IRIS IMAGE SEGMENTATION Problem statement Related work BY PAIRED - PowerPoint PPT Presentation

Iris image segmen- tation 1 / 28 Efimov Y. Matveev I. IRIS IMAGE SEGMENTATION Problem statement Related work BY PAIRED GRADIENT METHOD Proposed solution WITH PUPIL BOUNDARY REFINEMENT Edge detection Pairs for voting Accumulator analysis Polar representation Optimal path search Results Efimov Yuriy Experiments Matveev Ivan Conclusion Moscow Institute of Physics and Technology Federal Research Centre ”Computing Centre” of Russian Academy of Sciences October 11, 2016

Iris image segmen- Problem statement tation 2 / 28 Efimov Y. Matveev I. Input: Problem statement I — grayscale bitmap sized W × H . Every pixel is encoded in Related work one byte. Proposed solution Edge detection Pairs for voting Output: Accumulator analysis Polar representation An approximation of iris boundaries in an eye image I by two Optimal path search Results circles, i.e. to determine center coordinates and the Experiments corresponding radii ( x , y , r ) P and ( x , y , r ) I . Conclusion

Iris image segmen- Iris detection: related work tation 3 / 28 Efimov Y. Matveev I. 1. Daugman’s approach Problem statement Circular approximation parameters are determined by Related work Proposed solution integro-differential operator: Edge detection Pairs for voting Accumulator analysis ( r , x 0 , y 0 ) | G σ ( r ) ∂ � I ( x , y ) Polar representation max ds | Optimal path search ∂ r 2 π r ( x 0 , y 0 , r 0 ) Results Experiments 2. Wildes’ approach and its modifications Conclusion Searching for local maxima in the parameter space. There are modifications, allowing to reduce the computational complexity: gradient-based approaches, randomized algorithms for circle detection, separation of the accumulator parameter space. 3. Active contours

Iris image segmen- Pupil detection: related work tation 4 / 28 Efimov Y. Matveev I. Problem statement Related work 1. Projection methods Proposed solution Intensity projection method, gradient projection Edge detection Pairs for voting method, blob detection. Accumulator analysis Polar representation 2. Morphological methods Optimal path search Results A method of recursive erosion. Experiments 3. Hough methodology Conclusion 4. Contour-based methods Pupil boundary is considered to be a curve, determined directly by a sequence of pixels and not belonging to any existing class of figures.

Iris image segmen- Proposed solution tation 5 / 28 Efimov Y. Matveev I. Problem statement Input bitmap Related work Proposed solution A set of edge points Edge detection Pairs for voting Accumulator analysis Polar representation Pairs for a voting prosess Optimal path search Results Experiments Accumulator analysis Conclusion Polar transformation φ ϕ ρ ρ Optimal path search Result

Iris image segmen- Edge points selection tation 6 / 28 Efimov Y. Matveev I. To detect possible edges in an image Canny operator is Problem statement applied. In the neighborhood of the selected points gradient Related work components g x ( x , y ) and g y ( x , y ) are calculated using Sobel Proposed solution Edge detection masks and then gradient magnitude g ( x , y ) and angle Pairs for voting Accumulator analysis φ ( x , y ) are defined. A set of edge points Polar representation Optimal path search G = { x , y , g ( x , y ) , φ ( x , y ) } = { L , W } is formed. Results Experiments Conclusion

Iris image segmen- Paired Gradient method tation 7 / 28 Efimov Y. Matveev I. Problem statement Let q = ( x , y ) be an edge Main concept: Related work point. Then the selection Proposed solution criteria for a pair { q 1 , q 2 } , Edge detection Pairs for voting corresponding to a Accumulator analysis Polar representation hypothetical circle: Optimal path search Results Experiments || g ( q 1 ) || > T g , q o Conclusion ψ || g ( q 2 ) || > T g , q 2 q 1 ∠ ( g ( q 1 ) , g ( q 2 )) = ψ, g(q 1 ) g(q 2 ) || q 1 − q o || = || q 2 − q o ||

Iris image segmen- Paired Gradient method tation 8 / 28 Efimov Y. Matveev I. If the pair { q 1 , q 2 } is selected, then the parameters Problem statement p ( q 1 , q 2 ) = { x c , y c , r } of the correspondong hypothetical Related work circle are calculated as follows: Proposed solution the coordinates of an interception point q ∗ for the following Edge detection Pairs for voting Accumulator analysis lines Polar representation Optimal path search l 1 = q 1 − t 1 · g ( q 1 ) , Results Experiments l 2 = q 2 − t 2 · g ( q 2 ) Conclusion specify its center ( x c , y c ) and the radius can be found as � ( x 1 − x c ) 2 + ( y 1 − y c ) 2 . r = A set of hypothetical circle parameters P = { x i c , y i c , r i } M i =1 is formed, where M is the number of selected pairs.

Iris image segmen- Circular approximation tation 9 / 28 Efimov Y. Matveev I. Problem statement Center search: Related work The mentioned set P = { x i c , y i c , r i } M i =1 is used during the Proposed solution Hough voting process in the accumulator array Q . The Edge detection Pairs for voting zero-initialized array is filled with the center votes { x i c , y i c } : Accumulator analysis Polar representation Optimal path search M � Results if ( x , y ) = ( x i c , y i 1 , c ), � Q ( x , y ) = Experiments 0 otherwise. Conclusion i =1 An accumulator element, which received the most votes, i.e. the argument maxima q ∗ 1 = ( x ∗ c ) = argmax Q ( x , y ) is the c , y ∗ ( x , y ) most probable center position of the circle, approximating the most expressed iris boundary.

Iris image segmen- Circular approximation tation 10 / 28 Efimov Y. Matveev I. Center search: Problem statement Related work Proposed solution Edge detection Pairs for voting Accumulator analysis Polar representation Optimal path search Results Experiments Conclusion Figure: An accumulator array for ψ = 2 π 3

Iris image segmen- Circular approximation tation 11 / 28 Efimov Y. Matveev I. Problem statement Noise suppression: Related work Proposed solution Edge detection Considering the found eye Pairs for voting Accumulator analysis center position and using the Polar representation Optimal path search gradient information, a Results Experiments constraint may be introduced Conclusion for edge points in G : � q · g ( q ) � arccos < T a | q | · | g ( q ) |

Iris image segmen- Circular approximation tation 12 / 28 Radius detection: To determine the radius a distance Efimov Y. Matveev I. histogram H ( r ) is built: Problem statement H ( r ) = |{ q : q = ( x , y ) ∈ G , || q − q ∗ 1 || ∈ ( r − 0 . 5 , r + 0 . 5) }| . Related work Proposed solution Edge detection Its argument maxima corresponds to the sought-for radius Pairs for voting Accumulator analysis r ∗ 1 . Polar representation Optimal path search Results Edge points number normalized by r Experiments Conclusion 0.6 0.4 0.2 0 50 100 150 200 Distance r to edge points

Iris image segmen- Circular approximation tation 13 / 28 Efimov Y. Matveev I. Problem statement Related work Approximating the second boundary To detect the Proposed solution second iris boundary limiting constraints are imposed on its Edge detection Pairs for voting inner and outer radii: Accumulator analysis Polar representation Optimal path search r P > 1 Results 7 r I , Experiments Conclusion r P < 3 4 r I . � ( x I − x P ) 2 + ( y I − y P ) 2 . r P >

Iris image segmen- Circular approximation tation 14 / 28 Efimov Y. Matveev I. Approximating the second boundary: Values of the Problem statement original histogram in region r ∈ [0; 1 1 ] ∪ [ 3 1 ; 4 7 r ∗ 4 r ∗ 3 r ∗ 1 ], are set Related work to zero not to detect the already found iris boundary. New Proposed solution argument maxima corresponds to the second sought-for Edge detection Pairs for voting radius r ∗ 2 . Accumulator analysis Polar representation Optimal path search Results Edge points number normalized by r Edge points number normalized by r Experiments 0.6 0.6 Conclusion 0.4 0.4 0.2 0.2 0 0 50 100 150 200 50 100 150 200 Distance r to edge points Distance r to edge points

Iris image segmen- Pupil boundary refinement tation 15 / 28 Efimov Y. Matveev I. Polar representation: A polar transformation is applied to Problem statement Related work the edge map with the pole in ( x ∗ c ). A narrow zone of c , y ∗ Proposed solution the polar representation G p is considered, where Edge detection Pairs for voting y ∈ [ r P − 20; r P + 20]. Accumulator analysis Polar representation Optimal path search Results Experiments Conclusion

Iris image segmen- Pupil boundary refinement tation 16 / 28 Efimov Y. Matveev I. Problem statement Circular shortesh path method: Let there be a contour in Related work the polar representation, defined by a sequence of pixels: Proposed solution S = { ρ ( φ k ) } M k =1 . A cost for the path from ( n , ρ n ) to Edge detection Pairs for voting ( m , ρ m ) consists of two components: Accumulator analysis Polar representation Optimal path search Results C ( ρ n , ρ m ) = C 0 ( n , ρ n ) + C 1 ( ρ n , ρ m ) . Experiments Conclusion C 0 ( n , ρ n ) = g ( n , ρ n ) .  0, if ρ n = ρ m ,   C 1 ( ρ n , ρ m ) = T 1 , if | ρ n − ρ m | = 1 ,  ∞ , otherwise. 