Computer Vision is the study of theories and algorithms for automating the process of visual perception. Uncertainty abounds in every phase of computer vision. How to express and deal with uncertainty directly affect the computational complexity, applicability and robustness of computer vision algorithms. As a powerful tool for manipulating uncertainty, Fuzzy Mathematics has achieved a high degree of success and popularity in many areas. The history of its application in computer vision, however, is still very short; the methods and techniques are far from being mature. Therefore, the purpose of this paper is to give a deep study of fuzzy approach to computer vision. First, we employ the fuzzy number to deal with the uncertainty in three dimensional modeling and line extracting. While describing the uncertainty with the fuzzy number, the most important thing is to determine the shape of the fuzzy number. According to the source of uncertainties in the above procedures, we select trapezoidal fuzzy number to express the parameters of geometric primitives such as points, lines and planes. For consistent interpretation about geometric primitives between different coordinate frames, we also fuzzify the rotation matrix and translation vector by assigning appropriate fuzzy numbers to the rotation angles and translations. Feature matching plays an important role in computer vision. The ability to solve the correspondence problem reliably and efficiently depends to a great extent on the similarity, measure employed for this matching. To deal with the uncertainty in the matching procedure, we design a fuzzy similarity measure ( FSM ) which computes the possibility function, and decides the correspondence based on it. Fuzzy Similarity Measure takes global attributes as well as local attributes of the features into account, so it greatly increases the correct matching number between 3D model and 2D image features and makes the matching procedure robust. As an application, we employ the above approach in our Vision-Based Robot Navigation System to solve the uncertainty problems in robot self-localization. Besides, we control the camera to search the landmark in the environment actively - the idea of active vision, and we predict the pose of the robot and the appearance of the landmark in the image with a priori knowledge about the movement of the robot. As a result, the speed of matching procedure increases greatly. A large number of experiments in the real indoor environment demonstrate the usefulness of the proposed methodology.
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