Using Genetic Algorithms for Model-Based Object Recognition

Transcription

1 Using Genetic Algorithms for Model-Based Object Recognition George Bebis, Sushil Louis and Yaakov Varol Department of Computer Science University of Nevada Reno NV CISST 98 July 6-9, 998 Las Veg as, Nevada

2 MODEL-BASED OBJECT RECOGNITION Overview -Environment is rather constrained. -Search is confined within a finite set of observable models. MODEL DATABASE RECOGNITION SYSTEM Recognition requirements -Invariant to translation, rotation, and scale. -Robust to noise and occlusion.

3 Goal of recognition -The recovery of a geometric transformation which aligns the model(s) with the scene. model int_points model3 int_points model2 int_points model4 int_points

4 Planar Objects and 2D Affine Transformations -Assume "weak perspective" projection. -Different views of the same planar object are related through an affine transformation. p =Ap + b a b c d

5 IMAGE-SPACE APPROACHES Procedure -Identify a set of features from the unknown scene which approximately match a set of features from a model object. -Recover the geometric transformation that the model object has undergone. Examples of methods in this category -Interpretation tree (Grimson & Lozano-Perez, 987) -Alignment (Huttenlocher and Ullman, 99) -Geometric hashing (Lamdan et al., 99)

6 TRANSFORMATION-SPACE APPROACHES Procedure -Search the space of possible transformations. -Find a transformation which aligns a large number of model features with the scene. Examples of methods in this category -Hough-transform based methods (Ballard, 98). -Pose clustering techniques (Cass, 988)

7 GENETIC ALGORITHMS (GAs) Overview -Parallel search algorithms based on the mechanics of natural selection. -Operate iteratively on a population of structures. -Each structure represents a candidate solution. -Structures are modified at each iteration using selection, crossover, and mutation. Why using GAs for Object Recognition? -Genetic algorithms were designed to efficiently search large solution spaces. -Both the image and transformation spaces are very large!! - Image space: O(M 3 S 3 )possible alignments. - Tr ansformation space: much larger!! (six dimensional)

8 Previous use of GAs in Image Processing/Analysis -Feature selection (Roth and Levive, 994) -Image segmentation (Swets and Punch, 995) -Target recognition (Katz and Thrift, 994) -Object recognition (Singh et al., 997, Ansari et al., 992) -Image registration (Fitzpatrick et al., 984) Problem and Approaches -Recognize real, planar, objects from 2D images assuming that the viewpoint is arbitrary. -Genetic search in the image space (GA-IS) -Genetic search in the transformation space (GA-TS) Important issues -How to encode solutions? -How to modify solutions? -How to evaluate solutions?

9 IMAGE-SPACE GENETIC SEARCH Encoding -Atleast three model-scene point matches are need to compute the affine transformation. -Chromosome contains the binary encoded identities of the three pairs of points. -Model points: 9 (5 bits) -Scene points: 9-45 (6 bits) -Chromosome length: 3 x x 6 = 33 bits Model pt Model pt 2 Model pt 3 Scene pt Scene pt 2 Scene pt 3 5 bits 6 bits Fitness evaluation. Compute affine transformation. 2. Apply the transformation on all the model points. 3. Compute the error (BE) between transformed model points and scene points. BE = Σ M 2 d j i= (d j min distance between the j-th model point and the scene) Fitness = BE

10 ESTIMATING THE RANGES OF VALUES OF THE PARAMETERS OF AFFINE TRANSFORMATION x x 2... x M y y 2... y M... a a 2 b = x x 2... x M or Pc = p x () x x 2... x M y y 2... y M... a 2 a 22 b 2 = y y 2... y M or Pc = p y (2) -Assume that the image coordinates of the unknown views (p x,p y )are restricted to belong to a given interval, (e.g., by scaling the image coordinates in [,]). -Use Interval Arithmetic to find all the possible solutions of () and (2) assuming that p x and p y [,]. Pc I = p I x Pc I 2 = p I y

11 -Solving () and (2) using Singular Value Decomposition P = U P W P V T P c = P + p x or c = Σ( 3 u i p x )v i (3) w ii i= c 2 = P + p y or c 2 = Σ( 3 u i p y )v w i (4) ii i= Evaluate (3) and (4) using Interval Arithmetic (Moore, 966) t = [t, t 2 ], r = [r, r 2 ] t + r = [t + r, t 2 + r 2 ] t * r = [min(t r, t r 2, t 2 r, t 2 r 2 ), max(t r, t r 2, t 2 r, t 2 r 2 )] -Apply preconditioning to optimize the ranges. The computed ranges of values. Ranges of values range of a range of a2 range of b original [-2.953, 2.953] [-2.89, 2.89] [-.662, 2.662] preconditioned [-8, 8] [-.39,.39] [.,.]

12 TRANSFORMATION-SPACE GENETIC SEARCH Encoding -Each chromosome contains six fields. -Only the range of each coefficient needs to be represented. a assumes values in [-8, 8] Its range is: 8 - (-8) = 6 2decimal digit accuracy: 82 values must be encoded. 7bits are needed to encode 82 values. Decoding -Some encoded solutions might be invalid. 7bits can encode at most 28 values. [, 27] should be mapped to [, 8] a = MIN(a ) + (82/2 7 )) * Decimal(W) (W is the binary encoded solution corresponding to a ) Fitness evaluation -Same as before (less costly to compute now)

13 GENETIC OPERATORS -Two-point crossover (prcoss:.95). -Point mutation (pmut:.5). -Cross generational selection strategy. -Fitness scaling (scaling factor:.2). SIMULATIONS AND RESULTS -Three scenes (S, S2, S3) of increasing complexity. -S2, S3 are shown below (S was the same as model). -trials per scene..9 scene2 int_scene2.9 scene3 int_scene

14 Parameters Values of Parameters S S2 S3 Population Size 2 5 Generations (GA-IS) Generations (GA-TS) -All other parameters were the same for all scenes. Scene -Correct solutions were found in all trials. GS-IS GA-TS.7 SCENE_NO_HEADER best_sol_out_of_ worst_sol_out_of_.7 SCENE_NO_HEADER best_sol_out_of_ worst_sol_out_of_ best_f_out_of_ best_af_out_of_ 9999 best_f_out_of_ best_af_out_of_

15 Scene2 -Correct solutions were found in all trials. GS-IS GA-TS.9 SCENE_NO_HEADER best_sol_out_of_ worst_sol_out_of_.9 SCENE_NO_HEADER best_sol_out_of_ worst_sol_out_of_ best_f_out_of_ best_af_out_of_ best_f_out_of_ best_af_out_of_

16 Scene3 -The GA-TS approach missed the correct solution once. GS-IS GA-TS.2 SCENE_NO_HEADER best_sol_out_of_ worst_sol_out_of_. SCENE_NO_HEADER best_sol_out_of_ worst_sol_out_of_ best_f_out_of_ best_af_out_of_ best_f_out_of_ best_af_out_of_

17 M 3 = 9 3 = 969 Total number of matches = 3! xm 3 xs 3 Summary of results (GA-IS approach). Results Scene Scene Points Number of Matches GA IS matches Scene 9 5,633,766 8(.3) Scene2 4 57,442,32 47,8(.8) Scene ,5,66 33,25(.6) Total number of possible transformations: 82 2 x79 2 x 2 =428, 79, 7, 284 Summary of results (GA-TS approach). Results Scene Number of Transforms GA TS matches Scene 428,79,7,284 8 (.8) Scene2 428,79,7, (.2) Scene3 428,79,7, (.2)

18 Conclusions -Exact and near exact matches were found reliably and quickly. -GA-TS converges faster. -GA-IS finds better solutions. -GAs are a viable tool for searching the image and transformation spaces efficiently. Future work -Incorporate constraints into the fitness function (e.g, geometric constraints). -Consider more than one models. -Extend the work to the case of real 3D objects. -Consider parallel implementations for real time performance.