In this digital era of our world, huge amounts of digital image data are being collected on a daily basis. The collected image data is being stored for subsequent processing and use in a wide variety of applications. For this purpose, it is often important to accurately and precisely extract relevant information out of this data. In computer vision applications, for instance, an important goal is to understand the contents of an image and be able to automatically gain an understanding of a scene, implying an extraction and recognition of an object. This task is, however, greatly complicated by the acquired image data being often noisy, and target objects and background bearing textural variations.As a result, there is a strong demand for reliable and automated image processing algorithms, for image smoothing, textured image segmentation, object extraction, tracking, and recognition.The objective of this thesis is to develop image processing algorithms which are efficient, statistically robust and sufficiently general, in order to account for noise and textural variations in images, and which have the ability to extract and provide compact and useful descriptions of target objects in images, for object recognition and tracking purposes.The main contribution of the thesis is the development of image processing algorithms, which are based on the theory of curve evolution with connections to information theory and probability theory. These connections form the basis for extracting a compact object description, in the form of a polygonal contour. One contribution is the development of a new class of curve evolution equations designed to preserve prescribed polygonal structures in an image while removing noise. In conjunction with these flows, a local stochastic formulation of a well-studied curve evolution equation, namely the geometric heat equation, provides an alternative microscopic as well as macroscopic view, which in turn led to our proposal of vanishing at pre-defined directions. Under these flows, the limiting shape of a curve is a polygon, pre-specified by the form and the parameters of the specific flow. The second contribution of the thesis is the development of a new active contour model which merges the desirable polygonal representation of an object directly to the image segmentation procedure by adapting an information-theoretic measure into an active contour framework with an ultimately unsupervised texture segmentation goal. The polygon-propagating models we develop can capture texture boundaries more reliably than the continuous active contour models because the evolution of an active polygon vertex depends on an overall speed function integrated along its two adjacent polygon edges rather than on pointwise measurements along continuous contour points. In this way, higher-order statistics which provide more adapted information than the first and second-order, are captured through both the nature of the information-theoretic criterion we utilize, and the nature of the polygon-evolving ordinary differential equations we propose. A supplementary contribution in this sequel is a new global polygon regularizer algorithm which uses electrostatics principles. The final contribution of the thesis is the development of a simple and efficient boundary-based object tracking algorithm well-adapted to polygonal objects. This is an extension of the second contribution of the thesis, and the key idea here is centered around tracking a relatively few vertices together with their corresponding edges, which in turn yields a bookkeeping simplicity and hence efficiency.The parsimonious set of features provided by the three methods developed in this thesis are useful for object-based description and recognition tasks, and in addition, may provide a viable solution to a parsimonious, and economical representation of large data sets (e.g. a contour represented by a few landmarks).
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Curve and Polygon Evolution Techniques for Image Processing
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