FUZZY COLOUR IMAGE FUZZY COLOUR IMAGE SEGMENTATION APPLIED SEGMENTATION APPLIED TO ROBOT VISION TO ROBOT VISION J. Chamorro-Martínez D. Sánchez B. Prados-Suárez Department of Computer Science and Artificial Intelligence. University of Granada
Overview Overview Image Segmentation. ! - What’s image segmentation?. - Classification of image segmentation techniques. - Fuzzy colour image segmentation. ! Colour Information Processing. - Combining information. - Colour space. - Colour comparison (distance). Proposed Algorithm. ! – Seed points. – Fuzzy Regions. Applications ! Conclusions. !
Description Description Segmentation Technique Region growing based on the distance Region Definition Region Construction Fuzzy subset of Based on topographic connected pixels and colour information. Algorithm Colour Processing Colour Space Distance measure HSI Membership degree Distance measure
Concept Image Segmentation: : Concept Image Segmentation ! Image Segmentation = Dividing an image into significant regions.
Classification Image Segmentation: : Classification Image Segmentation There are three groups of techniques, depending on the way they define the concept of “ Region”. Pixel Based Techniques Edge Based Techniques Area Based Techniques Region : Set of pixels bounded by a colour contour Histogram Clustering Growing Split & Merge Based Algorithms Region Algorithms Chosen Method Region : Set of pixels satisfying Region : Set of connected pixels a class membership function satisfying an uniformity condition
: Fuzzy Regions Fuzzy Regions Image Segmentation: Image Segmentation Fuzzy Region: Fuzzy subset of pixels. Every pixel of the image has a membership degree to the region. Maximum membership Membership degrees to the red-bounded region. Minimum membership All the pixels in the image belong to all the regions to a certain degree.
: Processing Processing Colour Information Information: Colour Solutions to process colour information. Analyzing each band separately and Combining the information of each band in a combining the results single value before processing (ej. histogram of each band and its combination) (ej. gradient) Problem: These techniques apply the same combination rule to the whole image. Region growing algorithms must consider the particularities in the comparison of two colours Solution: To use a colour space which take into account the particularities of the distance between colours, allowing us to define a metric.
Colour Information: : Space and Distance Space and Distance Colour Information HSI colour space : It’s a perceptual colour space with three components (Hue, Saturation, Intensity). { } + + + 3 ( G B ) min R , G , B R G B = = 1 − = H arctan S I − − 2 R G B I 3 There are three chromaticity regions , defined as: ≤ Achromatic if I T i I = T MAX I > ≤ I P [ H , S , I ] is Semichro m atic if I T and S Ts i i i i i I i = Ts 1 5 > > Chromatic if I T and S Ts i I i The distance between two colours (p i =[H i ,S i ,J i ], p j =[H j ,S j ,J j ]) is defined as a combination of the difference between their components. 0 if p or p are achromatic i j dI 2 = d d 1 2 + d H π MAX I s = d ( p i p , ) if p or p are chromatic 2 j i j 2 d otherwise = 2 2 + (MAX I 255) d d S 1 2 = dc ( p , p ) i j 2 − − ≤ π | H H | if | H H | = − = − = i j i j d | S S | d | I I | d Chromatic zone π − − S i j I i j H 2 | H H | otherwise i j Semichromatic zone Achromatic zone
Algorithm: : Seed poits Seed poits Algorithm Seed points selection is critical in region growing algorithms => Our method is focused for the case of indoor doors detection. We suppose that all the doors have at least one corner point in its frame. Algorithm Calculate the Seed Points θ = {s 1 , s 2 , s 3 , ..., s q } Harri’s corner detection method Corner Detection D = 7 Two seeds are placed at a D Seed Placement = 7 distance D from each corner, in the direction of its gradient (one in each way) . D = 7 Construct the Fuzzy Sets ~ ~ ~ ~ ~ Gradient => Sobel Operator Θ = { S , S , S ,... S , } 1 2 3 q Maybe too many seeds into the same door => too many regions.
Algorithm: : Fuzzy Regions Fuzzy Regions Algorithm Algorithm Π Π Π Π ij π ij A given path in Π ij . Set of possible paths Calculate the seed points linking p i and p j . θ = {s 1 , s 2 , s 3 , ..., s q } Cost( π π ij ) π π Cost of the path π ij Two consecutive pixels in π ij . p r , p r+1 linking p i and p j . π ij Optimum path in Π ij . It links p i Construct the Fuzzy Sets Colour distance dc(p r ,p s ) * ~ ~ ~ ~ ~ Θ = between p r and p s and p j with minimum cost. { S , S , S ,... S , } 1 2 3 q Distance pi → pj. It’s the cost of the optimum path linking them. d p (p i , p j ) Region Growing We have to define: { } π = π ∋ • Distance Between Pixels = π * π * = π cos t ( ) max dc ( p , p ) | p , p dp ( p , p ) cos t ( ) arg min{ cost ( )} + + ij r r 1 ij r r 1 i j ij ij ij • Membership Function P 0 P 1 P 2 Path 1 = π 62 Big colour difference => ↑ ↑ ↑ dc ↑ Path 2 = π 62 ↓ dc (small colour jump) ↓ ↓ ↓ ⇓ P 3 P 4 P 5 ⇓ ↑ ↑ ↑ ↑ Cost( π 62 ) d p (p 6 ,p 2 )= Cost( π π 62 ) π π ↓ Cost( π 62 ) ↓ ↓ ↓ ⇓ P 6 P 7 P 8 * = π 62 π 62
Algorithm: : Fuzzy Regions Algorithm Fuzzy Regions – – Obtaining d Obtaining d p p ! Characteristics of the distance: – It’s sensitive to the presence of edges (edge => high distance in the consecutive pixels of the path which are on that edge). – It uses colour information (distances between colours). I = image NxM – It also uses topographic information (paths). s v = seed point ! Notation: – Contour(L) = Pixels in the contour of the region L. Inicialization: – Neighbor(p i ) = 8-neighborhood of p i . d p (s v ,s v ) = 0 Algorithm Algorithm – Card(L) = Cardinality of the region L. L = {s v } While Card(L) ≠ NxM End = ∋ ∋ (p ,p ) arg min {dc(p ,p |Contour(L ) p ;Neighbor( p )\L p }) in out i j i i j (p ,p ) i j = d ( p , s ) max[ d ( p , s ), d ( p , p )] p out v p in v c in out = U L L { p } out
Algorithm: : Fuzzy Regions Fuzzy Regions Algorithm Algorithm Calculate the seed points θ = {s 1 , s 2 , s 3 , ..., s q } Construct the Fuzzy Sets − * 1 d ( p , s ) Θ ∋ ≠ q 1 if p and p s µ = p i v ∑ ~ ~ ~ ~ ~ ( p ) µ = i i v * Θ = ~ { S , S , S ,... S , } ( p ) 1 d ( p , s ) i S q ~ ∑ 1 2 3 q v p i v i − d ( p , s ) otherwise * S 1 d ( p , s ) v = p i v v 1 p i v = Region Growing k 1 We have to define: • Distance Between Pixels ~ ~ Seed of the region . θ ∋ s v • Membership Function A fuzzy region. S S s v v v ~ Distance from píxel Set of fuzzy regions: d p * (p i , s v ) Θ ~ ~ ~ ~ Θ = { S , S ,..., S } p i to seed s v . 1 2 q µ ~ ( p ) Membership degree of the pixel p i to the fuzzy region . S ~ i S v v
Algorithm: : Fuzzy Regions Algorithm Fuzzy Regions - - Region Growing Region Growing Θ = Computational Complexity: O(qnK): { s , s ,..., s } 1 2 n Algorithm - q = number of seeds. - n = N x M Calculate the seed points For every seed, s v , in θ q times θ = {s 1 , s 2 , s 3 , ..., s q } - K = max{N, M} Construct the Fuzzy Sets For every pixel, p i , in I ~ ~ ~ ~ ~ Θ = { S , S , S ,... S , } 1 2 3 q Region Growing µ s p ( ) Compute ~ We have to define: i v In the algorithm to calculate d p a new step is included: O(nK) • Distance Between Pixels “Eliminate all the seeds, s u , verifying dp(s v ,s u ) < C” • Membership Function End ~ ~ ~ ~ Θ = { S , S ,..., S } The constat C has been fixed to 0.05. 1 2 q The maximum size of a contour is 2N+2M.
Results Results 5 12 10 34 4 14 3 12 • Robot Nomad 200 • Sony EVY-401 colour camera 4 8 9 30 The algorithm has segmented ... regions from ... seeds.
Conclusions Conclusions ! Although in the examples we can find degradation in the iluminance and zones with different brightness, this method segments the whole door without splitting it in several parts. ! The technique is based on the growth of regions, treated as fuzzy subsets. ! The colour information is processed using a distance measure defined in the HSI colour space. ! The membership function combines colour and topographic information. ! The combination of the proposed colour distance and the growing region process improves the results obtained with the classical techniques.
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