Local visual homing by matched-filter descent in image distances

In natural images, the distance measure between two images taken at different locations rises smoothly with increasing distance between the locations. This fact can be exploited for local visual homing where the task is to reach a goal location that is characterized by a snapshot image: descending in the image distance will lead the agent to the goal location. To compute an estimate of the spatial gradient in the distance measure, its value must be sampled at three noncollinear points. An animal or robot would have to insert exploratory movements into its home trajectory to collect these samples. Here we suggest a method based on the matched-filter concept that allows one to estimate the gradient without exploratory movements. Two matched filters--optical flow fields resulting from translatory movements in the horizontal plane--are used to predict two images in perpendicular directions from the current location. We investigate the relation to differential flow methods applied to the local homing problem and show that the matched-filter approach produces reliable homing behavior on image databases. Two alternative methods that only require a single matched filter are suggested. The matched-filter concept is also applied to derive a home-vector equation for a Fourier-based parameter method.