Variational Models for Segmentation of Texture Images

This dissertation is a contribution to computer vision and its analysis. The main work of this dissertation is to develop segmentation models for texture images. Texture segmentation aims at segmenting an image composed of textures, into distinct homogeneous regions with dissimilar texture features. For this purpose, some new variational texture image segmentation models are proposed. In these models, L0 norm smoothing and region based active contour approaches are utilized. Due to the smoothing and edge preserving properties of L0 gradient norm, the first proposed model utilizes L0 gradient norm for smoothing texture and minor details in the image and Mumford Shah data fidelity for segmentation. To get a texture free image, the model is minimized through alternating minimization algorithm and for segmentation, the model is minimized through Euler Lagrange’s equation. For efficient solution, the additive operator splitting method is applied to numerically solve the partial differential equations. As the L1 norm is more robust than L2 norm, therefore, in the next model, instead of the L2 norm, L1 norm is utilized in the data term and L0 gradient norm as a regularization for smoothing texture. For segmentation piecewise Mumford-Shah data term in level set formulation is used. Both the above models depend on the selection of initial contour and also producing staircasing problem. To resolve these issues, a convex variational model is proposed which is the unified form of L0 norm smoothing and convex minimization model. This model is independent of initial contour and overcome the problem of staircasing effect efficiently. Nevertheless, the model still producing problems when segmenting some hard textured images or when the image boundary is unclear and diffused. To overcome these problems, a joint smoothing and segmentation model by using piecewise smooth approximations is proposed. In this model, first, in the fidelity term instead of constant intensity means we approximated the image with piecewise smooth functions. Second, a signed pressure force function is utilized to stop the contours at minor or blurred boundaries and to speed up the process of contour movement. Third, L0 gradient norm is employed to smooth the textured image. In this dissertation, our second goal is to develop a texture image selective segmentation model. As in some cases it is very important to segment a region/part of interest from the whole image. Therefore to achieve this, some geometrical constraint are incorporated in the model. Furthermore, to fulfil our final goal, a multi-phase segmentation model via level set and L0 norm smoothing for texture images is proposed. This model may segment texture, noisy and inhomogeneous images more efficiently as compare to other state of the art models.