enough to include the large number of actions possible in this scenario. In fact, the accuracy of the method is very dependent of the quality of the dataset. In this sense, we constructed our dataset by acquiring depth images using a time-of-flight camera placed near the windshield in front of the driver. For the construction of the dataset, ten different cars were used to achieve the desired variability in terms of image background. For each one of the ten cars, five subjects acted as driver, performing different actions inside a car (e.g. driving, putting the seat belt, picking up the phone, and others) to give the robustness needed for the dataset. The combination of the different cars and different drivers allowed to construct a dataset with 12200 depth images. The dataset was then divided in training, validation, and testing set with 8820, 1730, and 1650 images each, respectively. In this work, the training dataset was used to train the method, the validation set was used to test the progress of the performance of the method during training, and the testing set was used for the final validation of the proposed method. Note that the cars in each set of images differ from each other to achieve an unbiased evaluation.

Concerning the ground truth for the different body parts, it was constructed by manual labelling of the joint positions. Fourteen joints were used, namely: head (H), neck (N), right/left shoulder (RS/LS), right/left elbow (RE/LE), right/left wrist (RW/LW), chest (C), pelvis (P), and right/left hip (RH/LH). Note that the performance of the method was only evaluated for these upper body joints once the lower body parts are naturally occluded when simulating a driving position. Moreover, the joint categorization (present or not) was also manually defined per image.

Data Augmentation

As above-mentioned, the ground-truth for the training dataset was obtained manually, which could represent a limitation in respect to the number of training images once manual labelling is a tedious and task. In this sense, besides the real dataset constructed, and as common in deep learning strategies, a data augmentation layer was implemented, allowing to generate more training images that the ones initially labelled. Moreover, this data augmentation strategy allowed to increase the variability of the training dataset. Traditionally, data augmentation strategies rely on image flip, rotation, and scaling. Although it is an effective way of increasing image variability during training, such strategies do not modify the intensity information of the image. Although such feature is not so problematic for RGB images, it can for depth ones, as changing the intensity of these images can be a useful way to simulate different camera positions in the world (i.e. the distance between the camera and objects). In this work, the implemented data augmentation layer can simulate these changes in terms of camera's position, allowing to create images where the objects (i.e., the driver) are closer or farther from the camera than they were in fact.

The first step of our data augmentation approach is to convert the 2D depth image in a 3D point-cloud, using the extrinsic parameters of the camera. Upon obtaining the 3D camera coordinates, all points can be transformed by applying a given translation, moving the 3D point cloud in any direction and in any axis. The final step consists in using the intrinsic camera parameters to transform the translated point-cloud into a new 2D depth image. In Fig. 3, it is possible to visualize two examples of the result of our data augmentation strategy: one simulates the camera closer to the driver (Fig. 3B) and the other simulates the camera located farther from the driver (Fig. 3C).

Implementation Details

In the implementation of any deep learning method, the definition and optimization of certain training parameters for each specific problem are fundamental and can have a significant importance in the final accuracy of the method. In this work, experiments were carried out to get the optimal settings for these parameters. Concerning the learning rate and the momentum, these parameters were experimentally set to 0.0004 and 0.9, respectively. For the model optimization, the Adam solver was used with a regularization term of 0.01. For the batch size, 10 images were used. Note that these parameters were chosen by evaluating the method in the validation dataset.

Results

One important task to correctly implement a deep learning strategy is to evaluate the progress of the training in the validation dataset. Besides being useful to conduct experiments related with the best parameters to be used in the deep learning strategy, the validation dataset is also needed to avoid problems like overfitting to the training data, which may cause failure of the method when applied in a different set of images. In this sense, evaluating the method's performance during training in the validation dataset allow us to detect when the training converges, avoiding overfitting problems. Figure 4 presents an example graph showing the progression of the loss during training in both training and validation datasets.

To evaluate the performance of the proposed method in the testing set, different evaluation metrics were used. The first metric consists in the distance (𝐷) between the detected joint and the ground truth in pixels. Moreover, the method's accuracy (𝐴𝑐, percentage of correctly detected joints), the precision (𝑃𝑟, fraction of correctly detected joints among all the correctly or wrongly detected joints) and the recall (𝑅𝑒, fraction of correctly detected joints among all the correctly detected joints and the wrongly nondetected joints) were also evaluated, being defined by equations ( 6) to [START_REF] Krueger | Preferences for shared autonomous vehicles[END_REF].

𝐴𝑐 = 𝑇 𝑃 + 𝑇 𝑁 𝑁 × 100 (6)
𝑃𝑟 = 𝑇 𝑃 𝑇 𝑃 + 𝐹 𝑃 × 100 (7)
𝑅𝑒 = 𝑇 𝑃 𝑇 𝑃 + 𝐹 𝑁 × 100 (8)
where 𝑇 𝑃 , 𝑇 𝑁 , 𝐹 𝑃 , and 𝐹 𝑁 correspond to the true positives, true negatives, false positives, and false negatives, respectively, and 𝑁 is the total number of testing images. Table 1 summarizes the method's performance for each joint on the testing dataset. The presented values for the distance metric correspond to the median of the distance errors obtained. Note that the information if a joint is correctly detected or not used in the estimation of the accuracy, precision, and recall is given by the third branch of the proposed network. Moreover, the results showed in the table were obtained using the model obtained in the ideal epoch for early training stopping, which were estimated using Fig. 4. In Fig. 5, the boxplots for the distance metric are presented to analyze the detection performance distribution in terms of percentiles and outlier points. Fig. 6 presents the evolution of the accuracy, precision, and recall for different distance thresholds (i.e. not using the information provided by the label categorization). In this case, a joint was considered correctly detected only if its distance error is bellow a given threshold. Finally, in Fig. 7, some example results of the proposed strategy for human body pose estimation are presented.

Discussion

This paper proposed a method for human body pose estimation in an in-car scenario.

As stated, an important study to be performed during the implementation of a deep learning strategy concerns the evolution of the training. For that, its performance during training must be evaluated both in the training and validation datasets. Analyzing Fig. 4, it is possible to visualize that the ideal timing for stopping the training would be approximately around the 60th epoch. After this point of the training, the graph suggests that the model may start suffering from overfit to the training dataset, resulting in a very good performance for the images presented in this dataset but a lower or equal performance in the validation dataset. After analyzing the ideal epoch for early stopping, the model obtained in this epoch was used for the final validation of the method in the testing set. Analyzing Table 1 it is possible to verify the good performance of the human body pose detection method, with a mean distance error for all joints of 7.6 pixels. Moreover, high values for the accuracy, precision, and recall were obtained, showing the method's robustness. The worst results were obtained for the wrist joints. This can be explained by the fact that these joints are frequently near the image's limits, which can lead to a lower accuracy of the deep learning strategy. Moreover, owing to the proximity of the camera to the driver, these joints are not always present in the camera' field-of-view, which hampers the training process for these joints. This less accurate detection for these extremity joints can also be visualized in Fig. 5, where it is possible to verify the larger mean and interquartile range for joints. Nevertheless, Fig. 5 corroborates the overall good performance of the method, with narrow boxplots being obtained for the majority of the joints. In Fig. 6, it is shown that the accuracy, precision, and recall are improved with the increase of the threshold for the distance, as expected. Analyzing this graph, one can verify that for a threshold distance of 15 pixels, these evaluation metrics present acceptable values.

Concerning the computational time required by the method, the proposed human body pose detection methods takes approximately 80 milliseconds per image, which gives a performance of 12 frames per second, which proves the nearly real-time capability of the method. Note that this runtime analysis was performed using a laptop with a NVIDIA GeForce GTX-1060 GPU.

One important aspect to take into account in the proposed method is its application in a real setup. In fact, to achieve a real-time estimation of the human body pose inside a car, a high computational power is needed, which can be a limitation for an in-car scenario. However, the constant growth in computation capability of the technology will allow the application of the proposed method in a real scenario. Another aspect to take into account is that the application of software in autonomous cars should follow some existing standards to ensure its applicability in a real scenario. Nevertheless, all these issues will be address in the future.

Conclusions and Future Work

This paper presented a framework to detect the human body pose in depth images acquired inside a car. This method consists in a deep learning strategy where a new convolutional network configuration with three branches was used for simultaneous learning of confidence maps for each joint position, body parts' associations, and joint categorization (regarding its existence in the image). The proposed framework was validated in 1650 depth images, achieving an average distance error of 7.6 pixels and an average accuracy, precision, and recall of 95.6%, 96.0%, and 97.8% respectively. Overall, the proposed human body pose estimation method proved to be successful and accurate to detect the driver's pose, while showing a nearly real-time performance.

In future work, we intend to expand the human body pose estimation to more than one person, allowing to monitor not only the driver but all the car' occupants. In addition, we also intend to modify the method to exploit the 3D information provided by the depth image to infer the 3D joint position.

Fig. 1 .

 1 Fig. 1. Overview of the proposed method. (A) Input depth image; (B) Heat map (output of first branch) for the head joint; (B) Part affinity fields (output of second branch) for the association between head and neck joints; (D) final human body pose estimation

Fig. 3

 3 Fig. 3 Data augmentation strategy. (A) Original depth image; (B) Augmented image that simulates the positioning of the camera closer to the driver; (C) Augmented image that simulates the camera being located farther from the driver

Fig. 4 -

 4 Fig. 4-Method's performance (loss in function of epochs) during training in the training (green line) and validation (red line) datasets.

Fig. 5 -

 5 Fig. 5-Boxplots for the distance errors obtained by the proposed method per joint. The ends of the whiskers represent the 10th and 90th percentiles and the crosses represent the mean values.

Fig. 6

 6 Fig. 6 Variation of accuracy (green line), precision (red line), and recall (blue line) for different distance thresholds in pixels.

Fig. 7

 7 Fig. 7 Qualitative results of the proposed human body detection method. The first row presents examples of good results. In the second row, some examples where the pose estimation failed for a few joints are illustrated, with the ground truth pose shown in dashed lines

Table 1 -

 1 Method's performance in the testing dataset, assessed in terms of distance error (𝐷, pixels), accuracy (𝐴𝑐, %), precision (𝑃𝑟, %), and recall (𝑅𝑒, %).

		H	N	RS	RE	R W	RS	RE	R W	C	P	R H	LH	Mea n
	𝑫	6,0	5,1	5,4	6,7	10, 8	6,7	6,4	10, 0	9,2	7,2	8,6	9,1	7,6
	𝑨𝒄	98, 8	99, 6	99,8	97, 8	85, 0	98, 5	96, 8	88, 1	99, 1	98, 8	92, 3	92, 4	95,6
	𝑷𝒓	99, 1	99, 7	99,8	98, 7	82, 6	98, 8	97, 8	83, 9	99, 4	99, 0	96, 8	96, 6	96,0
	𝑹𝒆	99, 7	99, 9	100, 0	99, 1	96, 0	99, 8	98, 9	90, 4	99, 8	99, 8	95, 1	95, 5	97,8