Reformulating active contours for object segmentation - Wang, Junyan (2012)
Object segmentation is a fundamental problem in computer vision. Active contour is a general mathematical model for object segmentation. In an active contour model, an energy functional is formulated based on the observations of visual properties of object boundaries or object regions enclosed by the boundaries. By minimizing the energy functional, we expect to locate the enclosing boundaries of the regions of objects. This thesis addresses the following three fundamental problems in object segmentation based on active contour. (I) How can we formulate active contour models for segmenting objects based on its boundary properties or its regional properties? (II) If the object boundary or the object region appears partially in the image, due to occlusion or cluttered scene, how can we reformulate the active contour models in order to segment the object and recover the original object shape? (III) Given a real image containing a clutter of objects, how can we incorporate the prior information of the object of interest in the active contour formulation for segmenting the object of interest correctly without user intervention? Most of the existing active contour models are based on edge detection, known as the edge-based active contours. The first contribution in this thesis is to address a well-known problem in the edge-based active contours, namely the problem of early termination of curve evolution. In this thesis, the problem is studied by examining the fundamental formulation of the edge-based active contour models. The formulation of edge-based active contour models often involves an edge indicator function. Conventionally, only the normal component of the gradient of the edge indicator function is considered. It is argued in the thesis that the tangential component should also be included. To include the tangential component, a new edge-based active contour model called the Geodesic Snakes and the corresponding curve evolution algorithm are developed for segmentation in edge-based active contour. The active contour models based on regional properties have been proposed as an alternative to the edge-based active contour models. The second contribution in this thesis is a novel region-based active contour model for coping with non-smooth image structures. For segmentation of non-smooth structures, such as textures, the image texture features have been previously used in the active contours. In this thesis, the problem of segmenting non-smooth image structures is formulated as a novel active contour model in terms of piecewise linear patch reconstruction, motivated by the Mumford-Shah model. It is also proven that the minimization of the patch reconstruction error leads to reduction of the segmentation error. Without requiring a separate process of feature extraction, the segmentation is accomplished in a principled way by minimizing the proposed single energy functional of piecewise linear patch reconstruction through curve evolution and optimal linear patch reconstruction. Due to occlusion and/or cluttered scene resulting in missing parts or overlapping objects in the image, the energy minimization of the generic active contour models by curve evolution cannot extract the object shape of interest correctly. An object of interest may also undergo some deformation causing changes to its observed shape. Depending on the type of the object the deformation may be rigid or non-rigid. The third contribution of this thesis is a novel deterministic model of rigid and nonrigid shape deformations based on curve evolution, giving rise to the Prior Variation Shape Evolution (PVSE) equation. The PVSE is used in minimizing active contour energy for locating the object boundary of the deformed and/or recovered shape. To segment the object of interest, an active contour is often initialized manually by an user. The fourth contribution in this thesis is a method to enable automatic contour initialization in active contours for segmenting the object of interest. By incorporating local feature matching and shape prior modeling into the active contour framework, a matching-constrained active contour model for automatic object segmentation is proposed. The initial contour, which is also the initial feasible solution to the constrained optimization, is generated by local feature matching followed by an affine invariant point-to-shape alignment. The first and second contributions address Problem (I), the third contribution addresses Problem (II) and the last contribution tackles Problem (III). These contributions are made to the following three emerging directions of research on active contours: (i) the boundary and region modeling, (ii) the incorporation of shape priors and, (iii) the automation of object segmentation.