Research On Key Problems Of Shape Representation And Analysis

Shapes carry many important properties of the objects in the real world. They play a central role in research fields such as object recognition, multimedia search, medical image analysis and computer assisted design&computer graphics. The shape variations are ubiquitous. Some of the variations reveal the properties of an object while the rest conceal them. This is due to the fact that the shape variations come from both various inside factors and outside interruptions. As a result, a shape should be ideally represented in the way that it should not only be robust to all the noises but also be invariant to some of the intrinsic variations in specific applications.Orientating at the properties of robustness and invariance, we conduct research on shape representation as well as its analysis and application in this thesis. Generally, we first propose new spline and polygonal shape representations to eliminate the noise effect, with the aim at preserving and extracting salient geometric shape features. Then we research the similar-transforms-invariant representation on non-rigid shape deformation and apply it in the computer aided diagnosis on intervertebral disc degeneration. The main contributions in the dissertation are as follows:1. The research on planar shape representation by a new type of spline is conducted. We first analyze the geometric properties of this spline model called elastic quadratic wire (EQW) and uncover the parameters’ affection on the performance of the EQW model. Taking the advantage of this, an improved version of the EQW model is proposed. The geometric feature along the contour can be adaptively preserved according to the saliency obtained by the discrete curve evolution (DCE) method. We then further incorporated the adaptive EQW model with an interactive image segmentation technique called Live Wire and apply it in extracting the objects’ boundaries in a few image modalities.2. An elastic quadratic patch (EQP) model is proposed, which is extended from the basic idea of EQW model, for robustly representing three dimensional shapes. In the model, an energy function quantifying0th and1st discontinuity is constructed based on overlapping quadratic patches for each controlling point and its neighborhood on the surface. This function is in the quadratic form and can be easily minimized explicitly through a specific vector of quadratic surface parameters. The EQP representation of the whole surface, which is as stable and geometry-preserving as the EQW model, can be then obtained through a pointwise iteration. The EQP model is able to preserve the details of the3D facial surface from the relatively high noise levels. 3. The research on planar shape representation by an efficient polygonal approximation is conducted. We describe the polygonal representation as the problem of the ε-isomerty shape reconstruction, which has some appealing properties such as the rigid descent reconstructing error and the quantitative relationship with a visual saliency metric. The mechanisms of point deleting, adding and adjusting are further proposed and incorporate into a new feature point extraction algorithm, which is efficient in approximating a shape, insensitive to arbitrary initialization and allows multiscale geometric features extraction.4. A novel framework of computer aided diagnosis (CAD) on disc degeneration is proposed. The disc degeneration is described with both shape and texture features. We quantify the non-rigid deformation between two shapes by approximating the geodesic length in the shape space. Similarly, the texture difference is measured with Bhattacharyya distance between intensity distributions of two disc regions. Then two measures are linearly combined as the appearance feature. We also introduce the idea of active learning into the CAD framework and present an improved transductive experimental design to better select representative instances for training the classifier. This technique achieves the comparable classifying accuracy with fewer training data and therefore alleviates the physicians’ burden.