## Learning Long Term Face Aging Patterns from Partially Dense Aging Databases

Jinli Suo1,2     Xilin Chen1     Shiguang Shan1     Wen Gao3
1Institute of Computing Technology, Graduate University of Chinese Academy of Sciences,China           2Lotus Hill Institute
3School of Electronics Engineering and Computer Science, Peking University

1. What's the Problem?
Studies on face aging are handicapped by lack of long term dense aging sequences as training data.

2. Intuitive Solution
 To deal with the problems of lacking long term dense aging databases to build face aging models, we propose an approach of learning long term face aging patterns from partially dense aging datasets. The approach is based on two assumptions: (i) Short term face aging patterns are relative simple and possible to be learned from currently available real aging sequences; (ii) Long term face aging is a smooth and continuous process composed of a series of short term aging patterns sequentially

3. Compositional Face Representation
 We decompose a human face into subregions under gudiance fom muscle structure; For each region, an aging specific AAM is built;

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4. Short Term Face Aging Modeling
 The patterns are learned from real aging sequences, which are available from public face aging databases We adopt flexible B-spline curves to fit the short term face aging patterns Sometimes nonage related appearance variations are highly mixed with age related variations, thus these samples are treated as outliers and excluded by adopting RANSAC strategy

5. Long Term Face Aging Modeling
 Denoting ${\bf C}^r_1$ and ${\bf C}^r_2$ as two learned patterns over two overlapping time spans $\tau_1$ and $\tau_2$ of region $r$, $\text{pc}$ is the index of principal components, $F_\text{pc}$ describes the correlation between component pc and face aging Distances are defined over an overlapping time span, here gradient operator is introduced to remove identity information and reflect only the "changes" of parameters in aging process: $\mathcal{D}({\bf C}^r_1, {\bf C}^r_2) = \frac{1}{|\tau_1 \cap \tau_2|} \int_{\tau_1 \cap \tau_2}(\sum_{pc=1}^{N^r}F_{\text{pc}} \cdot \left |\triangledown C^r_{1,\text{pc}}(t) - \triangledown C^r_{2,\text{pc}}(t)\right|\ )dt$ Our aging model is probabilistic andit favors the transition between similar patterns to force the smoothness of long term face aging: $P({\bf C}^r_2 | {\bf C}^r_1) \propto exp^{-\mathcal{D}({\bf C}^r_1,{\bf C}^r_2)}$ We concatenate two sequential short term face aging patterns at the timepoint with minimum slope differencesummed over all of the principal components: $t^* = \arg\min_{t \in \tau_1 \cap \tau_2} \sum_{pc=1}^{N^r}F_{\text{pc}} \cdot \left |\triangledown C^r_{1,\text{pc}}(t) - \triangledown C^r_{2,\text{pc}}(t)\right|$

6. Uncertainty of Face Aging
 Face aging is intrinsically uncertain due to the affects from external factors, e.g., health, life style, nutrition, etc. Similar to the Brownian motion, the uncertainty increases as time elapses. For an input young face, our algorithm generates multiple plausible aging results to illustrate the stochasticity of face aging.

7. Some Simulation Results
 Input Image Synthetic Synthetic Synthetic t t+10 t+20 t+30 Caucasianmale: Caucasianfemale: African-Americanmale: African-Americanfemale:

8. Publications
 Jinli Suo, Xilin Chen, Shiguang Shan and Wen Gao, "Learning Long Term Face Aging Patterns from Partially Dense Aging Databases", accepted by International Conference on Computer Vision(ICCV)'09.