Segmentation via Genetic Programming

Segmentation segments  Splitting an image into segments §Hard problem ill-defined  Conceptually ill-defined Segmentation

Segmentation Which segmentation is the correct one?

Segmentation

Segmentation

Segmentation §Tagging function: §Deciding function: Defining the problem

Segmentation §Berkley’s segmentation dataset and benchmark: Images + Human made segmentation maps Benchmark for segmentation algorithms The Dataset

Genetic Programming  Bio-Inspired  Bio-Inspired Artificial Intelligence method §Inspired by Darwin’s evolutionary principles What is Genetic Programming?

Genetic Programming  Variety  Variety of species individuals within the population  Competition  Competition for limited resources  Overproduction  Overproduction of offspring generation §Survival of the fittest Origin of Species, 1859 Darwin’s principles

Genetic Programming The computational model GnGnGnGn G n+1 = crossover mutation fitness

Segmentation via GP §Individuals are represented as LISP-like functions X2  (* x x) 2x-1  (- (* (+ 1 1) x) 1) Individual Representation

Segmentation via GP §Equivalent to tree representation Individual Representation

Segmentation via GP §Crossover Genetic Operators

Segmentation via GP §Mutation Genetic Operators

Segmentation via GP §Function Set: {+, -, *, %, neg, conv, opp, sqrt} §Terminal Set: {image, 0, 1, const, gradx, grady, ckernel} §Strongly-Typed GP: conv(matrix,kernel) +(matrix,matrix), +(kernel,kernel), +(kernel,number), … Building the trees

Segmentation via GP §An example: Gradient Magnitude (sqrt (+ (* (conv image gradx) (conv image gradx)) (* (conv image grady) (conv image grady)))) Building the trees

Segmentation via GP §Accuracy: §Modified Accuracy: Fitness measure

Segmentation via GP §Individuals produce ‘soft boundary maps’, need threshold value §Value too low – more points are reported (false positives) §Value too high – less points are reported (true negatives) Threshold

Segmentation via GP equal  Berkley’s benchmark: split the threshold range into N equal parts, threshold and keep best. unequal  My method: split the threshold range into N unequal parts, by equal increase in reported points, proportional to number of points in the human made segmentation map. Threshold

Segmentation via GP §Population size: §Generation count: unspecified §Crossover rate: 90% §Mutation rate: 10% §Selection: tournament of 3 §Tree depth: limited to 6-9 Sean Luke ’ s ECJ13 was used for running GP sessions Miscellaneous Evolutionary Parameters

Results A typical GP session

Results §Generation 0: best, 0.08 average §Generation 93: best, average §Fitness does not always increase! §Fitness leaps in best individual A typical GP session

Results Segmentation function (- (- (conv (* (conv image gradx) (conv image gradx)) (- (- (kernel ) grady) (- (kernel ) 0.0))) (conv (* (conv image gradx) (conv image gradx)) (- (- (kernel ) grady) (- (kernel ) 0.0)))) (- (- (- (conv image grady) (* )) (% (* ) )) (% (% (* ) (* )) (% (* ) (* ))))) Best Individual

Results Segmentation function gradx gradx grady gradxgradx grady grady (- (- (conv (* (conv image gradx) (conv image gradx)) (- (- (kernel ) grady) (- (kernel ) 0.0))) (conv (* (conv image gradx) (conv image gradx)) (- (- (kernel ) grady) (- (kernel ) 0.0)))) (- (- (- (conv image grady) (* )) (% (* ) )) (% (% (* ) (* )) (% (* ) (* ))))) Best Individual

Results Segmentation function (- (- (conv (* (conv image gradx) (conv image gradx)) (- (- (kernel ) grady) (- (kernel ) 0.0))) (conv (* (conv image gradx) (conv image gradx)) (- (- (kernel ) grady) (- (kernel ) 0.0)))) (- (- (- (conv image grady) (* )) (% (* ) )) (% (% (* ) (* )) (% (* ) (* ))))) Best Individual

Results Segmentation function (* (conv image gradx) (conv image gradx)) (* (conv image gradx) (conv image gradx)) (- (- (conv (* (conv image gradx) (conv image gradx)) (- (- (kernel ) grady) (- (kernel ) 0.0))) (conv (* (conv image gradx) (conv image gradx)) (- (- (kernel ) grady) (- (kernel ) 0.0)))) (- (- (- (conv image grady) (* )) (% (* ) )) (% (% (* ) (* )) (% (* ) (* ))))) Best Individual

Results Accuracy = (GM accuracy = 0.280) Best Individual

Results Accuracy = (GM accuracy = 0.193) Best Individual

Results Accuracy = (GM accuracy = 0.245) Best Individual

Results Accuracy = (GM accuracy = 0.119) Best Individual

Summary §It is possible to evolve segmentation functions using GP §Results are good, can be better §Evolved function ‘beats’ the gradient magnitude function §Improve results by more power Discussion

Summary §More CPU and RAM §More functions and terminals §Use ADFs §Evolve kernels separately §Evolve threshold function separately §Include more inputs: color images, textures, output of other edge detectors Future Work

References 1.The Berkley Segmentation Dataset and Benchmark 2.Koza, J. R.: Genetic Programming: On the programming of computers by natural selection. MIT press, Cambridge, Mass. (1992) 3.Tomassini M.: Evolutionary Algorithms. Swiss Scientific Computing Center, Manno. 4.Darwin, Charles: On the origin of species by means of natural selection. London, John Murray, Montana, D.J.: Strongly typed genetic programming. Evolutionary Computation 3 (1995) 199–230 6.Langdon, W.B.: Size fair and homologous tree genetic programming crossovers. Genetic Programming and Evolvable Machines 1 (2000) 95– Luke S.: ECJ 13 - a Java based Evolutionary Computation and Genetic Programming research system 8.Koza, J. R.: Genetic Programming II: Automatic Discovery of Reusable Programs. MIT press, Cambridge, Mass. (1994)