This paper presents a new technique for the three-dimensional recognition of symmetric objects from range images. Beginning from the implicit representation of quadrics, a set of ten coefficients is determined for sym...
详细信息
This paper presents a new technique for the three-dimensional recognition of symmetric objects from range images. Beginning from the implicit representation of quadrics, a set of ten coefficients is determined for symmetric objects like spheres, cones, cylinders, ellipsoids and parallelepipeds. Instead of using these ten coefficients trying to fit them to smooth surfaces (patches) based on the traditional way of determining curvatures, a new approach based on two-dimensional geometry is utilized. For each symmetric object a unique set of two-dimensional curves is obtained from the various angles at which the object is intersected with a plane. Utilizing the same ten coefficients obtained earlier and based on the discriminant method, each of these curves is classified as a parabola, a circle, an ellipse, or a hyperbola. Each symmetric object is found to possess a unique set of these two-dimensional curves whereby it can be differentiated from the others. In other words, it is shown that instead of using the three-dimensional discriminant which involves evaluation of the rank of its matrix, it is sufficient to utilize the two-dimensional discriminant which only requires three arithmetic operations. This approach seems to be more accurate and computationally inexpensive compared to the traditional approaches.
Mutually inhibitory networks are the fundamental building blocks of many complex systems. despite their apparent simplicity they exhibit interesting behavior. We analyze a special class of such networks and provide pa...
详细信息
Mutually inhibitory networks are the fundamental building blocks of many complex systems. despite their apparent simplicity they exhibit interesting behavior. We analyze a special class of such networks and provide parameters for reliable K-winner performance. We model the network dynamics using interactive activation and compare our results to the sigmoid model. When the external inputs are all equal we can derive network parameters that reliably select the units with the larger initial activations because the network converges to the nearest stable state. Conversely, when the initial activations are all equal we can derive networks that reliably select the units with larger external inputs because the network converges to the lowest energy stable state. But when we mix initial activations with external inputs we get anomalous behavior. We analyze these discrepancies, giving several examples. We also derive restrictions on initial states which ensure accurate K-winner performance when unequal external inputs are used. Much of this work was motivated by the K-winner networks described by Majani et al. They use the sigmoid model and provide parameters for reliable K-winner performance. Their approach is based primarily on choosing an appropriate external input, the same for all units, that depends on K. We extend their work to the interactive activation model and analyze external inputs, constant but possibly different for each unit, more closely. Furthermore, we observe a parametric duality in that changing the range of activations (ie : m to M) can have the same effect as introducing equal external inputs.
暂无评论