978-1-4244-5998-8/10/$26.00 ©2010 IEEE A New Method for Texture Image Segmentation Idrissi Sidi Yassine, Samir Belfkih, Said Najah, Khalid Zenkouar Département d’informatique Laboratoire GRETIC Faculté des sciences et techniques Fés Maroc Abstract— In this paper we present a new texture descriptor based on the shape operator defined in differential geometry. Then we describe the texture feature analysis process based on the spectral histogram. After that we describe a new algorithm for texture segmentation using this descriptor, statistics based on the spectral histogram, and mathematical morphology. Many results are presented to illustrate the effectiveness of our approach. Keyword—Textures Segmentation, Spectral Histogram, Differential Geometry, Mathematical Morphology. I. INTRODUCTION Texture image segmentation is a fundamental problem in computer vision with a wide variety of applications. The texture can be regarded as a similarity grouping in an image. The local sub-pattern properties give rise to the perceived lightness, uniformity, density, roughness, regularity, linearity, frequency, phase, directionality, coarseness, randomness, fineness, smoothness, granulation, etc. Because texture is regarded as a rich of source of visual information, it is difficult to define the properties that can be used effectively to characterize all textures and to find a set of properties that can be used to distinguish textures found in a given image. And it is also difficult to determine the texture region boundary accurately because the texture is a region property rather than a point property. The common approaches to solve the textured image segmentation problem can be classified to be either supervised or unsupervised algorithm based on whether the number of textures contained in the image is known in advance or not. The typical methods are region growing, estimation theory based on maximum likelihood, split-and-merge, Bayesian classification, probabilistic relaxation, clustering, the Mumford-Shah model, etc. In this paper, we choose the spectral histograms as the texture feature and adopt an effective computing method to evaluate the similarity between histograms. Spectral histogram consists of histograms of response images of chosen filters. It can capture local spatial patterns through filtering and global patterns through histograms and constraints among different filters compared with the above texture analysis methods. Based on the determined texture features, we can obtain the initial segmentation result. Skeleton extracting algorithm based on mathematical morphology is applied to determine the texture region boundary accurately. The outline of our paper is as follows: In section 2, we introduce the intrinsic texture descriptor. Then in section3, we describe the texture feature analysis process based on the spectral histogram. In Section 4, skeleton extracting algorithm applied to obtain the accurate texture region boundary. Experimental results are shown and discussed in Section 5. Finally, Section 6 gives the conclusion. II. NEW TEXTURE DESCRIPTOR A. Previous Work In this work, we are particularly interested in the Beltrami representation introduced by Sochen, Kimmel and Malladi in [1]. Sochen et al proposed a new efficient representation of images by considering images as a Riemannian manifold embedded in a higher dimensional space. For instance, a standard 2 dimensional gray value image 2 : I IR IR + → can be viewed as a surface  with local coordinates (, ) x y embedded in 3 IR by a smooth mapping: 1 2 3 :( , ) ( , , (, )) X xy X xX yX Ixy → = = = . (1) This manifold-based representation of images offers two main advantages. Firstly, it allows to use efficient tools borrowed from differential geometry to perform different image processing tasks such as denoising or segmentation as we will do in this paper. The second main advantage is the ability to work with arbitrary N dimensional images. Sagiv, Sochen and Zeevi in [2] used the Beltrami framework to represent the texture image as a 2-D dimensional manifold embedded in a space of N + 2 dimensions, where N is the number of Gabor responses. They used the first fundamental form [3], also called metric tensor, of the texture manifold to define an intrinsic edge detector like in [11]. The idea of using the metric tensor to intrinsically define the edges between different homogeneous texture regions is efficient in the context of differential geometry. Indeed, the first fundamental form describes the distortion or rate of change of the manifold and so can detect boundary between different parts of the manifold corresponding to different homogeneous textures. More precisely Sagiv et al used the geodesic active contour model [4] to drive the evolving contour toward the boundaries between two different texture regions by considering the edge detector function or stopping function as the inverse of the determinant of the metric tensor. This can be explained in the following way. If we consider the definition of the first fundamental form: , X X g μν μ ν   ∂ ∂ = < >   ∂ ∂   . (2) Where μ ,ν , x y = in the (, ) x y - basis, we have in the case of gray scale images, (, ,) X xyI = and 2 1 xx x g I = + ,