1. Recovering Intrinsic Images from a Single Image 28/12/05 Dagan Aviv Shadows Removal Seminar

2. Relies on: Marshall F. Tappen, William T. Freeman and Edward H. Adelson. “Recovering Intrinsic Images from a Single Image.” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 9, pp. 1459-1472, September, 2005 Matt Bell and William T. Freeman. “Learning Local Evidence for Shading and Reflectance” Proc. Int’l Conf. Computer Vision, 2001.

3. Motivation Interpreting real-world images Distinguish the different characteristics of the scene Shading and reflectance – two of the most important characteristics

4. Short Introduction Image is composed of Shading Intrinsic and Reflectance Intrinsic images

5. Our Goal Decompose an Input Image into its Intrinsics Simple Approaches like Band Filtering won't help us. for example:

6. Our Approach Recovering the images using multiple cues Implicit assumption – surfaces are lambertian (a good starting point…) Classify Image Derivatives

7. Separating Shadows and Reflectance As shown in the preceding talk: Recovering S and R using derivatives of the input image I

8. Creating The Intrinsic Image Building S and R is performed in the same manner as shown in the last talk (Weiss)  - convolution operator imgX - S or R F – estimated derivative f – derivative filter – ([-1 1] in out case) f(-x,-y) – reverse copy of f(x,y)    

9. Binary Classification Assumption – each derivative is caused either by Shadings or Reflectance This reduces our problem into a binary classification problem

10. Classifying Derivatives 3 Basic phases: 1. Compute image derivatives 2. Classify each derivative as caused by shading or reflectance 3. Invert derivatives classified as shading to find shading images. The reflectance image is found in the same way.

11. Classifying Derivatives The Classifying stage is achieved using two forms of local evidence: 1. color information 2. statistical regularities of surfaces (Gray-scale information)

12. Color Information When speaking of defusive surfaces : And lights have the same color, changes due to shading should affect R,G and B proportionally

13. Color Information Let and be RGB vectors of two adjacent pixels. A change due to shading can be represent as: α is scalar (intensity change)

14. Color Information If the changes are caused by a reflectance change After normalizing and, the dot product will result 1 if the changes are due to shadings ( ) Practically a threshold is chosen manually so: If - shading Else - reflectance

15. Color Information The threshold eliminates chromatics artifacts caused by JPEG compression for example The chosen threshold: cos 0.01 When speaking of non-lambertian surfaces: the results are less satisfying

16. Color Information - examples Input Image Shading Imagereflectance Image

17. Color Information - examples Black on white may be interpreted as intensity change. Resulting in misclassification

18. Color Information - examples As before - the face is incorrectly placed in the shadings image The hat specularity is added to the reflectance image

19. Gray-scale Information Shading patterns have a unique appearance We will examine ROIs wrapping each derivative in a gray-scale image to find shadow patterns

20. Gray-scale classifier The Basic Feature where I is the ROI (patch) surrounding a derivative and w is a linear filter the non-linear F is the result in the center of the ROI 

21. Training the classifier Two tasks are involved: 1. choosing the filters set – which will build the features 2. training the classifier on the features

22. AdaBoost (in general) Both Tasks are achieved by the chosen classifier – AdaBoost First introduced in 1995 by Freund and Schapire The main idea is to boost a “weak classifier” – a classifier with error slightly less than 0.5

23. AdaBoost The classifier is trained by giving it a training set is a binary mapping from the X domain to the Y domain – {-1,+1} In our case X is a set of synthetic images of shadings and reflectance, -1 is for reflectance and +1 is for shading

24. AdaBoost AdaBoost is also gets the weak classifier as an input The learning stage is iterative At each round t, AdaBoost weights the training set and run the weak classifier The weak classifier job is to find an hypothesis h such that:

25. AdaBoost Elements that were misclassified will get a higher weight for the next iteration AdaBoost also weights the classifier votes At the end – once the desired number of rounds has run, all the weighted votes is gathered to compute the final strong classification H.

26. AdaBoost – toy example Original Training Set

27. AdaBoost – toy example Round 1

28. AdaBoost – toy example Round 2

29. AdaBoost – toy example Round 3

30. AdaBoost – toy example Final result

31. AdaBoost – matlab source See the next archive for AdaBoost Matlab implementation (and more)

32. Our AdaBoost The Weak Classifier where and recall that If otherwise 

33. So AdaBoost needs to choose w s, threshold s and s w – a set of patches constructed from 1 st and 2 nd derivatives of Gaussian filters The training set (which the I’s patches is derived from) is a set of synthetic images Our AdaBoost

34. The training set is evenly divided between shading: and reflectance: Our AdaBoost

35. The shading images were lit from the same direction An assumption – when an input image is given, the light direction is known Preprocess - rotate the input image so the light will match the light in the training set Our AdaBoost

36. GrayScale Information - examples

37. The shading image is missing some edges These edges didn”t appear in the training set

38. GrayScale Information - examples

39. Misclassification of the cheeks – due to weak gradients

40. Combing Informations The final result is based on a statistical calculation of conditional probability Assumption: both classifiers (color and gray- scale) are statistically independent Bayes rule: Each Pr is computed with some modifications on the classifiers

41. Combing Informations – The Pillow Example

42. Handling Ambiguities Ambiguities - In the former slide for example – the center of the mouse Shading example Input imageReflectance example

43. Derivatives that lie on the same contour should have the same classification The mouth corners are well classified as reflectance Handling Ambiguities

44. Areas where the classification is clear are to propagate their classification to disambiguate other areas Achieved by a Markov Random Field – which generalize Markov Chains Handling Ambiguities

45. First a potential function is applied on the image finding the “most interesting” gradients Then the propagation starts from points having both strong derivatives and no ambiguities Handling Ambiguities

46. Final Results

50. Thank you The End