A Lie group approach to a neural system for three-dimensional interpretation of visual motion

Abstract

A novel approach is presented to neural network computation of three-dimensional rigid motion from noisy two-dimensional image flow. It is shown that the process of 3-D interpretation of image flow can be viewed as a linear signal transform. The elementary signals of this linear transform are the 2-D vector fields of the six infinitesimal generators of the 3-D Euclidean group. This transform can be performed by a neural network. Results are also reported of neural network simulations for the 3-D interpretation of image flow and a comparison of the performance of this approach with that using conventional methods. Computer simulation results verify the Lie-group-based neural network approach to three-dimensional motion perception.

Development of localized oriented receptive fields by learning a translation-invariant code for natural images

“…A number of other authors have previously explored the general application of Lie group theory to visual perception [21,25,36], computer vision [66,67] and image processing [48]. The experiments presented herein involved two-dimensional translations of image stimuli, but other transformations such as scaling and rotation within the image plane can be accommodated if these are included in the training data [56].…”

Real time stereo-based biologically inspired 3D motion classifier cells

“…In a neural system for interpreting optical flow [18], the computation of a 3D motion from a 2D image flow or a motion template finds the optimal coefficient values in a 2D signal transform. The ideal optical motion υ opt caused by motion of a point (x, y, d) on a visible surface d = ρ(x, y), is …”

Fast Depth-Integrated 3d Motion Estimation and Visualization for an Active Vision System

“…In this part, the functionality of the proposed algorithm will be described. In a neural system for interpreting optical flow (Tsao et al, 1991), the computation of a 3D motion from a 2D image flow or a motion template finds the optimal coefficient values in a 2D signal transform. The ideal optical motion υ opt caused by motion of a point (…”

“…The visualization difference between a projected 3D point into a 2D plane using the equations proposed in (Tsao et al, 1991) and the 3D homogeneous transformation matrix resulting from multiplying the current 3D spatial position and the perspective matrix must be taken into consideration. Hence, in order to represent a similar visualization of the projected 3D point in the real 3D spatial domain using the OpenGL libraries, transformation functions have to be applied to estimate the OpenGL transformation matrix coefficients (t x ,t y ,t z for translation motion and θ x , θ y , θ z for rotation motion) from the pre-estimated 3D motion parameter coefficients of the projected motion c i (eq.…”