Neural network analog of the ICP algorithm

The paper deals with the problem of overlapping two point-data clouds. Traditionally, iterative or variational methods are used to solve such problems. However, these methods are ineffective to solve tasks with a large number of points in the clouds or in the cases of task series with real-time cloud mapping. For those tasks, it is more appropriate to use neural network technique and deep learning methods. The overlap of point-data clouds is understood as finding the displacement vector between them and the rotation matrix of the clouds relative to each other. First of all, point-data clouds are reduced to the zero displacement by means of some transformation. To find the rotation matrix for transformed clouds the authors proposed a simple neural network implementation of the ICP algorithm. This implementation consists of two stages substantially formed by neural networks. At the first stage, a two-layer probabilistic network acts as a metric classifier. The first layer of the probabilistic network is composed of radial-basis elements – Gaussians. The Gaussian activation function makes it possible to identify the output of the first layer with the probability showing the proximity of the points of the superimposed clouds. The second layer of this network is competitive. As a result of the probabilistic network, the points of these two clouds are ranked according to the degree of proximity. The point-data clouds sorted by proximity are sent to the second single-layer neural network. On the second stage, the rotation matrix is calculated using the learning procedure according to the Hebb rule. In the case of small point clouds (less than 10 thousand points), it is more appropriate to use a pseudo-inverse rule (calculations using a pseudoinverse Penrose-Moore matrix) based on the Hebb rule. At the output of the second stage, the rotation matrix is obtained, with which we can easily calculate the displacement vector of the original point clouds. The approbation of the proposed point-data cloud overlap method showed a good match on samples from the ModelNet40 database.