| The vision makes it possible for the human beings to be aware of the world around them. With the help of human vision, people can observe the world and meanwhile can also tell the change of the factors, such as position, depth of field and so on, that are caused by the variation of the vision. The task to duplicate the effect of human vision by electronically perceiving and understand an image is called the computer vision.Although the computer in the modern world is powerful to do even everything in our social life, the computer vision is not easy to be realized. The reason is that we live in a three-dimensional (3D) world, and when the computers try to analyze the objects in 3D space, the visual sensors available usually give two-dimensional (2D) image, and this projection to a lower number of dimensions incurs an enormous loss of information. Dynamic scenes such as those to which we are accustomed, with moving objects or a moving camera, make computer vision even more complicated. Thus, the major task to make the computer vision possible is to infer three-dimensional information from images that are taken from different viewpoints.At present, there are two approaches to achieve the major task of the computer vision. The first approach is based on previous camera calibration. However, calibration can not be used in active systems due to its lack of flexibility. Note that in active system, the optical and geometrical characteristics of the cameras might change dynamically depending on the imaging scene and camera motion. The second approach is based on computing the epipolar geometry between both imaging sensors.Two perspective images of a single rigid object/scene are related by the so-called epipolar geometry- the intrinsic projective geometry between two views, which can be described by a 3×3 matrix of rank-2. It is independent scene structure, and only depends on the cameras'internal parameters and relative pose. The matrix is called fundamental matrix. The fundamental matrix can be computed from the correspondences of the imaged scene points alone, without requiring knowledge of the cameras' internal parameters or relative pose. It contains all geometric information that is necessary for establishing the correspondences between two images, from which three-dimensional structure of the perceived scene can be inferred. Consider two images of the same three-dimensional scene taken from different viewpoints. If a point m = (u , v,1)Tin the first image and a point m ' = (u ', v',1)T in the second image correspond to the same physical 3D point in space, then m 'T Fm = 0, where F is a 3×3 matrix, called fundamental matrix. Although matrix F has nine elements, it has only seven degrees of freedom. Fundamental matrix is the basic tool in 3D reconstruction from two images.The importance of the fundamental matrix has been stressed in the last few years and it is now believed that it will have a significant role in future applications of computer vision. Applications using the fundamental matrix include 3D-structure recovery, motion segmentation and camera self-calibration, depth from stereo, structure from motion, ego-motion and image coding etc. Therefore an accurate and robust estimation of the fundamental matrix is crucial in computation vision. In a stereo vision system where the camera geometry is calibrated, it is possible to calculate such a matrix from the camera perspective projection matrices through calibration. When the intrinsic parameters are known but the extrinsic ones (the rotation and translation between the two images) are not, the problem is known as motion and structure from motion, and has been extensively studied in computer vision. We are interested here in different techniques for estimating the fundamental matrix from two images that are not calibrated, i.e., the case where both the intrinsic and extrinsic parameters of the images are unknown. Up till now, many methods have been proposed to compute the fundamental matrix from correspondences. These methods can be divided into three classes: linear methods, iteration methods and robust methods.We have studied the theory of the fundamental matrix, and proposed several new methods for estimating fundamental matrix.The speed of the original RANSAC depends on two factors. Firstly, the level of contamination determines the number of random samples that have to be taken to guarantee a certain confidence in the optimality of the solution. Secondly, the time spent evaluating the quality of each of the hypothesized model parameters is proportional to the size N of the data set. About RANSAC algorithm, improve the sampling strategy as follows: when the count of the trial is larger than some value, draw samples sometimes from the set of inliers and then sometimes from the set of all the data points, do sampling like this till the algorithm is over. When the count of the trial is less than some value, do sampling as the original RANSAC. Here the"some value"is fully discussed in chapter 4.The structure of the PROSAC algorithm is similar to RANSAC. First, hypotheses are generated by random sampling. The samples, unlike in RANSAC, are not drawn form all data, but from a subset of the data with the highest quality. The size of the hypothesis generation set is gradually increased. The samples that are more likely to be uncontaminated are therefore examined early. In fact, PROSAC is designed to draw the same samples as RANSAC, only in a different order. The hypotheses are verified against all data. As in RANSAC, the algorithm is terminated when the probability of the existence of solution that would be better than the best so far becomes low (smaller than 5%). About the Randomized RANSAC, when the count of the trial is larger than some value, the randomly chosen point used in pretest is from the inliers set. When the count of the trial is less than some value, the randomly chosen point used in pretest is from the entire data set. Here the"some value"is also discussed in chapter 4.The results of the exams show that the new algorithms are significantly improved in time and much more robust, and the time of the executions have been reduced by 30% ~ 60%. |
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