Hippolyte D'albis

Héctor Pifarré

Arolas

Mortality Convergence Across High-Income Countries: An Econometric Approach *

This work is devoted to the study of the variations of mortality patterns across a sample of high-income countries since 1960. We study changes in age-at-death distributions through two main indicators, life expectancy and Gini coefficient. We contribute to the ongoing debate over the existence of convergence amongst industrial countries in adult mortality by offering two main empirical regularities. First, we apply econometric tools commonly used in the economic growth literature to assess the existence of convergence across the countries in our sample; our results show that the convergence hypothesis is rejected when we consider the entire sample of industrialized countries. Second, we provide preliminary evidence of convergence among a subset of countries. In this way, we offer empirics that justify further exploration into the theoretical underpinnings of subgroup convergence while presenting evidence against convergence of all industrialized countries.

Introduction

This work is devoted to the study of the variations of mortality patterns across high-income countries beginning in the 1960's. We explore the question of whether age-at-death distributions have become more similar across this particular subsample of countries-that is, if there has been a process of convergence. We study distributions through their mean, i.e. the life expectancy, and their dispersion, measured with the Gini coefficient. According to this concept, we study convergence by observing the evolution of the dispersion of the distributions for the two indicators in our sample of high-income countries.

Convergence is identified if the distribution across countries of a given indicator has become less unequal across time. We apply existing tools developed in economic growth literature to study mortality convergence (see [START_REF] Durlauf | Growth econometrics[END_REF], for a review of the literature). Using two ideas of convergence developed for economic growth, we can explore various aspects of the convergence process. First, we measure the extent to which gains in both mortality inequality reduction and life expectancy depend on initial levels of both in each country-that is, whether countries with lower starting life expectancy (or higher Gini index) have grown (or reduced) their indicators at a greater rate. This mode of convergence is denoted beta-convergence.

Second, we observe the evolution of dissimilarities across countries. Our analysis directly contributes to the discussion on whether there is a greater dispersion of life expectations and mortality inequality across countries. This idea is captured in the concept of sigma-convergence or distributional con-vergence. Additionally, we explore how these modes of convergence have behaved differently for particular periods since the 1960's. Furthermore, a major contribution of this paper is the consideration of convergence without the necessity of approaching the same mortality distribution among all countries. We propose the idea that there exist subgroups of countries that may converge to different mortality distributions and constitute what is known in economic growth literature as convergence clubs. We denote this difference as conditional convergence versus unconditional convergence.

We derive three main results from our econometric analysis. The first is on the catching-up process of adult mortality among developed countries for the period of 1960-2009. We show that there are greater improvements in the life expectancies of countries with lower life-expectancies while the overall dispersion among high-income countries has not decreased. The second is on the reduction of mortality inequality. Countries starting with larger Gini coefficients have also experienced greater reductions in their coefficients. Despite that, however, it is also the case that dissimilarities in Gini coefficients across countries have not been reduced over time. Based on our evidence we conclude that according to our idea of convergence there is no reduction in the difference in mortality patterns between high-income countries. While we do not find evidence of convergence in the whole sample, our third result is preliminary evidence on the existence of sigma convergence among certain groups of countries or clubs. We implement a simple methodology to detect existing clubs and test the hypothesis of this type of convergence; our findings indicate the existence of such a phenomenon in the period of 1960-2009, although we do find evidence against conditional convergence in both indicators in some subperiods.

Our paper is a contribution to the literature on convergence in mortality patterns between countries. The topic has indeed been explored by a number of papers. [START_REF] Wilson | On the scale of global demographic convergence 1950-2000[END_REF] suggests that there has been a process of demographic convergence from the 1950's that involves both mortality and fertility. The author studies the world distribution of life expectancy and finds a decrease in its dispersion. This trend is nevertheless not observed for life expectancy at older age in high income countries [START_REF] Glei | Diverging trends in life expectancy at age 50: A look at causes of death[END_REF]). Other contributions have focused on convergence in inequality. For instance, Peltzman (2009) shows that the inequality within countries, as measured by the Gini coefficient, decreases for a sample of countries. [START_REF] Edwards | Changes in world inequality in length of life: 1970-2000[END_REF] focuses on the length of life of a large sample of countries. By comparing a number of statistics for two given years (1970 and 2000) , he establishes that there is convergence in length of life at birth but not in adult mortality, specially among developed countries. In addition, he decomposes the total variance of the indicators in two sources: within and across countries. His findings indicate that even though the within variation has reduced, the across countries variation has remained broadly constant. A number of papers have studied the evolution of mortality patterns. In particular, Clark (2011) corroborates [START_REF] Peltzman | Mortality inequality[END_REF] findings but points out, in addition, that life expectancy improvements have been greater for developing countries while infant mortality reductions are larger in high-income countries. Eggleston and Fuchs (2012) study life expectancy in industrialized countries and point out that most gains in life expectancy have occurred in adult mortality, particularly concentrated after age 65. Finally, [START_REF] Bergh | Good for living? On the relationship between globalization and life expectancy[END_REF] study the effect of globalization on life expectancy and find that even controlling for a number of other explanatory variables, the index of globalization of a country is positively related to better life expectancies. These works have focused on one particular moment of the distribution and commented on its trends, leaving room for a formal more thorough analysis of the whole mortality distribution. This is addressed, in the contribution most closely related to our paper, by [START_REF] Edwards | Inequality in life spans and a new perspective on mortality convergence across industrialized countries[END_REF]. Their work exploits the properties of the mortality distribution in order to assess whether there is convergence across countries and decomposes it in terms of convergence in mean and variance.

Earlier works in the topic often assess convergence considering life expectancy. Our approach differs from these works in two main aspects. First, we study both the evolution of life expectancy and the dispersion of the distribution for different countries and identify whether they converge in this additional dimension. This approach has been used in works like [START_REF] Edwards | Inequality in life spans and a new perspective on mortality convergence across industrialized countries[END_REF]. A novelty in our work is the usage of the Gini index instead of the variance (or the standard deviation) as a measure of dispersion. This measure has been extensively used recently in the demography literature dealing with mortality inequalities (for a discussion of its advantages, see [START_REF] Shkolnikov | Gini coefficient as a life table function: Computation from discrete data, decomposition of differences and empirical examples[END_REF]. Many other measures have been used to measure longevity dispersion, a survey is provided in [START_REF] Robine | Redéfinir les phases de la transition épidémiologique à travers l'étude de la dispersion des durées de vie: le cas de la France[END_REF]. The use of the Gini coefficient can be justified by the fact that age-at-death distributions, even when truncated at age 10 or older, are not normally distributed. According to the Gini coefficient, inequalities within countries have decreased for all the high-income countries of our sample. However, by using the standard deviation of age-at-death distributions, [START_REF] Edwards | Inequality in life spans and a new perspective on mortality convergence across industrialized countries[END_REF] conclude that inequalities have remained broadly constant.Second and most importantly, our methodology is also radically different from that of Edwards and Tuljapurkar's (2005) because while they consider convergence as the shrinking of the distance to an ideal mortality distribution (that of Sweden 2002), we directly assess how the whole distributions of Gini coefficients and life expectancies across all countries considered have evolved. In Edwards and Tuljapurkar's (2005) in order to have convergence it suffices that all individual countries improve their life expectancies and reduce their Ginis.

The paper is organized as follows. We first present our data set and discuss the indicators chosen for our analysis. We proceed in section 3 by formally analyzing the impact of initial conditions on the historical growth rate of our indicators. In the last two sections we analyze whether distributional convergence can be established. Concluding remarks are in section 6.

Indicators and descriptive statistics

Our object of study, mortality patterns, is extracted from the period lifetables available in Human Mortality Database. The scope of our analysis is narrowed to a group of high-income countries (see list in Appendix 7.1). We consider, but do not restrict to, the whole life-table. We also study adult mortality, as measured by deaths of age 10 or more, and female mortality.

Following [START_REF] Edwards | Inequality in life spans and a new perspective on mortality convergence across industrialized countries[END_REF], we hence may discuss the particular effects of changes in infant mortality and isolate the sex differences in mortality evolution. Although this section of the paper focuses on the mortality distribution of the female population over 10 at time of death, the descriptive statistics for other distributions, including distributions with infant mortality, can be found in Appendix 7.3.

The first indicator we consider is the life expectancy. A first look at the evolution of life expectancies reveals a common trend in all the countries in the sample: they have increased steadily in all countries and there does not appear to be an obvious slowdown in the amelioration of life spans. This pattern is also observed among the other distributions we consider (see Figures 7,[START_REF] Edwards | Changes in world inequality in length of life: 1970-2000[END_REF] and 9 in Appendix 7.3). Further scrutiny reveals that the speed of amelioration has not been the same for all countries. In the time span considered, new differences across countries are created by the variety of growth rates. For instance, life expectancy in Japan has evolved from the last to the first position.

In our analysis we recognize the importance of studying the life-tables dynamics beyond life expectancy changes by focusing on an important and additional piece of information of the distribution, its dispersion that measures inequality in longevity. Given the non normality of the distribution, which we formally test in Appendix 7.2, we rely on a scale independent measure of inequality. We propose to compute a Gini coefficient to capture the dispersion of the distribution. The Gini coefficient consists in a comparison of the cummulative distribution of years by fraction of the population of the actual distribution and the cummulative of an hypothetical egalitarian distribution in which every member of the society lives for the same number of years. As usual, a Gini coefficient equal to zero indicates perfect equality, that is, all individuals have died at the same age; the closer to one, the less egalitarian a distribution is. A number of different formulations have been proposed for the study of life tables (see [START_REF] Shkolnikov | Gini coefficient as a life table function: Computation from discrete data, decomposition of differences and empirical examples[END_REF]. Most notably, it is possible to rephrase the concept in terms of differences between individual ages at death. We follow this approach and, since we may truncate our distributions at age 10 to eliminate child mortality, we present the following formula to compute the Gini coefficient at any age :

  = P  P    ()   () |  () +  () -  () - ()| 2 (  ) 2   
where   is the life expectancy at exact age ,   is the number of survivors at exact age  (with  0 = 100 000),   is the number of deaths between ages  and  + 1, and the   is the average length of survival between ages  and  + 1 for persons dying in the interval.

Let us now turn to the descriptive statistics. In Figure 2, we display the series of Gini coefficients computed for female's truncated distributions.

Convergence and initial conditions

A first way of assessing convergence across countries hinges on a negative relationship between the growth rate of a variable and its initial value. In economic growth empirics, the econometric analysis of such a relationship is named a beta-convergence analysis.

Formally, let  be a variable (i.e. the logarithm of the life expectancy or the Gini coefficient) and   be an observation of  for country  at date  = 0 1   . Early statistical analyses of convergence have focused on the properties of coefficient  in regressions of the following equation:

  =  +  0 +    (1)
where

  = 1  (  - 0 )
is the average growth rate of the variable at stake between the initial and terminal dates. The idea is to study whether countries with lower, for life expectancy, (or higher, in the case of the Gini index) values have experienced larger increases (or, respectively, decreases). The confirmation of the hypothesis of beta-convergence corresponds to a negative estimate for the linear regression coefficient  in equation [START_REF] Becker | The quantity and quality of life and the evolution of world Inequality[END_REF].

We display our results of for estimations vis à vis life expectancy in Table 1. This table reports the results for regressions based on equation (1) for the five periods we consider. They indicate that beta-convergence has taken place in the period 1960-2009; countries with lower initial life expectancies have experienced the largest increases in life expectancies. However, it is interesting to note that the process has not been the same for the entire time span and that for certain periods it depends on whether the distribution is truncated. For the whole distribution, the initial condition is significantly negative up until 1980, followed by a period of no beta-convergence in 1990-2009. Thus most of the catching-up process occurred up to 1980, while further convergence afterwards occurred only for the sample as a whole.

-0018 * (-4822) -0012 * (-2793) -0005 (-1165) -0012 * * (-1897) 10 -0018 * (-4130) -0016 * (-3121) -0009 * * (-1890) -0003 (-0833) -0010 (-1684) 0 -0021 * (-6124) -0020 * (-4172) -0014 * (-2380) -0004 (-0686) -0010 (-0676) 10 -0021 * (-3588) -0017 * (-2417) -0010 (-1575) -0002 (-0314) -0009 (-1567)
Notes: the  denote OLS estimates for  in eq. ( 1) for the whole ( = 0) and truncated ( = 10) distributions of both genders ( = ) and females only ( = ) The results of the beta-convergence analysis applied to the Gini coefficient are presented in Table 2. As before, we estimate equation ( 1) for the same periods. For all distributions we consider, the initial value significantly affects the (negative) growth rate until the period 1980-2009, when the catching-up process between higher and lower inequality countries ceased. -0016

(-0965) 10 -0020 * (-21932) -0024 * (-13834) -0023 * (-5752) -0027 * (-2997) -0019 (-1169) 0 -0021 * (-18357) -0025 * (-11367) -0022 * (-4906) -0020 * (-2482) -0002 (-0177) 10 -0021 * (-22347) -0025 * (-13423) -0023 * (-5440) -0017 * (-2268) -0004 (-0557)
Notes: the  denote OLS estimates for  in eq. ( 1) for the whole ( = 0) and truncated ( = 10) distributions of both genders ( = ) and females only ( = ) populations. t-statistics are in (.). * denotes significance at 5%.

Table 2. beta-convergence in Gini coefficients

While beta-convergence is informative and necessary for convergence, it is by no means a sufficient condition. In the short-run, a larger growth rate does not imply catching up. The difference in starting values could result in lower absolute values of amelioration for that period of time. Furthermore, countries may experience non monotonic dynamics or may converge to different steady-states. Given these limitations, we turn to the more demanding concept of distributional convergence.

Distributional convergence

In this section we focus on the dynamics of the shape of the cross-countries distributions of our mortality indicators, i.e. life expectancy and Gini coefficient at ages 0 and 10. Figures 3 and4 plot the variance1 of these distributions. The evolution of the variances provides an illuminating hint: there are no appreciable differences between the late 1970's and the end of the period and, upon existence, the decrease takes place over the period 1960-1975. But for truncated distributions (Figure 4), the variance of life expectancies of female population is even higher nowdays than in 1960. This already suggests preliminary evidence against a process of convergence and, as formalized below, we show this graphical intuition to be true.

Distributional convergence, also named sigma-convergence, is formally studied as follows. Let  be a variable (logarithm of life expectancy or Gini coefficient) and   be an observation of  for country  at date . Let 

  =  +  + +    (2)
where   is the mean growth rate of variable  between  and + for country , and where the slope of the relationship is defined as:

 = 1  µ 1 - (    + )  2 + () ¶ 
If the estimate for  is significant and negative, this means, using the Cauchy-Schwartz inequality, that the standard deviation has decreased over time, i.e.

  ()   + ()
Conversely, if the estimate of  is non-negative, nothing about convergence can be deduced from equation [START_REF] Bergh | Good for living? On the relationship between globalization and life expectancy[END_REF]. Even if  is positive and significant, there is not enough evidence to tell anything about convergence. It does not mean there is divergence.

Our test for sigma-convergence (Table 3) establishes the fact that the dissimilarities across high-income countries in life expectancy have not shrunk. The distribution of the life expectancies at age 10 of high-income countries stands as unequal as it was in the beginning of the period. Furthermore, this result is robust to gender differences, the inclusion of infant mortality and holds for most of the subperiods considered. It confirms, if needed, that beta-convergence does not guarantee a trajectory towards a less disperse cross section. For an intuition of this result, recall the particular case of Japan, a country which started from last place in life expectancy and ended in the top position. Although this is only an example, it illustrates the possibility that the catching-up process is not related to the reduction of the differences.

0010 (1204) 0002 (0354) 0002 (0370) -0005 (-0665) 10 0017 * (3098) 0014 * (2287) 0005 (0913) 0002 (0557) -0004 (-0598) 0 0021 * (2972) 0017 * (2345) 0010 (1394) 0006 (1253) -0004 (-0575) 10 0021 * (4914) 0019 * (3684) 0011 * * (1879) 0007 (1461) -0003 (-0552)
Notes: the  denote OLS estimate for  in eq. ( 2) for the whole ( = 0) and truncated ( = 10) distributions of both genders ( = ) and females only ( = ) populations. t-statistics are in (.). * and ** denotes significance at 5% and 10%.

Table 3. sigma-onvergence in life expectancy

Our results regarding sigma-convergence in Gini coefficients (Table 4) are also supportive of a non-convergence hypothesis overall. If we consider the entire (both genders) distribution of adult mortality, we can only reject the hypothesis of convergence for the most recent subperiods. In the remaining subperiods, the coefficient  is positive but not significantly so. For the females-only distribution, we obtain significantly positive  for the entire time span as well as the last subperiod. Still, it is worth noting that in no case does the hypothesis of convergence hold. Furthermore, if we restrict ourselves to considering female mortality, for the whole period 1960-2009, we reject with significance the hypothesis of convergence. 1960-2009 1970-2009 1980-2009 1990-2009 2000-2009 0 0006

(0274) 0006 (0362) 0004 (0412) 0021 * * (1816) 0028 * * (1889) 10 0003 (0126) 0003 (0137) 0001 (0101) 0018 (1456) 0024 (1561) 0 0037 * * (1873) 0023 (1313) 0005 (0481) 0012 (1185) 0018 * * (1781) 10 0042 (1682) 0024 (1158) 0004 (0332) 0009 (0934) 0016 (1474)
Notes: the  denote OLS estimate for  in eq. ( 2) for the whole ( = 0) and truncated ( = 10) distributions of both genders ( = ) and females only ( = ) We conclude that for both indicators, life expectancy and mortality inequality, the cross section of high-income countries stands as disperse in 2009 as in 1960. We have formally tested this hypothesis with the sigma-convergence regression and according to this idea of convergence, there has not been a reduction of differences among the adult mortality patterns of developed countries. Our results regarding beta-convergence show that the relative positions of countries in the sample, however, have been altered, indicating that there have indeed been relevant changes, but not with regards to convergence.

Although our findings rely on the definition of convergence, we believe that convergence is best assessed by the study of the moments of the cross section of countries. Even should a common steady state across countries exist (whereby countries necessarily approach a single life table distribution), in the meanwhile and for a particular period of history, convergence still should be assessed by how countries compare relative to one another. By doing so, one avoids the fundamental problem of identifying the steady state, as our measure of convergence is independent of it. In the next section we carry the analysis one step further and suggest that the presumption that there exists a unique steady state must be formally tested.

Conditional distributional convergence

In the previous section we implicitly assumed that mortality indicators of all countries were to converge to the same value, denoted as a steady state.

In a different form, as emphasized in the introduction, this is the underlying hypothesis for earlier work [START_REF] Edwards | Inequality in life spans and a new perspective on mortality convergence across industrialized countries[END_REF]. We now study conditional convergence, where groups of countries converge to different steady states (this hypothesis has also been discussed in [START_REF] Lee | Perspectives on Mortality Forecasting III. The Linear Rise in Life Expectancy: History and Prospects[END_REF].

Our discussion focuses on life expectancy and Gini coefficients, as this choice reflects our interests in obtaining measures independent of the scale of measurement and reflective of relative distances between countries.

We want to explore the hypothesis of the existence of structural differences among countries that have manifested in a permanent influence on groups of countries, leading to different steady states. Possible examples of particular factors might include climatic conditions, dietary or smoking habits and national health systems (for further discussion, see Preston, 1980). In this paper, we propose a preliminary exploration of this hypothesis. A more rigorous analysis would require evidence of the relevant conditions for the determination of the different steady states.

The following algorithm is used for determining clubs: we begin with  = 1   countries each of which we follow with a given indicator-the life expectancy or the Gini coefficient-over time and find no convergence.

Seeing no convergence amongst N countries, we systematically remove a single country from the group and compute the difference between the initial and final variances of the indicator for each possible N-1 set (N sets in total).

We then select the set that shows the greatest decrease in variances and see if sigma-convergence occurs in this set. If not, we continue the removal process and systematically remove a single country from the N-1 set and compute the difference between the initial and final variances of the indicator for each possible N-2 set (N-1 sets in total). We again test for sigma-convergence. We iterate until we find a subset of countries for which there is sigma-convergence or until the sample is reduced to a number of countries where results would no longer be statistically satisfactory. Finally, we repeat the algorithm for the distribution of both sexes and that of only females. As a robustness check, we perform the algorithm for the distributions including child mortality.

The following are the results for testing only for sigma-convergence in our adjusted samples. The reason is that since beta-convergence is observed for the whole sample, it will necessarily be observed for the adjusted ones.

Moreover, we ultimately judge the existence of convergence on the results of the sigma-convergence tests. We have different adjusted samples for every indicator and distribution; a list of them is provided in the Appendix.

Graphically, the evolutions of the variances of both indicators, as characterized in Figures 5 and6, differ greatly from those presented in Figures 3 and4, since a decrease is now observed even when child mortality is excluded.

We observe a sharp decrease in the variance of the life expectancy, which is especially pronounced in the earlier part of the time span (1960)(1961)(1962)(1963)(1964)(1965)(1966)(1967)(1968)(1969)(1970). The results of our estimation (Table 5) reveal that there has been con- -00005

(-0051) -0005 (-0388) 10 0012 * (2060) 0008 (1038) -0004 * * (-1384) -00007 (-0077) -0005 (-0394)
Notes: the  denote OLS estimate for  in eq. ( 2) for the whole ( = 0) and truncated ( = 10) distributions of both genders ( = ) and females only ( = ) To better understand this result, we test for convergence in male-only mortality (see Table 6) and find that there is convergence for both samples (adult males and whole sample) when considering the entire time span. This result is weakened for the male adults sample, since the later subperiods do not show statistically significant evidence of convergence (1980-2009 onwards).

Given this evidence, we conclude that the observed convergence is not likely to be driven by a reduction in the differences across sexes. Notes: 0 and 10 denote OLS estimate for  in eq. ( 2)

for whole and truncated distribution of male populations. * denotes significance at 5%.

-0006 * * (-1791) -0007 * * (-1599) 0014 (0961) 0027 * * (1481) 10 -0010 * (-2321) -0011 * * (-1437) -0011 * * (-1843) 0011 (0696) 0025 (1246) 0 0032 * * (1451) 0017 (0755) -00008 * (-2059) 0011 (0867) 0029 * (2323) 10 0036 (1153) 0017 (0067) -0002 * (-2158) 0008 (0615) 0027 * (2035)
Notes: the  denote OLS estimate for  in eq. ( 2) for the whole ( = 0) and truncated ( = 10) distributions of both genders ( = ) and females only ( = ) populations. t-statistics are in (.). * and ** denotes significance at 5% and 10%.

Table 7. sigma-convergence in Gini coefficients, adjusted samples

Conclusion

In this work, we tested the hypothesis of convergence in adult mortality patterns in high-income countries for a period of 49 years. First, we evaluated convergence with the underlying idea that all countries are approaching a common steady state, or what is termed unconditional convergence. To do so, we proposed a concept of convergence based on observing whether the distribution of some given indicators have become less disperse over time.

Our results empirically reject this hypothesis for both life-expectation and mortality inequality as measured by the Gini coefficient. Nevertheless, we also provided evidence that there have been changes in this period in the relative positions of countries in terms of both life expectancy and mortality inequality.

Second, we conducted a pioneer exploration of the idea of the existence of convergence clubs, formed by groups of countries that converge to a common steady state distribution of mortality. Our results support the hypothesis of conditional convergence in both the Gini coefficient and life expectancy; however, this mode of convergence does not hold for certain subperiods.

Given there is convergence for the male-only sample, we conclude that this is likely not due to a reduction in the dissimilarities across genders.

There are many related issues which we do not address in this paper out of an understanding of both the scopes of the issues and the constraints of this paper. Some of these issues deserve further attention in next step projects. For instance, we do not provide an account of the changes in mortality causes that have driven the changes observed in the mortality distributions, nor tried to relate them to the health policies adopted by the different countries. A natural next step would be to investigate the causes of death that have evolved similarly for all countries and identify the ones creating the differences we still observe. For older ages, this has been recently studied by the National Research Council (2010). Furthermore, although we have introduced the idea of conditional convergence, we have studied it only up to the extent of illustrating the justification for further exploration. A rigorous analysis would require identifying the common traits relevant to mortality patterns among countries constituting a convergence club. Naturally, the possibility of more than one convergence club should also be considered.

  Figure 1 presents the series of female's life expectancies at age 10 between 1960 and 2009 for the countries in our sample.

Figure 1 .

 1 Figure 1. Life expectancy at age 10, females.

Figure 2 .

 2 Figure 2. Gini at age 10, females. The evolution pattern of the Gini coefficients is much less clear than that of the life expectancy. In both the case of the female-only distribution and the case of both genders (Figure 12 in Appendix 7.3) there is a common trend of the reduction of mortality inequalities. However, some countries have shown increasing inequalities over the early years of the sample, such as the case of the United States, or more notably, Denmark. As expected, the decrease in Gini coefficients is more pronounced if child mortality is included (see Figures 10 and 11 in Appendix 7.3).

Figure 3 .Figure 4 .

 34 Figure 3. Variances of life expectancy and Gini at age 0

13

  Documents de Travail du Centre d'Economie de la Sorbonne -2012.76

Figure 5 .Figure 6 .

 56 Figure 5. Variances of life expectancy and Gini at age 0, adjusted samples

  vergence in life expectancy (both at birth and at age 10) for the mortality distributions including both genders. In particular, for the whole sample, convergence occurs in the entire time span and the middle periods 1970-2009 to 1990-2009 but not for the last period 1960-2009. In the case of the entire adult population, convergence only occurs in the last periods, 1980-2009 and onwards. Interestingly, we do not find support for the hypothesis of convergence for the female-only distribution for the period 1960-2009. There is, however, evidence of convergence for the restricted female samples for the period 1980-2009.

Finally, one could

  question our choice of studying countries instead of individuals. Indeed, if the focus is on welfare[START_REF] Edwards | The cost of uncertain life span[END_REF], it seems reasonable to have individuals as unit of analysis (see Bourguignon and Christian Morrisson, 2002, for a work that takes this approach and more recently Life expectancy at 0 in the female population: USA, Denmark, Scotland, Italy, Japan.Life expectancy at 10 in the female population: USA, Denmark, Scotland, Italy, Japan.Gini of age-at-death at 0 in the whole population: USA, Scotland, Italy, Finland, United Kingdom Gini of age-at-death at 10 in the whole population: USA, Scotland, Italy, United Kingdom, Finland Gini of age-at-death at 0 in the female population: USA, Scotland, Italy, Spain, Denmark.Gini of age-at-death at 10 in the female population: USA, Scotland, Italy, Spain, Denmark.

7. 2

 2 Testing the normality assumption Cramer-von Mises, Anderson-Darling, and Watson nonparametric empirical distribution tests can be used to verify the normality for truncated ages-atdeath distributions for Sweden and United States for the year 2000. These tests are based on the comparison between the empirical distribution and the theoretical normal distribution functions and use the estimates for the mean and standard deviation of the empirical distributions based on the data. For a general description of empirical distribution function testing, see d'Agostino and Stephens (1986). The results in Table8summarize the outcome of the other distributions we consider are reproduced below.

Figure 7 .

 7 Figure 7. Life expectancy at age 0, females.

Figure 10 .

 10 Figure 10. Gini coefficient at age 0, females.

Figure 8 .

 8 Figure 8. Life expectancy at age 0, both genders.

Figure 11 .

 11 Figure 11. Gini coefficient at age 0, both genders.

Figure 9 .

 9 Figure 9. Life expectancy at age 10, both genders.

Figure 12 .

 12 Figure 12. Gini coefficient at age 10, both genders.

Table 5 .

 5 sigma-convergence in life expectancy, adjusted samples

	populations. t-statistics are in (.). * and ** denotes significance at 5% and 10%.

Table 6 .

 6 sigma-convergence in Life expectancy, adjusted samples We find conclusive results regarding the Gini index (Table7) in favor of the conditional convergence hypothesis. When we consider the entire period, convergence is robust to the inclusion of child mortality. It is noteworthy that convergence occurred in the first part of the time span (until the period 1990-2009, not included), especially for future work unpacking the causal explanations behind convergence from an historical standpoint among others.

	Restricting our sample to female mortality has similar results as that of life
	expectancy.
		1960-2009 1970-2009 1980-2009 1990-2009 2000-2009
	0	-0006 * * (-1635)

Documents de Travail du Centre d'Economie de la Sorbonne -2012.76

One could have also computed a variance weighted by the relative size of the countries as in Wilmoth et al. (2010).12 Documents de Travail du Centre d'Economie de la Sorbonne -2012.76

We thank Ronald Lee and Shripad Tuljapurkar for stimulating comments and the European Research Council (ERC Stg Grant DU 283953) for financial support. 1

 [START_REF] Becker | The quantity and quality of life and the evolution of world Inequality[END_REF]. Studying the convergence patterns across countries, however, improves our understanding of crucial topics such as the existance of a common mortality distribution or what are the factors that contribute to the dynamics of mortality. Issues that are directly related to specific applications such as the forecasting of mortality dynamics (see for instance Li and [START_REF] Li | Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method[END_REF] or the evaluation of national health policies.

Appendix

Samples of countries

Throughout the paper, we use a number of different samples. First, we have tested unconditional convergence on the following sample of high-income countries.

Whole sample: Australia, Austria, Belgium, Canada, Switzerland, Italy, Japan, West Germany, Portugal, Sweden, USA, Denmark, Spain, Finland, Luxembourg, Netherlands, Norway, New Zealand, France, Northern Ireland, Scotland, Britain, Ireland, Israel Second, we have constructed a number of adjusted samples, obtained according to the method described in the text, to test for conditional convergence. For simplicity, we report the countries excluded from the whole sample.

Life expectancy at 0 in the whole population: USA, Denmark, Scotland, Australia, Japan.

Life expectancy at 10 in the whole population: USA, Denmark, Scotland, Switzerland, Japan statistical tests.

Sweden United States Parameter estimates

Mean 90089

[7457]

90094

[8683]

Standard deviation 127290

[14832]

Anderson-Darling 1280 When evaluated formally, the tests demonstrate that the hypothesis that the distributions of ages-at-death for Sweden and the United Sates, even when truncated below age 10, follow a normal distribution is rejected at the 1% significance level. This conclusion provides evidence that the Kullback-Leiber divergence approach seems inappropriate for studying distributional convergence in mortality.

Further descriptive statistics

In the core of the text, we presented the indicators computed with distributions of the age-at-death truncated at age 10 for female. The indicators for


Alexis Joly

Julien Champ

Pierre Letessier

Nicolas Hervé

Olivier Buisson

Marie-Luce Viaud

Visual-Based Transmedia Events Detection

Keywords: H.3 [Information Storage And Retrieval]: Miscellaneous Event Detection, Transmedia, mining

This paper presents a visual-based media event detection system based on the automatic discovery of the most circulated images across the main news media (news websites, press agencies, TV news and newspapers). Its main originality is to rely on the transmedia contextual information to denoise the raw visual detections and consequently focus on the most salient transmedia events.

INTRODUCTION

Automatically detecting, tracking and indexing media events is crucial for structuring and searching news media as well as huge audio-visual archives. Text-based search and mining methods are definitely a powerful tool in this regard but in this work we are rather interested in visual news contents, i.e. images illustrating the news delivered to the general public. The visual content of a media event is actually an integral part of its semantic and even sometimes the main reason of its existence or media impact (the Jyllands-Posten Muhammad cartoons are for instance the main reason of the worldwide media controversy itself). However, one of the limitation of current visual search and mining methods, is that they suffer from a high level of noise, even when they attempt to stick on accurate visual matches such as copies, near-duplicates or rigid objects [START_REF] Joly | Content-based copy retrieval using distortion-based probabilistic similarity search[END_REF][START_REF] Philbin | Lost in quantization: Improving particular object retrieval in large scale image databases[END_REF]. Frequent visual items are actually likely to depict undesired contents from the media event mining perspective (commercials, inserted texts, banners, etc.). The main claims of our approach is that (i) many of these false positives can be filtered by considering only transmedia visual matches and (ii) most salient media events can be easily detected by looking at the transmedia contextual information. As an example, a press agency picture that is circulated over several websites, TV channels and newspapers is more likely to depict a salient media event than a highly frequent image on a single news media.

NEWS CRAWLING AND INDEXING

Four categories of news media are crawled and indexed by our system with more or less streams in each category: Category 1 -Press agencies: the whole stream of AFP's multimedia content is indexed in our system. AFP is the oldest press agency in the world and one of the three largest.

Each multimedia news report includes at least one image, a core text and a set of metadata. Category 2 -News websites: about 1,500 French websites are crawled from RSS feeds and indexed in our system. Targeted websites are news pure players (12), radios (14), TVs (17), press (71), blogs (339), political actors such as senators, deputies, presidential candidates (646), trades unions (19), political parties (263) and institutions (62). Category 3 -Newspapers: 7 national newspapers are collected numerically and indexed in our system (La Croix, Liberation, Le Monde, 20 Minutes, Direct Matin, les Echos, le canard enchaine). Category 4 -TV news: News & magazines from 10 French TV channels are collected and indexed in our system: 5 public broadcasting, 3 generalist private channels and 2 news channels.

To ensure a homogeneous integration of these heterogeneous contents, each news document follows a specific workflow depending on its media support. The first step collects native streams metadata and imports additional resources (subtitles, manually annotated notice from TV and Radio databases). Then the content is segmented and structured (title, summary, paragraphs, author, date). Hyperlinks, videos, images are extracted and Media Metadata Files gathering media description (caption, size, duration, author...) are generated. TV and Radio streams are processed by a speech-to-text software. Finally, textual documents are processed by a named entity recognition tool (peoples, places and organizations) and a noun phrases extractor. As discussed further, these enriched metadata are used on top of our visual-based media events detector to automatically build the description of the related media events in the GUI.

All pictures encountered in the streams are considered for content-based visual indexing. A weekly visual index is therefore constructed at the end of each week. For the last category (TV streams), one visual frame is extracted every second and indexed. Visual indexes are built according to the following steps: SIFT features are first extracted from all images and then converted to space-efficient and time-efficient binary hash codes using RMMH [START_REF] Joly | Random maximum margin hashing[END_REF]. 256 hash functions are generated with this family and used to convert SIFT features into 256-bits hash codes. Hash codes are stored in two ways (with full replication): (i) a simple document-oriented storage allowing to get efficiently the hash codes of a given query document (ii) a hash table using the first 24 bits of the hash codes as keys and the full hash code as value. This allows performing efficient approximate KNN-search of any query hash code using the a posteriori multi-probe strategy of [START_REF] Joly | A posteriori multi-probe locality sensitive hashing[END_REF] and a Hamming distance as similarity metric during the filtering step.

Precise Visual Search: The search of a query image in the visual index of a week is done using the method first introduced in [START_REF] Joly | Logo retrieval with a contrario visual query expansion[END_REF]. It allows the discovery of different kinds of trust-full visual matches such as copies, part-based copies, near-duplicates, and even smaller rigid visual objects such as logos, trademarks, buildings, faces of the same person with the same pose, manufactured objects, etc. The basic principle is the following: approximate KNN's of each local feature of the query image are searched in the index and the resulting candidate visual matches are filtered with a RANSAC-like geometry consistency checking. Retrieved images are finally further filtered by the a contrario thresholding method described in [START_REF] Joly | Logo retrieval with a contrario visual query expansion[END_REF] and that allows a good control of the false positives rate.

Transmedia Search strategy: In order to drastically reduce the search load, TV frames are not searched at all (but might be still retrieved in the index by the queries of the other 3 media categories). Since we are mostly interested in transmedia visual matches, this is actually a useful trick that does not prevent to discover pictures or objects instantiated in at least two media categories (including the TV category). All images of the three other media categories are searched in the visual index of the week they belong as well as in the two neighboring weeks.

Clustering & Transmedia filtering: The matching graphs produced by the previous step for a given period of interest is then processed by the MCL algorithm [START_REF] Van Dongen | A cluster algorithm for graphs[END_REF] in order to group images in relevant clusters. Finally, we rank the discovered clusters according to a diversity score in the number of media supports (i.e. using the transmedia context). More practically, we first assigned off-line a prefixed weight to any of the considered media. This is done by first equally weighting the media categories: a mass of 0.25 is assigned to each of the 4 categories. The mass of a given media category is then distributed uniformly between all the media streams or programs belonging to it. The mass of AFP stream for instance remains equal to 0.25 whereas the mass of each of the TV channels is 10 times lower. Now, the diversity score of a discovered cluster is computed by summing the weights of the media composing it. Only the top-k clusters according to this score are finally kept as interesting visual media events. Note that the key issue of this transmedia filtering is to effectively remove a lot of noisy clusters such as ads, channels settings, newspapers headers, banners, etc. Visual matches arising across all media categories are actually much more unlikely to be false positives than mono-media visual matches. Figure 1 illustrates a noisy cluster that was pruned by the transmedia contextual reranking and filtering and, on the other side, the top-3 clusters selected by our method for a given week. It well shows that the clusters can have more or less visual diversity in the detected patterns (from small objects to duplicated images). But still, they all correspond to very salient media events for that week.

NAVIGATION IN NEWS IMAGES

A front-end GUI built on top of the system allows browsing the image of the day, the image of the week or the image of the month thanks to an interactive timeline. Snapshots of the GUI are presented in Figure 4. The image of each period (day, week or month) and the associated description and keywords were computed as follows: (i) our clustering & contextual reranking method is applied to the visual matching graph restricted to the respective period (ii) only the top-1 cluster (according to the diversity score) is kept (iii) the most frequent keywords in the cluster's metadata are computed (iv) we then choose the image of the cluster hav-

Figure 1 :

 1 Figure 1: (left) A pruned noisy cluster, (right) top-3 selected clusters for the first week of Sept 2011 (presidential primary, USOpen, mediator scandal) ing the highest number of occurrences of these keywords and use the corresponding description as event description. Figure 4 presents the result obtained for three successive weeks from the 3rd of October 2011 to the 24th of October 2011.

Figure 2 :

 2 Figure 2: Images of the weeks


Thomas Guionnet
email: thomas.guionnet@inria.fr

Laurent Guillo
email: laurent.guillo@inria.fr

Christine Guillemot
email: christine.guillemot@inria.fr

HEVC implements a candidate vector list for merge and skip modes. The construction of this list is normatively specified. A simplification of the candidate list construction process has been proposed in JCTVC-G593. The impact of this simplification on the HEVC coding performance is negligible while decreasing the complexity. It has been adopted and is implemented in the HM 6.1, hence also in the current HTM 3. It is reported in this document that in the context of 3D video coding, the simplification of the candidate list construction has a non-negligible impact on the encoding performance of the side views (0.4% loss on average). The base view is unaffected, thus confirming that the simplification has a negligible impact on the HEVC coding performance.

Introduction

In JCTVC-G593 [START_REF] Bici | Non-CE13: Simplification of merge mode[END_REF], a simplification of the merge candidate list construction process is proposed. More specifically, the complexity is decreased by reducing the number of necessary vector comparisons during the pruning of the candidate list. Moreover, it becomes possible to implement a shortcut in the decoder, by constructing the candidate vector list only up to the required index. The counterpart of this simplification is that the pruning of candidate vectors is not perfect anymore. A motion vector can be present several times in the list, thus impairing its efficiency. This phenomenon has a negligible impact on the HEVC coding performance though.

In the 3D video coding context, it has been observed that the impact of the pruning process simplification is non-negligible on the side views, as shown in Table 1.

Experimental results

The experiment has been conducted with HTM 3.0 and evaluation is based on common test conditions [START_REF] Schwarz | Common test conditions for 3DV experimentation[END_REF].

The simplified pruning process is deactivated by setting the macro SIMP_MRG_PRUN to 0 in the typedef.h file.

Results are provided in Table 1. It is clearly observed that the coding performance is almost unchanged on view 0. On the other hand 0.4 % is gained on side views on average by deactivating the simplified pruning process. A maximum of 1.1% gain is reported on PoznanHall2 view 1.

The HTM 3.0 has been modified in order to deactivate the simplified pruning process only on side views, thus keeping an HEVC compliant base view. Similar results are obtained, as shown in Table 2.

Table 1: Results obtained with HTM 3.0 and SIMP_MRG_PRUN set to 0, compared to HTM 3.0. video 0 video 1 video 2 video only enc time Balloons 0,0% -0,6% -0,7% -0,3% 100,5% Kendo -0,1% -0,4% -0,7% -0,3% 100,1% Newspapercc 0,0% -0,2% -0,3% -0,1% 97,7% GhostTownFly 0,0% 0,0% -0,1% 0,0% 103,5% PoznanHall2 0,0% -1,1% -0,4% -0,4% 100,4%

PoznanStreet -0,1% -0,2% -0,3% -0,2% 99,2% UndoDancer 0,0% -0,3% -0,5% -0,2% 103,0% 1024x768 0,0% -0,4% -0,6% -0,3% 99,4% 1920x1088 0,0% -0,4% -0,3% -0,2% 101,5% average 0,0% -0,4% -0,4% -0,2% 100,6%

Conclusion

The pruning process simplification process proposed in [START_REF] Bici | Non-CE13: Simplification of merge mode[END_REF] has a non-negligible impact on side views encoding in the HTM 3.0. Therefore, it may be suggested to deactivate or modify this feature on side views.

Table 2 : Results obtained with HTM 3.0 and SIMP_MRG_PRUN deactivated on views 1 and 2, compared to HTM 3.0.

 2

		video 0 video 1 video 2 video only enc time dec time
	Balloons	0,0%	-0,3%	-0,5%	-0,2%	100,5%	87,6%
	Kendo	0,0%	-0,3%	-0,6%	-0,3%	100,5%	86,2%
	Newspapercc	0,0%	-0,1%	-0,2%	-0,1%	99,3%	87,1%
	GhostTownFly	0,0%	-0,1%	-0,3%	-0,1%	102,3%	92,8%
	PoznanHall2	0,0%	-1,2%	-0,6%	-0,5%	104,0%	92,3%
	PoznanStreet	0,0%	-0,3%	-0,3%	-0,1%	98,7%	90,8%
	UndoDancer	0,0%	-0,2%	-0,4%	-0,1%	103,9%	91,1%
	1024x768	0,0%	-0,3%	-0,4%	-0,2%	100,1%	87,0%
	1920x1088	0,0%	-0,4%	-0,4%	-0,2%	102,2%	91,8%
	average	0,0%

-0,4% -0,4% -0,2% 101,3% 89,7%

Date Saved: 2012-11-21 5 Patent rights declaration(s) INRIA does not have any current or pending patent rights relating to the technology described in this contribution.

Joint Collaborative Team on 3D Video Coding Extension Development of ITU-T SG 16 WP 3 and ISO/IEC JTC 1/SC 29/WG 11 1st Meeting: Stockholm, SE,


Thomas Guionnet
email: thomas.guionnet@inria.fr

Laurent Guillo
email: laurent.guillo@inria.fr

Christine Guillemot
email: christine.guillemot@inria.fr

HEVC implements a candidate vector list for merge and skip modes. When merge or skip modes are selected, a merge index is written in the bitstream. This index is first binarized using a unary code, then CABAC encoded. A CABAC context is dedicated to the first bin of the unary coded index while the remaining bins are considered as equiprobable. This strategy is efficient as long as the candidate list is constructed such as being ordered by decreasing index occurrence probability. In the context of 3D video encoding, an inter-view motion vector predictor is added at the first position of the candidate list. It is reported in this document that the inter-view motion vector predictor is not always the most probable candidate. It actually depends on the video sequence characteristics. Therefore, a dynamic candidate vector list ordering is proposed. Coding gains of 0.1 % on average are observed on side views and up to 0.6% is attained for the GTFly sequence view 2.

Introduction

HEVC relies on a candidate vector list for merge and skip modes. The efficiency of this approach depends on two parts: first the relevance of the vectors present in the list and second the encoding efficiency of the selected merge index. The candidate vector list is designed such that the vectors are ordered by decreasing likelihood of selection. This property is then exploited for merge index coding. The merge index is binarized using a unary code, then CABAC encoded. Except for the first bin, the bins are considered as equiprobable when fed to the CABAC. Therefore, the main factor ensuring efficient merge index coding is the unary code associated to the decreasing likelihood ordering of the vectors.

In the context of 3D video coding, an inter-view motion vector predictor is added into the candidate list. This vector is especially relevant and thus selected very often. Therefore, it is always placed at first position in the candidate list. By doing simple statistics, it has been observed that although this vector is the most likely to be selected on average, its relevance depends on pictures or even sequences characteristics. Therefore, a dynamic list reordering process is proposed in order to improve the efficiency of inter-view motion vector prediction.

Proposed method

The proposed process is performed symmetrically in the encoder and decoder. It is described on the decoder side.

A Merge index histogram is computed on the fly. In order to avoid constraining dependencies and robustness loss, the process is reinitialized at the same points as the entropy coder (for instance at the beginning of each slice). The histogram is not initialized with 0 values, but with arbitrary exponentially decreasing values as shown in Table 1. It brings stability when the process begins by avoiding taking index swapping decision without statistically significant data accumulation. Given a current histogram, a conversion table can be simply calculated. It allows deriving the merge index to encode given the actual index in the list, and conversely the actual index in the list given a decoded index. Each time a Merge index is decoded from the bitstream, it is converted to its actual position in the list and the histogram is updated accordingly. The conversion table is updated only at the end of each LCU.

Experimental results

The experiment has been conducted with HTM 3.0 and evaluation is based on common test conditions [START_REF] Schwarz | Common test conditions for 3DV experimentation[END_REF].

Results are provided in Table 2. 0,0% 0,0% 0,0% 0,0% 0,1% 0,0% 99,5% 100,8% Kendo 0,0% 0,0% -0,1% 0,0% -0,1% 0,0% 101,0% 101,2% Newspapercc 0,0% 0,1% -0,1% 0,0% 0,3% 0,2% 103,1% 100,0% GhostTownFly 0,0% -0,5% -0,6% -0,1% -0,1% -0,1% 107,7% 100,6% PoznanHall2 0,0% 0,1% 0,1% 0,0% 0,0% 0,0% 107,2% 99,0%

PoznanStreet 0,0% 0,0% 0,1% 0,0% 0,0% 0,0% 108,1% 100,5% UndoDancer 0,0% -0,3% -0,2% -0,1% 0,0% 0,0% 106,3% 101,6% 1024x768 0,0% 0,0% 0,0% 0,0% 0,1% 0,1% 101,2% 100,7% 1920x1088 0,0% -0,2% -0,1% 0,0% 0,0% 0,0% 107,3% 100,4% average 0,0% -0,1% -0,1% 0,0% 0,0% 0,0% 104,7% 100,5%

Conclusion

A merge index coding improvement is proposed. The likelihood of merge index values is evaluated by filling dynamically a histogram. The shortest codeword can then be assigned to the most likely merge index. The reported coding gains are low on average (0.1 % on side views) but can be high (up to 0.6%) depending on the sequence characteristics. Improvement is expected by refining the histogram initialization procedure. The complexity of the proposed method is negligible.

As this method achieves relevant gains with no added complexity, we propose to include it in a core experiment for further study.

Table 2 :

 2 Results obtained with HTM 3.0 and Merge list reordering, compared to HTM 3.0. video 0 video 1 video 2 video only synthesized only coded & synthesized enc time dec time Balloons

Table 1 : Initialization values of the merge index histogram

 1

	32 16 8 4 2 1

Date Saved: 2012-11-21 6 Patent rights declaration(s) INRIA does not have any current or pending patent rights relating to the technology described in this contribution.

Joint Collaborative Team on 3D Video Coding Extension Development of ITU-T SG 16 WP 3 and ISO/IEC JTC 1/SC 29/WG 11 1st Meeting: Stockholm, SE,


Thomas Guionnet
email: thomas.guionnet@inria.fr

Laurent Guillo
email: laurent.guillo@inria.fr

Christine Guillemot
email: christine.guillemot@inria.fr

HEVC implements a candidate vector list for merge and skip modes. The construction of this list has been extensively studied in the JCT-VC group (see for instance JCTVC-G039). It has been shown in JCTVC-I0293 that it is possible to improve the HEVC coding performance by adding in the merge list copies of the first candidate shifted by an arbitrary offset. The same basis is considered in this document and applied to disparity compensation. A gain of 0.4 % is obtained on average on side views.

Introduction

HEVC relies on a candidate vector list for merge and skip modes. The efficiency of this approach depends highly on the relevance of the vectors present in the list. The construction of this list has been extensively studied [START_REF] Bross | CE9: Summary Report of Core Experiment on MV Coding and Skip/Merge Operations[END_REF]. During the last JCT-VC meeting, it has been shown in [START_REF] Yamamoto | Merge candidate refinement for uni-predictive block[END_REF] that it is possible to improve the HEVC coding performance by adding in the merge list copies of the first candidate shifted by an arbitrary offset. More precisely, in [START_REF] Yamamoto | Merge candidate refinement for uni-predictive block[END_REF], if there is available space in the candidate vector list, up to two new candidates are added: the first vector of the list shifted by an offset of (-4; 0) and (4; 0). It corresponds to a horizontal shift of -1 and 1 pixel respectively. In the context of video encoding of multiple rectified views, having a fine horizontal adjustment may be desirable for efficient disparity compensated prediction. Therefore, it is proposed to extend the candidate vector list with candidates pointing to the base view and shifted by horizontal offsets.

Proposed method

Let us remind that a candidate in the merge list may contain one or two vectors (L0, L1 or both). The candidate list construction proceeds as follows.

1. Construct the list as currently specified.

2. Scan the list from the first to the last position. The first candidate found in the list which has either its L0 or L1 vector (or both) pointing to the base view is selected. If no such candidate exists, the process ends. The offsets considered are (-4; 0) and (4; 0), as in [START_REF] Yamamoto | Merge candidate refinement for uni-predictive block[END_REF]. Note that the method is valid for both unidirectional and bi-directional vectors. In the latter case, the offsets are applied to only one of the two vectors.

Experimental results

The experiment has been conducted with HTM 3.0 and evaluation is based on common test conditions [START_REF] Schwarz | Common test conditions for 3DV experimentation[END_REF].

Results are provided in Table 1. GhostTownFly 0,0% -0,5% -0,4% -0,1% -0,1% -0,1% 106,3% 101,8% PoznanHall2 0,0% -0,6% -0,2% -0,2% -0,2% -0,2% 103,7% 99,7% PoznanStreet 0,0% -0,4% -0,2% -0,2% -0,1% -0,1% 104,7% 100,0% UndoDancer 0,0% -0,3% -0,2% -0,1% 0,0% 0,0% 104,1% 101,4% 1024x768 0,0% -0,5% -0,5% -0,2% -0,1% -0,1% 100,6% 100,9% 1920x1088 0,0% -0,4% -0,3% -0,1% -0,1% -0,1% 104,7% 100,7% average 0,0% -0,4% -0,4% -0,2% -0,1% -0,1% 102,9% 100,8%

Furthermore, a simpler version in which the first candidate of the list is systematically selected, whether it is disparity compensated or not, has been implemented. Results are reported in Table 2.

Conclusion

An extension of the merge list is proposed. It is targeted at improving disparity compensated prediction. A 0.4% coding gain on side views on average is obtained. The complexity of the decoder is increased by less than 1%.

Given the reported gains, we propose to include the method in a core experiment for further study.

3 .

 3 Derive two refined candidates by adding two offsets to the selected candidate as follows a. If the L0 vector is pointing to base view, add the offsets to the L0 vector only b. Else if the L1 vector is pointing to base view, add the offsets to the L1 vector Page: 2 Date Saved: 2012-11-21

Table 1 : Results obtained with HTM 3.0 and Merge list extension with DCP candidate, compared to HTM

 1

	3.0.

Table 2 : Results obtained with HTM 3.0 and Merge list extension with first candidate, compared to HTM 3.0.

 2

		video 0 video 1 video 2 video only synthesized only coded & synthesized enc time	dec time
	Balloons	0,0%	-0,3%	-0,4%	-0,2%	#VALEUR!	#VALEUR!	100,8%	101,3%
	Kendo	0,0%	-0,4%	-0,5%	-0,2%	#VALEUR!	#VALEUR!	104,2%	102,9%
	Newspapercc	0,0%	-0,8%	-0,2%	-0,3%	#VALEUR!	#VALEUR!	104,9%	100,9%
	GhostTownFly	0,0%	-0,3%	-0,2%	-0,1%	#VALEUR!	#VALEUR!	108,4%	103,2%
	PoznanHall2	0,0%	-0,6%	-0,7%	-0,3%	#VALEUR!	#VALEUR!	106,0%	99,5%
	PoznanStreet	0,0%	-0,3%	-0,1%	-0,1%	#VALEUR!	#VALEUR!	107,4%	100,0%
	UndoDancer	0,0%	-0,2%	-0,1%	-0,1%	#VALEUR!	#VALEUR!	107,8%	102,2%
	1024x768	0,0%	-0,5%	-0,4%	-0,2%	#VALEUR!	#VALEUR!	103,3%	101,7%
	1920x1088	0,0%	-0,3%	-0,3%	-0,1%	#VALEUR!	#VALEUR!	107,4%	101,2%
	average	0,0% -0,4% -0,3%	-0,2%	#VALEUR!	#VALEUR!	105,6% 101,4%

Page: 3 Date Saved: 2012-11-21

Patent rights declaration(s)INRIA does not have any current or pending patent rights relating to the technology described in this contribution.

Joint Collaborative Team on 3D Video Coding Extension Development of ITU-T SG 16 WP 3 and ISO/IEC JTC 1/SC 29/WG 11 1st Meeting: Stockholm, SE,


Thomas Guionnet
email: thomas.guionnet@inria.fr

Laurent Guillo
email: laurent.guillo@inria.fr

Christine Guillemot
email: christine.guillemot@inria.fr

HEVC implements a candidate vector list for merge and skip modes. When merge or skip modes are selected, a merge index is written in the bitstream. This index is first binarized using a unary code, then CABAC encoded. A CABAC context is dedicated to the first bin of the unary coded index while the remaining bins are considered as equiprobable. This strategy is efficient as long as the candidate list is constructed such as being ordered by decreasing index occurrence probability. In the context of 3D video encoding, an inter-view motion vector predictor is added at the first position of the candidate list. It is reported in this document that the inter-view motion vector predictor is not always the most probable candidate. It actually depends on the video sequence characteristics. Therefore, a dynamic candidate vector list ordering is proposed. Coding gains of 0.4 % on average are observed on side views and up to 1.0% is attained for the Ghost Town Fly sequence for both side views.

Introduction

HEVC relies on a candidate vector list for merge and skip modes. The efficiency of this approach depends on two parts: first the relevance of the vectors presents in the list and second the encoding efficiency of the selected merge index. The candidate vector list is designed such that the vectors are ordered by decreasing likelihood of selection. This property is then exploited for merge index coding. The merge index is binarized using a unary code, then CABAC encoded. Except for the first bin, the bins are considered as equiprobable when fed to the CABAC. Therefore, the main factor ensuring efficient merge index coding is the unary code associated to the decreasing likelihood ordering of the vectors.

In the context of 3D video coding, an inter-view motion vector predictor is added into the candidate list. This vector is especially relevant and thus selected very often. Therefore, it is always placed at first position in the candidate list. By doing simple statistics, it has been observed that although this vector is the most likely to be selected on average, its relevance depends on pictures or even sequences characteristics. Therefore, a dynamic list reordering process is proposed in order to improve the efficiency of inter-view motion vector prediction. This document is the follow up of JCT3V-A0133 [2], as part of the core experiment CE5.h. A cross-check is available in JCT3V-B0097.

Proposed method

Dynamic merge index principle

The proposed process is performed symmetrically in the encoder and decoder. It is described on the decoder side.

For simplification purpose, the proposed method is applied only for merge index values below 3. A Merge index histogram is computed on the fly. In order to avoid constraining dependencies and robustness loss, the process is reinitialized at the same points as the entropy coder (for instance at the beginning of each slice). The histogram is not initialized with 0 values, but with arbitrary exponentially decreasing values as shown in Table 1. It brings stability when the process begins by avoiding taking index swapping decision without statistically significant data accumulation. Given a current histogram, a conversion table can be simply calculated. It allows deriving the merge index to encode given the actual index in the list, and conversely the actual index in the list given a decoded index. 0 1 2 Each time a Merge index is decoded from the bitstream, it is converted to its actual position in the list and the histogram is updated accordingly. The conversion table is updated only at the end of each LCU.

Dynamic merge index process

The method can be summarized as follows:

Slice decoding process: associate a merge index histogram array (merge_idx_histo) and a conversion table (merge_idx_conv) to each starting slice decoding process. The merge_idx_histo and merge_idx_conv arrays are initialized as depicted in Table 1 andTable 2 respectively. Merge index parsing process: for each parsed merge_idx, set

 merge_idx = merge_idx_conv [merge_idx]  merge_idx_histo[merge_idx] = merge_idx_histo[merge_idx] + 1
Coding unit decoding process: At the end of each LCU decoding process, update merge_idx_conv according to the current state of merge_idx_histo. An example of merge index histogram and its associated conversion table are provided in Table 3 andTable 4 respectively

Parsing process adaptation to dynamic merge index

The merge index is binarized using the truncated unary (TU) binarization process. Up to 5 bins can be generated. The first bin is encoded using a CABAC context while the remaining bins are considered as equi-probable (bypass).

When using dynamic merge index, index re-allocation can happen at any moment. It obviously impacts the statistics of the first bin, which is encoded using CABAC. Therefore, we define a set of CABAC contexts for the first bin, one for each possible permutation of indexes. Thus, we have 6 different CABAC contexts for the first bin, adressed by the state of merge_idx_conv.

Moreover, as the dynamic merge index strategy tends to affect significantly the 3 first bins statistics, CABAC contexts are proposed for up to 3 bins. Therefore, for each of these 3 bins, 6 CABAC contexts are defined in order to take into account all possible merge index permutations. The initialisation data for all these contexts is provided in Table 6. The usage of these contexts is summarized in Table 5 andTable 7. ,3,6,9,12,15,18, 21,24,27,30,33 1,4,7,10,13,16,19 ,22,25,28,31,34 2,5,8,11,14,17,20 ,23,26,29,32,35 bypass bypass na

Experimental results

The experiment has been conducted with HTM 4.0.1 and evaluation is based on common test conditions [1].

Two tests were run:

-the first one is related to the integration in HTM 4.0.1 of [2] described in section 2.1 and 2.2.

-the second one implement in addition the strategy described in section 2.3 which takes advantage of CABAC contexts for the first three bins to take into account all possible merge index permutations

Results are respectively provided in Table 8 and Table 9.

Conclusion

The coding cost of merge index can be significantly reduced by adopting a dynamic merge index reallocation strategy which takes into account all possible merge index permutations, followed by an adapted parsing and context-based CABAC coding strategy. No complexity is added. We propose to adopt it.

[1] Dmytro Rusanovskyy, Karsten Müller, Anthony Vetro, « Common test conditions for 3DV Core Experiments », JCT3V-A1100, July 2012, Stockholm, Sweden.

[2] Thomas Guionnet, Laurent Guillo, Christine Guillemot, « CE5.h related: Reducing the coding cost of merge index by dynamic merge candidate list re-ordering », JCT3V-A0133, July 2012, Stockholm, Sweden. Balloons 0,0% -0,2% -0,2% -0,1% -0,1% -0,1% 100,4% 100,6% Kendo 0,0% -0,1% 0,0% 0,0% 0,0% 0,0% 100,6% 100,9% Newspapercc 0,0% -0,1% -0,3% -0,1% -0,1% -0,1% 100,0% 98,9% GhostTownFly 0,0% -1,0% -1,0% -0,2% -0,2% -0,2% 102,3% 99,7% PoznanHall2 0,0% -0,1% -0,4% -0,1% -0,1% -0,1% 102,3% 98,3% PoznanStreet 0,0% -0,6% -0,4% -0,2% -0,2% -0,2% 99,8% 99,6% UndoDancer 0,0% -0,7% -0,6% -0,2% -0,2% -0,2% 100,1% 99,7% 1024x768 0,0% -0,1% -0,1% -0,1% 0,0% 0,0% 100,3% 100,1% 1920x1088 0,0% -0,6% -0,6% -0,2% -0,2% -0,2% 101,1% 99,3% Average 0,0% -0,4% -0,4% -0,1% -0,1% -0,1% 100,8% 99,7%

6

  Patent rights declaration(s)INRIA may have current or pending patent rights relating to the technology described in this contribution and, conditioned on reciprocity, is prepared to grant licenses under reasonable and non-discriminatory terms as necessary for implementation of the resulting ITU-

Table 1 : Initialization values of the merge index histogram

 1

	32 16 8

Table 2 : Initialization values of the conversion table

 2

Table 3 : Initialization values of the merge index histogram Table 4: Initialization values of the conversion table

 3

	1 2 0

Table 5 : Association of ctxIdx and syntax elements for each slice type in the initialisation process of merge_idx.

 5

	merge_idx_conv		Init type
	combination	0	1	2
	[0, 1, 2]		0..2	18..20
	[0, 2, 1]		3..5	21..23
	[1, 0, 2]		6..8	24..26
	[1, 2, 0]		9..11	27..29
	[2, 0, 1]		12..14 30..32
	[2, 1, 0]		15..17 33..35

Table 6 : Values of variable initValue for merge_idx ctxIdx.

 6

	Initialisation
	variable

Table 7 : Assignment of ctxIdxInc to merge_idx syntax element with context coded bins

 7

	Page: 4	Date Saved: 2012-11-21

Table 8 : Results obtained with HTM 4.0.1 and dynamic merge index, compared to HTM 4.0.1.

 8

						synthesized	coded &
		video 0	video 1 video 2 video only	only	synthesized	enc time dec time
	Balloons	0,0%	-0,1%	-0,1%	0,0%	-0,1%	-0,1%	100,7%	102,9%
	Kendo	0,0%	0,0%	0,0%	0,0%	0,0%	0,0%	101,1%	103,0%
	Newspapercc	0,0%	-0,1%	0,0%	0,0%	0,1%	0,1%	100,1%	101,7%
	GhostTownFly	0,0%	-0,2%	-0,3%	-0,1%	0,0%	-0,1%	102,1%	102,5%
	PoznanHall2	0,0%	0,1%	-0,1%	0,0%	0,0%	0,0%	102,4%	104,1%
	PoznanStreet	0,0%	-0,7%	-0,3%	-0,1%	-0,1%	-0,1%	100,8%	102,0%
	UndoDancer	0,0%	-0,2%	-0,3%	-0,1%	-0,1%	-0,1%	101,7%	101,1%
	1024x768	0,0%	-0,1%	0,0%	0,0%	0,0%	0,0%	100,6%	102,5%
	1920x1088	0,0%	-0,3%	-0,2%	-0,1%	-0,1%	-0,1%	101,7%	102,4%
	Average	0,0%	-0,2% -0,1%	0,0%	0,0%	0,0%	101,3% 102,5%

Table 9 : Results obtained with HTM 4.0.1 and dynamic merge index followed by parsing adaptation and CABAC context for the first three bins

 9

Joint Collaborative Team on 3D Video Coding Extension Development of ITU-T SG 16 WP 3 and ISO/IEC JTC 1/SC 29/WG


Thomas Guionnet
email: thomas.guionnet@inria.fr

Laurent Guillo
email: laurent.guillo@inria.fr

Christine Guillemot
email: christine.guillemot@inria.fr

HEVC implements a candidate vector list for merge and skip modes. The construction of this list has been extensively studied in the JCT-VC group (see for instance JCTVC-G039). It has been shown in JCTVC-I0293 that it is possible to improve the HEVC coding performance by adding in the merge list copies of the first candidate shifted by an arbitrary offset. The same basis is considered in this document and applied to disparity compensation. A gain of 0.3 % is obtained on average on side views.

Introduction

HEVC relies on a candidate vector list for merge and skip modes. The efficiency of this approach depends highly on the relevance of the vectors present in the list. The construction of this list has been extensively studied [START_REF] Bross | CE9: Summary Report of Core Experiment on MV Coding and Skip/Merge Operations[END_REF]. During the 9th JCT-VC meeting, it has been shown in [START_REF] Yamamoto | Merge candidate refinement for uni-predictive block[END_REF] that it is possible to improve the HEVC coding performance by adding in the merge list copies of the first candidate shifted by an arbitrary offset. More precisely, in [START_REF] Yamamoto | Merge candidate refinement for uni-predictive block[END_REF], if there is available space in the candidate vector list, up to two new candidates are added: the first vector of the list shifted by an offset of (-4; 0) and (4; 0). It corresponds to a horizontal shift of -1 and 1 pixel respectively. In the context of video encoding of multiple rectified views, having a fine horizontal adjustment may be desirable for efficient disparity compensated prediction. Therefore, it is proposed to replace some candidates in the merge list with candidates pointing to the base view and shifted by horizontal offsets. This document is the follow up of JCT3V-A0134 [START_REF] Guionnet | CE5.h related: Merge candidate list extension for disparity compensated prediction[END_REF], as part of the core experiment CE5.h. It provides an updated description of the proposed method and results of the integration into HTM 4.0.1. A cross-check is available in JCT3V-B0098. The candidate list construction proceeds as follows.

Proposed method

1. Construct the list as currently specified (example result depicted on Figure 1).

2.

Scan the list from the first to the fourth position. The first candidate found in the list during this scan which has either its L0 vector or L1 vector or both pointing to another view is marked as selected candidate (see for example Figure 2). A vector mvLX is pointing to another view if the viewId of current coding unit is not equal to the viewId of reference refIdxLX. If no such candidate exists, the process ends.

3. Let m be the index of the selected candidate. The index m is greater or equal to 0 and lower or equal to 3. The selected candidate is defined by mvL0 m , mvL1 m , refIdxL0 m , refIdxL1 m , predFlagL0 m , and predFlagL1 m . Two refined candidates candDCPa and candDCPb are constructed as follows:

a. If mvL0 m is pointing to another view:

 mvL0candDCPa = mvL0 m + (4, 0)  mvL1candDCPa = mvL1 m  refIdxL0candDCPa = refIdxL0 m  refIdxL1candDCPa = refIdxL1 m  predFlagL0candDCPa = predFlagL0 m  predFlagL1candDCPa = predFlagL1 m  mvL0candDCPb = mvL0 m + (-4, 0)  mvL1candDCPb = mvL1 m  refIdxL0candDCPb = refIdxL0 m  refIdxL1candDCPb = refIdxL1 m  predFlagL0candDCPb = predFlagL0 m  predFlagL1candDCPb = predFlagL1 m
b. Else (mvL1 m vector is pointing to another view):

 mvL0candDCPa = mvL0 m  mvL1candDCPa = mvL1 m + (4, 0)  refIdxL0candDCPa = refIdxL0 m  refIdxL1candDCPa = refIdxL1 m  predFlagL0candDCPa = predFlagL0 m  predFlagL1candDCPa = predFlagL1 m  mvL0candDCPb = mvL0 m  mvL1candDCPb = mvL1 m + (-4, 0)  refIdxL0candDCPb = refIdxL0 m  refIdxL1candDCPb = refIdxL1 m  predFlagL0candDCPb = predFlagL0 m  predFlagL1candDCPb = predFlagL1 m 4.
Write the two refined candidates in the list as follows:

a. If m < 3 (illustrated by Figure 3 and Figure 4)

 mvL0 5 = mvL0 3  mvL1 5 = mvL1 3  refIdxL0 5 = refIdxL0 3  refIdxL1 5 = refIdxL1 3  predFlagL0 5 = predFlagL0 3  predFlagL1 5 = predFlagL1 3  mvL0 3 = mvL0candDCPa  mvL1 3 = mvL1candDCPa  refIdxL0 3 = refIdxL0candDCPa  refIdxL1 3 = refIdxL1candDCPa  predFlagL0 3 = predFlagL0candDCPa  predFlagL1 3 = predFlagL1candDCPa  mvL0 4 = mvL0candDCPb  mvL1 4 = mvL1candDCPb  refIdxL0 4 = refIdxL0candDCPb  refIdxL1 4 = refIdxL1candDCPb  predFlagL0 4 = predFlagL0candDCPb  predFlagL1 4 = predFlagL1candDCPb
b. Else (m = 3, illustrated by Figure 5)

 mvL0 4 = mvL0candDCPa  mvL1 4 = mvL1candDCPa  refIdxL0 4 = refIdxL0candDCPa  refIdxL1 4 = refIdxL1candDCPa  predFlagL0 4 = predFlagL0candDCPa  predFlagL1 4 = predFlagL1candDCPa  mvL0 5 = mvL0candDCPb  mvL1 5 = mvL1candDCPb  refIdxL0 5 = refIdxL0candDCPb  refIdxL1 5 = refIdxL1candDCPb  predFlagL0 5 = predFlagL0candDCPb  predFlagL1 5 = predFlagL1candDCPb

Experimental results

The experiment has been conducted with HTM 4.0.1 and evaluation is based on common test conditions [START_REF] Rusanovskyy | Common test conditions for 3DV Core Experiments[END_REF].

Results are provided in Table 1. Newspapercc 0,0% -0,5% -0,5% -0,2% 0,0% -0,1% 96,9% 99,0% GhostTownFly 0,0% -1,1% -0,8% -0,3% -0,2% -0,2% 97,3% 101,5% PoznanHall2 0,0% 0,2% -0,3% -0,1% -0,1% -0,1% 97,9% 99,2%

PoznanStreet 0,0% -0,5% -0,3% -0,2% -0,1% -0,2% 95,6% 100,5% UndoDancer 0,0% -0,3% -0,2% -0,1% -0,1% -0,1% 96,9% 100,9% 1024x768 0,0% -0,2% -0,3% -0,1% 0,0% 0,0% 96,9% 100,4% 1920x1088 0,0% -0,4% -0,4% -0,2% -0,1% -0,1% 96,9% 100,5% average 0,0% -0,3% -0,3% -0,1% -0,1% -0,1% 96,9% 100,5%

Conclusion

Given the reported gains with no added complexity, we suggest to adopt the proposed method.

5 References

Figure 1 :

 1 Figure 1: Candidate vector list for merge and skip mode example.

Figure 1

 1 Figure 1 depicts a typical example of motion vector candidate list. Each motion vector candidate is defined as  the luma motion vectors mvL0 and mvL1,  the reference indices refIdxL0 and refIdxL1,  the prediction list utilization flags predFlagL0 and predFlagL1.

Figure 2 :

 2 Figure 2: Selection of a disparity compensated candidate.

Figure 3 :

 3 Figure 3: Displacement of the fourth candidate to the last position in the candidate list.

Figure 4 :

 4 Figure 4: Overwriting of fourth and fifth candidates by newly generated candidates.

Figure 5 :

 5 Figure 5: Overwriting of fifth and last candidates by newly generated candidates

Table 1 : Results obtained with HTM 4.0.1 and Merge list extension with DCP candidate, compared to HTM

 1

	4.0.1

Patent rights declaration(s) INRIA may have current or pending patent rights relating to the technology described in this contribution and, conditioned on reciprocity, is prepared to grant licenses under reasonable and non-discriminatory terms as necessary for implementation of the resulting ITU-T Recommendation | ISO/IEC International Standard (per box 2 of the ITU-T/ITU-R/ISO/IEC patent statement and licensing declaration form).

Joint Collaborative Team on 3D Video Coding Extension Development of ITU-T SG 16 WP 3 and ISO/IEC JTC 1/SC 29/WG