1. Point Distribution Models Active Appearance Models Compilation based on: Dhruv Batra ECE CMU Tim Cootes Machester

2. Essence of the Idea (cont.)  Explain a new example in terms of the model parameters

3. So what’s a model Model “Shape” “texture”

4. Active Shape Models training set

5. Texture Models warp to mean shape

6. Intensity Normalisation  Allow for global lighting variations  Common linear approach Shift and scale so that  Mean of elements is zero  Variance of elements is 1  Alternative non-linear approach Histogram equalization  Transforms so similar numbers of each grey- scale value

7. Shape: Review of Construction Mark face region on training set Sample region Normalise Statistical Analysis The Fun Step

8. Multivariate Statistical Analysis  Need to model the distribution of normalised vectors Generate plausible new examples Test if new region similar to training set Classify region

9. Fitting a gaussian  Mean and covariance matrix of data define a gaussian model

10. Principal Component Analysis  Compute eigenvectors of covariance, S  Eigenvectors : main directions  Eigenvalue : variance along eigenvector

11. Eigenvector Decomposition  If A is a square matrix then an eigenvector of A is a vector, p, such that  Usually p is scaled to have unit length,|p|=1

12. Eigenvector Decomposition  If K is an n x n covariance matrix, there exist n linearly independent eigenvectors, and all the corresponding eigenvalues are non- negative.  We can decompose K as

13. Eigenvector Decomposition  Recall that a normal pdf has  The inverse of the covariance matrix is

14. Fun with Eigenvectors  The normal distribution has form

15. Fun with Eigenvectors  Consider the transformation

16. Fun with Eigenvectors  The exponent of the distribution becomes

17. Normal distribution  Thus by applying the transformation  The normal distribution is simplified to

18. Dimensionality Reduction  Co-ords often correllated  Nearby points move together

19. Dimensionality Reduction  Data lies in subspace of reduced dim.  However, for some t,

20. Approximation  Each element of the data can be written

21. Normal PDF

22. Useful Trick  If x of high dimension, S huge  If No. samples, N<dim(x) use

23. Building Eigen-Models  Given examples  Compute mean and eigenvectors of covar.  Model is then  P – First t eigenvectors of covar. matrix  b – Shape model parameters

24. Eigen-Face models  Model of variation in a region

25. Applications: Locating objects  Scan window over target region  At each position: Sample, normalise, evaluate p(g)  Select position with largest p(g)

26. Multi-Resolution Search  Train models at each level of pyramid Gaussian pyramid with step size 2 Use same points but different local models  Start search at coarse resolution Refine at finer resolution

27. Application: Object Detection  Scan image to find points with largest p(g)  If p(g)>p min then object is present  Strictly should use a background model:  This only works if the PDFs are good approximations – often not the case

28. Back (sadly) to Texture Models raster scan Normalizations

29. PCA Galore Reduce Dimensions of shape vector Reduce Dimension of “texture” vector They are still correlated; repeat..

30. Object/Image to Parameters modeling ~80

31. Playing with the Parameters First two modes of shape variationFirst two modes of gray-level variation First four modes of appearance variation

32. Active Appearance Model Search  Given: Full training model set, new image to be interpreted, “reasonable” starting approximation  Goal: Find model with least approximation error  High Dimensional Search: Curse of the dimensions strikes again

33. Active Appearance Model Search  Trick: Each optimization is a similar problem, can be learnt  Assumption: Linearity  Perturb model parameters with known amount  Generate perturbed image and sample error  Learn multivariate regression for many such perterbuations

34. Active Appearance Model Search  Algorithm:  current estimate of model parameters:  normalized image sample at current estimate

35. Active Appearance Model Search  Slightly different modeling:  Error term:  Taylor expansion (with linear assumption)  Min (RMS sense) error:  Systematically perturb and estimate by numerical differentiation

36. Active Appearance Model Search (Results)

37. Sub-cortical Structures Initial PositionConverged

38. Random Aside  Shape Vector provides alignment = 43 Alexei (Alyosha) Efros, 15-463 (15-862): Computational Photography, http://graphics.cs.cmu.edu/courses/15-463/2005_fall/www/Lectures/faces.ppt

39. Random Aside  Alignment is the key 1. Warp to mean shape 2. Average pixels Alexei (Alyosha) Efros, 15-463 (15-862): Computational Photography, http://graphics.cs.cmu.edu/courses/15-463/2005_fall/www/Lectures/faces.ppt

40. Random Aside  Enhancing Gender more same original androgynous more opposite D. Rowland, D. Perrett. “Manipulating Facial Appearance through Shape and Color”, IEEE Computer Graphics and Applications, Vol. 15, No. 5: September 1995, pp. 70-76

41. Random Aside (can’t escape structure!) Alexei (Alyosha) Efros, 15-463 (15-862): Computational Photography, http://graphics.cs.cmu.edu/courses/15-463/2005_fall/www/Lectures/faces.ppt Antonio Torralba & Aude Oliva (2002) Averages: Hundreds of images containing a person are averaged to reveal regularities in the intensity patterns across all the images.

42. Random Aside (can’t escape structure!) “100 Special Moments” by Jason Salavon Jason Salavon, http://salavon.com/PlayboyDecades/PlayboyDecades.shtml

43. Random Aside (can’t escape structure!) “Every Playboy Centerfold, The Decades (normalized)” by Jason Salavon 1960s1970s1980s Jason Salavon, http://salavon.com/PlayboyDecades/PlayboyDecades.shtml