Color segmentation by ordered mergings

The paper deals with the use of the various color pieces of information for segmenting color images and sequences with mathematical morphology operators. It is divided in four parts. The first one is concerning the choice of the color space suitable for morphological processing. The choice of a connection which induces a specific segmentation is discussed in section 2. Section 3 presents the color segmentation approach which is based on a non-parametric pyramid of watersheds, with a comparative study of different color gradients. In section 4 is introduced another multiscale color segmentation algorithm, relying on the merging of chromatic-achromatic partitions ordered by the saturation component. 1. CHOICE OF A COLOR SPACE A recent study [7] has shown that many color spaces (HLS, HSV, ... ) having been developed for computer graphic applications, are unsuited to image processing. A convenient representation must yield distances, or norms, and provide independence between chromatic and achromatic components. We adopt here an improved family of HLS systems that satisfy these prerequisites, and compare it with other spaces, such as Lab. This space is named Imploved HLS (IHLS). There are three versions of IHW. using the norm L I , the norm Lz or the norm m a r min. The equations of transformation between RGB and the new HLS systems are given in [7] [13]. For the sake of simplicity, all the examples of the paper were obtained according to the equations: L = 0.212R + 0.715G + 0.072B. S = max(R,G,B) min(R,G,B), H' = 2. CHOICE OF CONNECTIONS Another recent study 1121 proposes a theory where the segmentation of an image is defined as the maximal partition of its space of definition, according to a given criterion. See also Serra's paper in this conference [14]. The criterion cannot be arbitrary and permits to niaximize the partition if and only if the obtained classes are connected components of some connection (connective criterion). Therefore, the choice of a connection induces specific segmentation. In this paper, four connections are investigated, namely flat-zones, quai-flat zones, jump connection and watershed connection. 3. NON-PARAMETRIC PYRAMID OF WATERSHEDS The watershed transformation, a pathwise connection, is one of the most powerful tools for segmenting images. The watershed lines associate a catchment basin to each minimum of the function [ I ]. Typically, the function to flood is a gradient function which catches the transitions between the regions. Using the watershed on a grey tone image without any preparation leads to a strong over-segmentation (large number of minima). There are two alternatives in order to solve the over-segmentation. The fist one consists in initially determining markers for each region of interest: using the homotopy modification, the gradient function has as local minima only the region markers. The need of a criterion for defining the markers can make diffcult the generalisation. The second alternative involves a non-parametric approach which is based on merging the catchment basins of the watershed image belonging to almost homogenous regions; this technique known as waterfall algorithm [2] is discussed below. Both strategies can he performed in a hierarchical framework which levels yield different degrees of partition of the images structures. The watershed method is meaningful only for grey tone images (is based on the existence of a total ordering relation in a complete lattice). However, it can be easily used for segmenting color images by defining a scalar gradient function corresponding to the color image. 0-7803-7750-8/03/$17.00 02003 IEEE 11 125 3.1. Color gradients The color gradient function at the point x is associated to a measure of color disimilarity or distance between the point and the set of neighbours at distance one from x : , K(x). For our purposes, three definitions of gradient have been used, Morphological gradient, of(.): This is the standard morphological (Beucher algorithm) gradient for grey level images (f : E -+ T , where E is an Euclidean or digital space and T is an ordered set of greylevels)[IO],Vf= 6 ~ ( f ) E K ( ~ ) . Circularcentred gradient, V,a(z): If a(.) is afunction containing angular values ((I : E -+ C, where C i s the unit circle), the circular gradient is calculated by the expression[6],VCa(t) = V[a(z)+a(y),y E I i (z)]A [ a ( z ) t a ( y ) , y E K ( z ) ] w b e r e a + d = I a a ' I iff I a a' I< 90" and a i a' = 180"I a a' I iff I a a' I< 90". Euclidean gradient, V ~ f ( z ) : Very interesting for vectorial functions ( f (x) = (f~(x), ...,f,,( z))), it is based on computing the Euclidean distance d E [9], VEf(Z) = V [ ~ E ( ~ , Y ) , Y E Ji(r)] A [ d ~ ( z , y ) , y E l i (x)] . Let f be a color image, its components in the IHLS color space are ( f ~ , f ~ , fs) and k t ( f ~ , fa, fd be the components for the Lab color space. We define a series of gradients for 9: ( I ) Luminance gradient: VLf(z) = Vf~( . c ) ; ( 2 ) Hue circular gradient: V H f ( i ) = VJH(Z): ( 3 ) Satumtion weighing-based color gmdient: Vsf(z) = fs ( . ) x V J H ( I ) +fi(z) x V ~ L (z) (where f; is the negative of the saturation component): (4) Supemum-based color gradient: Va"pf(x) = v [ V ~ , ~ ( z ) , f J f ~ ( x ) , V ~ f H ( . ~ ) j ; (5)Chmmatic gradient: Vcf(z) = VF(fa, fb)(z): (6) Perceptual gradient: Vpf(z) = V ~ ( { f , , f ~ , f b ) ( ~ ) . InFigure 1 isdepicted a comparative of the gradients of a color image.