Clustering is an important problem, which has been applied in many research areas. However, there... more Clustering is an important problem, which has been applied in many research areas. However, there is a large variety of clustering algorithms and each could produce quite different results depending on the choice of algorithm and input parameters, so how to evaluate clustering quality and find out the optimal clustering algorithm is important. Various clustering validity indices are proposed under this background. Traditional clustering validity indices can be divided into two categories: internal and external. The former is mostly based on compactness and separation of data points, which is measured by the distance between clusters' centroids, ignoring the shape and density of clusters. The latter needs external information, which is unavailable in most cases. In this paper, we propose a new clustering validity index for both fuzzy and hard clustering algorithms. Our new index uses pairwise pattern information from a certain number of interrelated clustering results, which focus more on logical reasoning than geometrical features. The proposed index overcomes some shortcomings of traditional indices. Experiments show that the proposed index performs better compared with traditional indices on the artificial and real datasets. Furthermore, we applied the proposed method to solve two existing problems in telecommunication fields. One is to cluster serving GPRS support nodes in the city Chongqing based on service characteristics, the other is to analyze users' preference. INDEX TERMS Pairwise pattern, clustering validity, clustering analysis, fuzzy c-means.
2017 International Smart Cities Conference (ISC2), 2017
For safety and reliability of self-driving cars, their control system must use the relative veloc... more For safety and reliability of self-driving cars, their control system must use the relative velocity of vehicles. The relative velocity can be estimated by differentiating the measured distance between cars with respect to time. However, inevitable measurement noise in the distance measurements will be amplified by the derivative operation. In this paper, we provide, as an alternative, a time-to-contact based approach to estimating the relative velocity, which can also be fused with measurements from other sensors, if desired. The system is implemented on Android smart phones running in real-time. Index Terms-Self-driving cars, car-following control, time to contact, machine vision, android smartphones.
Computer Graphics and Image Processing, Oct 1, 1982
A method is proposed for determining the motion of a body relative to a fixed environment using t... more A method is proposed for determining the motion of a body relative to a fixed environment using the changing image seen by a camera attached to the body. The optical flow in the image plane is the input, while the instantaneous rotation and translation of the body are the output. If optical flow could be determined precisely, it would only have to be known at a few places to compute the parameters of the motion. In practice, however, the measured optical flow will be somewhat inaccurate. It is therefore advantageous to consider methods which use as much of the available information as possible. We employ a least-squares approach which minimizes some measure of the discrepancy between the measured flow and that predicted from the computed motion parameters. Several different error norms are investigated. In general, our algorithm leads to a system of nonlinear equations from which the motion parameters may be computed numerically. However, in the special cases where the motion of the camera is purely translational or purely rotational, use of the appropriate norm leads to a system of equations from which these parameters can be determined in closed form.
Journal of the Optical Society of America, Apr 1, 1987
Finding the relationship between two coordinate systems using pairs of measurements of the coordi... more Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. I present here a closed-form solution to the least-squares problem for three or more points. Currently various empirical, graphical, and numerical iterative methods are in use. Derivation of the solution is simplified by use of unit quaternions to represent rotation. I emphasize a symmetry property that a solution to this problem ought to possess. The best translational offset is the difference between the centroid of the coordinates in one system and the rotated and scaled centroid of the coordinates in the other system. The best scale is equal to the ratio of the root-mean-square deviations of the coordinates in the two systems from their respective centroids. These exact results are to be preferred to approximate methods based on measurements of a few selected points. The unit quaternion representing the best rotation is the eigenvector associated with the most positive eigenvalue of a symmetric 4 X 4 matrix. The elements of this matrix coordinates of the points.
Journal of the Optical Society of America, Oct 1, 1991
Relative Orientation is the recovery of the position and orientation of one imaging system relati... more Relative Orientation is the recovery of the position and orientation of one imaging system relative to another from correspondences between five or more ray pairs. It is one of four core problems in photogrammetry and is of central importance in binocular stereo, as well as in long range motion vision. While five ray correspondences are sufficient to yield a finite number of solutions, more than five correspondences are used in practice to ensure an accurate solution using least squares methods. Most iterative schemes for minimizing the sum of squares of weighted errors require a good guess as a starting value. The author has previously published a method that finds the best solution without requiring an initial guess. In this paper an even simpler method is presented that utilizes the representation of rotations by unit quaternions.
One can recover the motion of an observer in a static environment directly from first derivatives... more One can recover the motion of an observer in a static environment directly from first derivatives (spatial and temporal) of image brightness, accumulated over a large part of the image. There is no need to extract features and to determine correspondences between features in successive frames. This is fortunate, since the correspondence problem in the case of motion vision is even harder than it is for binocular stereo, where matching features have to lie on corresponding epipolar lines. Motion vision—at least short-range motion vision—should be easier than binocular stereo, not harder. In the case of rigid body motion there is also no need to first estimate the optical flow, since it is so highly constrained.
For safety and reliability of self-driving cars, their control system must use the relative veloc... more For safety and reliability of self-driving cars, their control system must use the relative velocity of vehicles. The relative velocity can be estimated by differentiating the measured distance between cars with respect to time. However, inevitable measurement noise in the distance measurements will be amplified by the derivative operation. In this paper, we provide, as an alternative, a time-to-contact based approach to estimating the relative velocity, which can also be fused with measurements from other sensors, if desired. The system is implemented on Android smart phones running in real-time. Index Terms-Self-driving cars, car-following control, time to contact, machine vision, android smartphones.
Computer vision, graphics, and image processing, 1983
In this paper, we show how to recover the motion of an observer relative to a planar surface dire... more In this paper, we show how to recover the motion of an observer relative to a planar surface directly from image brightness derivatives. We do not con~pute the optical flow as an intermediate step. We derive a set of nine non-linear equations using a least-squares formulation. A simple iterative scheme allows us to find either of two possible solutions of these equations. An initial pass over the relevmt image region is used to accumulate a number of moments of the image brightness derivatives. All of the quantities used in the iteration can be efficiently computed from these totals, without the need to refer back to the image. A new, compact notation allows us to show easily that there are at most two planar solutions.
Clustering is an important problem, which has been applied in many research areas. However, there... more Clustering is an important problem, which has been applied in many research areas. However, there is a large variety of clustering algorithms and each could produce quite different results depending on the choice of algorithm and input parameters, so how to evaluate clustering quality and find out the optimal clustering algorithm is important. Various clustering validity indices are proposed under this background. Traditional clustering validity indices can be divided into two categories: internal and external. The former is mostly based on compactness and separation of data points, which is measured by the distance between clusters' centroids, ignoring the shape and density of clusters. The latter needs external information, which is unavailable in most cases. In this paper, we propose a new clustering validity index for both fuzzy and hard clustering algorithms. Our new index uses pairwise pattern information from a certain number of interrelated clustering results, which focus more on logical reasoning than geometrical features. The proposed index overcomes some shortcomings of traditional indices. Experiments show that the proposed index performs better compared with traditional indices on the artificial and real datasets. Furthermore, we applied the proposed method to solve two existing problems in telecommunication fields. One is to cluster serving GPRS support nodes in the city Chongqing based on service characteristics, the other is to analyze users' preference. INDEX TERMS Pairwise pattern, clustering validity, clustering analysis, fuzzy c-means.
2017 International Smart Cities Conference (ISC2), 2017
For safety and reliability of self-driving cars, their control system must use the relative veloc... more For safety and reliability of self-driving cars, their control system must use the relative velocity of vehicles. The relative velocity can be estimated by differentiating the measured distance between cars with respect to time. However, inevitable measurement noise in the distance measurements will be amplified by the derivative operation. In this paper, we provide, as an alternative, a time-to-contact based approach to estimating the relative velocity, which can also be fused with measurements from other sensors, if desired. The system is implemented on Android smart phones running in real-time. Index Terms-Self-driving cars, car-following control, time to contact, machine vision, android smartphones.
Computer Graphics and Image Processing, Oct 1, 1982
A method is proposed for determining the motion of a body relative to a fixed environment using t... more A method is proposed for determining the motion of a body relative to a fixed environment using the changing image seen by a camera attached to the body. The optical flow in the image plane is the input, while the instantaneous rotation and translation of the body are the output. If optical flow could be determined precisely, it would only have to be known at a few places to compute the parameters of the motion. In practice, however, the measured optical flow will be somewhat inaccurate. It is therefore advantageous to consider methods which use as much of the available information as possible. We employ a least-squares approach which minimizes some measure of the discrepancy between the measured flow and that predicted from the computed motion parameters. Several different error norms are investigated. In general, our algorithm leads to a system of nonlinear equations from which the motion parameters may be computed numerically. However, in the special cases where the motion of the camera is purely translational or purely rotational, use of the appropriate norm leads to a system of equations from which these parameters can be determined in closed form.
Journal of the Optical Society of America, Apr 1, 1987
Finding the relationship between two coordinate systems using pairs of measurements of the coordi... more Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. I present here a closed-form solution to the least-squares problem for three or more points. Currently various empirical, graphical, and numerical iterative methods are in use. Derivation of the solution is simplified by use of unit quaternions to represent rotation. I emphasize a symmetry property that a solution to this problem ought to possess. The best translational offset is the difference between the centroid of the coordinates in one system and the rotated and scaled centroid of the coordinates in the other system. The best scale is equal to the ratio of the root-mean-square deviations of the coordinates in the two systems from their respective centroids. These exact results are to be preferred to approximate methods based on measurements of a few selected points. The unit quaternion representing the best rotation is the eigenvector associated with the most positive eigenvalue of a symmetric 4 X 4 matrix. The elements of this matrix coordinates of the points.
Journal of the Optical Society of America, Oct 1, 1991
Relative Orientation is the recovery of the position and orientation of one imaging system relati... more Relative Orientation is the recovery of the position and orientation of one imaging system relative to another from correspondences between five or more ray pairs. It is one of four core problems in photogrammetry and is of central importance in binocular stereo, as well as in long range motion vision. While five ray correspondences are sufficient to yield a finite number of solutions, more than five correspondences are used in practice to ensure an accurate solution using least squares methods. Most iterative schemes for minimizing the sum of squares of weighted errors require a good guess as a starting value. The author has previously published a method that finds the best solution without requiring an initial guess. In this paper an even simpler method is presented that utilizes the representation of rotations by unit quaternions.
One can recover the motion of an observer in a static environment directly from first derivatives... more One can recover the motion of an observer in a static environment directly from first derivatives (spatial and temporal) of image brightness, accumulated over a large part of the image. There is no need to extract features and to determine correspondences between features in successive frames. This is fortunate, since the correspondence problem in the case of motion vision is even harder than it is for binocular stereo, where matching features have to lie on corresponding epipolar lines. Motion vision—at least short-range motion vision—should be easier than binocular stereo, not harder. In the case of rigid body motion there is also no need to first estimate the optical flow, since it is so highly constrained.
For safety and reliability of self-driving cars, their control system must use the relative veloc... more For safety and reliability of self-driving cars, their control system must use the relative velocity of vehicles. The relative velocity can be estimated by differentiating the measured distance between cars with respect to time. However, inevitable measurement noise in the distance measurements will be amplified by the derivative operation. In this paper, we provide, as an alternative, a time-to-contact based approach to estimating the relative velocity, which can also be fused with measurements from other sensors, if desired. The system is implemented on Android smart phones running in real-time. Index Terms-Self-driving cars, car-following control, time to contact, machine vision, android smartphones.
Computer vision, graphics, and image processing, 1983
In this paper, we show how to recover the motion of an observer relative to a planar surface dire... more In this paper, we show how to recover the motion of an observer relative to a planar surface directly from image brightness derivatives. We do not con~pute the optical flow as an intermediate step. We derive a set of nine non-linear equations using a least-squares formulation. A simple iterative scheme allows us to find either of two possible solutions of these equations. An initial pass over the relevmt image region is used to accumulate a number of moments of the image brightness derivatives. All of the quantities used in the iteration can be efficiently computed from these totals, without the need to refer back to the image. A new, compact notation allows us to show easily that there are at most two planar solutions.
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Papers by Berthold Horn