| A basic problem, in such areas as image analysis, computer vision, automatic navigation, diagnosis based on medical image and image database retrieval, is the automatic segmentation, description and recognition of objects in image. It has important application in robot, cars without drivers, intelligent computer and so on. The general process of recognition of objects is the following: Firstly, segment objects from the image. Secondly, calculate the invariant independent of transformation of objects according to the description of contour. Finally recognize the object with some algorithms in pattern recognition. Due to complexity of images in realistic world, objects in image blocks mutually. Besides, during the creation of photograph, noise are introduced and objects are distorted under perspective transformation. The existing approaches to recognize objects exhibit obvious limitation. In fact, the validity and generality of recognition approach of objects depend on mathematics model introduced. In this dissertation, segmentation, description and recognition of objects are studied systematically by the variogram function and implicit polynomial(IP) curve.The variogram function comes from linear geological statistics, which exhibits not only the stochastic but also the structural properties of image data. The rnultiscale edge detection and texture image segmentation are studied based on the variogram function. At the same time, according to the excellent capability of IP curves, we study fitting and description of objects, determination of invariants of objects, symmetry detection and recognition of objects based on IP curves. In all, the main contributions in the dissertation are as follows:(1)A method of determining automatically the scale of the multiscale edge detection is proposed based on the variant distance of the variogram function, and a method of segmenting texture images is also presented. The variograin values are taken as stochastic and structural properties of texture images and variant distance is taken as the size of image window. The experimental results show that these two algorithms are efficient and computational complexity is low.(2)We prove that necessary and sufficient conditions for bounded and closed IP curves are that second-degree polynomial factor curves in the leading binomial productVAbstractdecomposed from the leading form of [P are ellipses. In addition, the conditions to avoid the loop of [P curve are given. The method of obtaining ellipses by decomposing II?would help to accurately describe objects and calculate their invariants.(3)The methods of determining the degree of II?curves based on the boundary of objects and tightly fitting objects with IP curve are proposed. The algorithms would help to fit and describe objects automatically by computer.(4)We prove that shapes of ellipses obtained from the leading binomial of [P are independent of the decomposing methods, and two ellipse equations removing their constants satisfy the same relation of transformation as two [P curves under the perspective transformation. On the basis of the theory, the methods of calculating Euclidean and affine invariants are proposed. The experimental results show that the invariants are efficient and robust to recognize objects and even to recognize the object with some information missing.(5)The algorithm of the symmetry detection is presented base on II?curves. In contrast to the existing methods which can detect one type of symmetry, the advantage of the algorithms is that it can detect both type and axis of symmetry. Due to the introduction of [P curves, the method detects the symmetry and axis of objects by using the expressions of function instead of using the optimization method. Consequently, the computational cost of the method is low.In addition, the methods presented by the dissertation can also be applied to character recognition, speech segmentation and recognition, obstacle avoidance for robot, image data...
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