2. Lecture 13 Shape from Shading

3. 2 Looking at finding normal, not distance Normal: Describe the shape Assuming point light source is far away p,q are unknowns Ellipse

4. 3 SFS: Data Constraint Given an intensity value I, (p,q) are constrained to be an ellipse q p

5. 4 Self Occluding If know self occluding, we can estimate normal. Normal for self occluding edges are perpendicular to the edge in 2D

6. 5 SFS In human : tends to assume that light is above

7. 6 SFS: SFS: Classical Work Horn and Schunk Use (p,q) Problem: Self Occluding p,q undefined At occluding edge dz/dx p  ∞, q  ∞ To rectified this, sphere coordinates ( ,  ) are used

8. 7 Photometric Stereo 2/3 lights -Given L1, Observe I1 -Given L2, Observe I2 -Given L3, Observe I3 Have 3 lights at different directions with distance ∞ -Turn on L1, take pictures -Turn on L2, take pictures -Turn on L3, take pictures

9. 8 Photometric Stereo I(x,y) = k d I d (N.L) =  N.L  = Albedo = whiteness

10. 9 Photometric Stereo 4 unknowns : albedo and normal known unknown

11. 10 Photometric Stereo I = L.N 1

12. 11 Photometric Stereo

13. 12 Remaining Topic Genetic Algorithm Neural Network Motion Processing Structure Tracking (Fovea – Center Of Vision) Camera Calibration Object Recognition Models

14. 13 Genetic Algorithm Optimization Technique Based on “Survival of Fittest” 1.Population Size – Fixed Each solution is an individual 2.Fitness of Individual – Fitness of “Chromosome” (small part) “Goodness” 3.Crossover – Combining Parts of 2 or more individuals New child is put into population. May die. 4.Mutation – “Random change done to Part of an Individual”

15. 14 Genetic Algorithm Charls Darwin – “Survival of Fitness” proposed how species develop Moth - Industrial Revolution YellowBlack 99%1% 70%30% 20%80%

16. 15 Genetic Algorithm Algorithm: 1.Create a random solution of 20 individuals Sort by fitness { (1,__), (2, __), (3, __), …. } 2.R = Random(0,1) if (R<0.9) /* Cross Over */ Use 2 or more solutions to create new one else Create a new random Individual Insert new individual in to population if it is fitter than the worst one Repeat Until the top 20 does not change

17. 16 Problem Statement: Input The Order Book consists of Many Instances of a Set of Patterns Each Piece of garment can be placed at 0 degrees or 180 degrees

18. 17 Problem Statement: Output W L Place all the pieces in the order book to use minimum fabric length on a fixed width roll Method: Genetic Algorithm

19. 18 About Genetic Algorithms  An optimization method that mimics the evolution of life using concepts of survival of the fittest within a fixed population.  Parts of Genetic Algorithm: Individual – a solution with known fitness Population – set of individuals forming the genetic pool Fitness Function – a measure of the goodness of an individual Creating a New Individual through Reproduction: 1. Self Replication 2. Crossover 3. Mutation Output, result reported as the most fit individual in population.

20. 19 Related Work: Pargas and Jain 1993 [8] R. P. Pargas and R. Jain. A Parallel Stochastic Optimization Algorithm for Solving 2D Bin Packing Problems. IEEE Int. Conf. on A.I. for Applications. 1993.  A stochastic approach to bin packing 2-D figures  Similar to genetic algorithms and simulated annealing  Has 80% efficiency on regular shapes  Tested on objects that can be packed to 100% efficiency  For garments, efficiency cannot be 100%  We compare to human expert for benchmark

21. 20 G. Roussel and S. Maouche, “Improvements About Automatic Lay-Planning For Irregular Shapes on Plain Fabric” IEEE Proc. Systems Man and Cybernetics, System Engineering, 1993.  Shape layout problem for garment pieces  Use a heuristic tree search algorithm called  -admissible algorithm  Reasonable results  Too much time spent back-tracking  Tends to have a local minimum problem Related Work: Roussel and Mouche 1993 [9]

22. 21 Related Work: Ismail and Hon [11] H.S. Ismail and K.B. Hon. The Nesting of two- dimensional Shapes Using Genetic Algorithms. Proceedings of The Institution of Mechanical Engineers Part B, Journal of Engineering Manufacture. 1995.  Minimize Raw Mat for cutting 2-D pieces  Uses Genetic Algorithms and Heuristics  Simple shapes used  Raw Material width not fixed, unrealistic

23. 22 Related Work: Bounsaythip et al [10] C. Bounsaythip, S. Maouche and M. Neus. Evolutionary Search Techniques Application in Automated Lay- Planning Optimization Problem. IEEE Int. Conf. on Intelligent Systems for the 21st Century, 1995.  Minimize unoccupied space by Evolutionary Algorithm  Shape representation by Comb Code  Efficiency Measure: Length of Raw Mat (Fabric).  Used pant garment pieces, regular shapes  Good Results due to regular shapes used.

24. 23 Related Work: Bounsaythip and Maouche [12] C. Bounsaythip and S. Maouche. Irregular Shape Nesting And Placing With Evolutionary Approach”. IEEE Int. Conf. On Systems Man and Cybernetics. 1997.  Use the comb code representation for each garment piece  Shape placement represented as hierarchical tree  Allow orientations of 0, 90, 180, and 270 degrees  Crossover: combine parts of tree, removing redundancy  Results presented on relatively simple shapes, making it difficult to assess the efficiency achieved

25. 24 Placing Items from Order Book The Order Book consists of Many Instances of a Set of Patterns Each Piece of garment can be placed at 0 degrees or 180 degrees Each garment piece is polygonal Smooth contours (splines) approximated by convex hull first 1 23 4567 8 910 11121314

26. 25 Placement Method: Check for Overlaps Upon placing a new polygon, must check that: 1. NO vertex is INSIDE other polygons 2. NO other polygon’s vertex is INSIDE Convex Polygons Assumed

27. 26 Our Genetic Algorithm 1. Set and Randomly Initialize the Population of size P = 15 2.Divide Individual into chromosome strips. Compute strip efficiency. 3. Crossover, Mutation, and Selection: Repeat If random (0, 1) < crossover probability Create a New Individual by Crossover: Repeat Sample for a chromosome from the solution biased by efficiency Recompute chromosome efficiency based on Order Book balance Until No Efficient Chromosome Available Fill Remaining Solution Randomly by Order Book balance Else Create New Individual by Mutation: Fill Randomly from Order Book Insert the solution into the new population Check for Survival of Fittest P = 15 Until(Population has converged)or(No improvement in Best Solution)

28. 27 Step 1: Initial Random Population S1 = [(5, 1), (3, 0), (4, 1), (1, 1), (2, 0), 15] S2 = [(1, 0), (3, 0), (2, 1), (3, 0), (4, 0), 17] S3 = [(5, 1), (3, 0), (7, 1), (1, 1), (2, 0), 20] S4 = [(1, 0), (5, 0), (4, 0), (3, 1), (2, 0), 21] S5 = [(1, 0), (3, 0), (5, 0), (2, 1), (4, 0), 23] S6 = [(4, 0), (5, 0), (1, 1), (2, 0), (3, 0), 25] S7 = [(3, 1), (4, 0), (5, 1), (2, 0), (1, 0), 27] S8 = [(5, 1), (4, 0), (3, 1), (2, 1), (1, 0), 29] S9 = [(3, 0), (2, 0), (1, 0), (5, 1), (4, 1), 32] S10 = [(4, 1), (3, 0), (1, 1), (2, 1), (5, 1), 34] An Individual Solution: S = [(F 1, O 1 ), (F 2, O 2 ),…,(F n, O n ), L)] whereS - completed order bookF i - garment piece number O i - orientation at 0 or 180 degreesL - Length of Fabric used 5 3 4 1 2 7

29. 28 Step 2: Determine Strips W L str1 L str2 L L str3 Each Strip is determined by largest piece along column. Efficiency of each strip is Computed, used for crossover

30. 29 Crossover: Sampling Within Population P = LBLB  LB LB

31. 30 Crossover: Sampling for Efficient Strips P = EBEB  EB EB After sampling from population for 4 best solutions, Crossover takes place using efficient strips first

32. 31 Crossover: Efficiency Decreases over Time Efficiency decreases as Order Book fills up Once Efficiency too low, fill remaining items randomly highlowered

33. 32 Mutation: New Random Individual When Efficiency low, fill randomly is partly like mutation Mutation by generating a new random solution This new individual usually does not survive Our results are compared with layout by human expert

34. 33 Experimental Result 1: Rectangles 6 Sets in Order Book G.A.: 1:15 Hrs.

35. 34 Rectangles by Human Expert Manually: 0:25 Hrs.

36. 35 Experimental Result 2: Shirt Pieces 10 Sets in Order Book

37. 36 Shirt Pcs. (10 orders) by G.A. G.A.: 51:08 Hrs.

38. 37 Shirt Pcs. (10 orders) by Human Manually: 1:25 Hrs.

39. 38 Experimental Result 3: Multi-Edged Shapes by G.A. 3 Sets in Order Book

40. 39 Multi-Edged G.A. vs. Human G.A.: 0:57 Hrs.

41. 40 52 54 56 58 60 62 051015202530354045505560657075 Iterati ons E % 1 2 3 5 4 Finding Crossover Number

42. 41 Finding Good Population Size 50 52 54 56 58 60 62 051015202530354045505560657075 E % Iterations 10 15 20 25 30

43. 42 Discussion and Conclusion  Main Problem: successive crossover reduces efficiency of good strips.  Efficiency 3-5% lower than human expert, while taking more time.  Efficiency depends on the complexity of the piece, making it hard to compare results among researchers. high lowered