10Shape Recognition with Contour Propagation Fields

For example, one can make use of those motion-sensitive maps discussed in chapter 8. If the connectivity of such a motion-sensitive map is altered in such a way that it corresponds to the CPF pattern, then the motion-sensitive map would react only to input of corresponding contour flow (or CPF). We now call such a motion-sensitive map, with a specific connection pattern bearing a CPF, a shape map (SM). For each shape, a separate shape map is created. Recognition would occur by feeding the contour flow across each shape map. Only, the map with corresponding CPF will generate a vigorous response, and that map response serves as recognition signal. This comparison process is in some sense a template matching system. We therefore call it CPF matching, or CPFM.

10.2Architecture

An architecture for a CPFM can be constructed with the components discussed in chapters 7 and 8. Figure 51 shows the principal architecture for both solutions. The input shape (input) is fed into a propagation map (PM) and analysed by a set of orientation columns (OCs). On top of that, a set of direction-selective columns (DCs) determine the direction into which a wave propagates. (The use of such a direction-selective cells would of course be also beneficial for the SAT, but has not been modeled yet). The direction selectivity can be obtained by cross-correlating the input of two neighboring orientationselective cells, very much according to the principles discussed in the introduction of the motion detection chapter (number 8). At the very top of the architecture is the set of shape maps (SM), each representing an individual shape. Each shape map receives input from the direction-selective columns.

Shape map A shape-sensitive map is basically equivalent to a propagation map, except of two modifications: 1) The connection between two neurons are modeled as two unidirectional connections, see figure 52. 2) Most of its connections are turned off, and only those are turned on, whose direction corresponds to a local direction of the CPF. For example, the connections around the center neuron shown in figure 52 are turned off (grey) except those two pointing toward the right (black): this local piece of shape map, will prefer contour propagation toward the right only. To learn a novel shape, the shape is squeezed through the architecture and the evolving CPF is ‘burned’ into an ‘unwritten’ shape map, which then becomes part of the system. Once the novel shape map has been burned, it basically consists of lines of connected neurons.

The architecture suffers from the problem of a coarse connectivity, in particular the SM. Specifically, a direction column provides 16 distinguishable directions, whereas a SM neuron has only 8 neighbors

Figure 51: Architecture for a CPFM. From bottom to top: the input shape (input) is dipped into the propagation map (PM), where it propagates inward and outward (gray outlines). The orientation columns (OCs) and the direction columns (DCs) determine the contour-propagation field (CPF) which is then fed into each shape map (SM).

and thus 8 directions, which is too coarse for representing simple shapes distinctively. For the present study, the problem is solved by using two propagation layers for each shape map, each one propagating the input from 8 different directions.

Figure 52: a. Reciprocal, unidirectional connections in a propagation map for one unit. b. Only one direction of the ‘directed connections’ is turned on (black), the others are turned off (gray): this map will prefer contour input moving towards the right only.

10.3Testing

We have simulated this architecture with integrate-and-fire neurons, except of the block of direction selective cells, which has been computed by traditional bit-wise (computer) correlation for reason of simplicity. To determine the recognition signal, the entire spiking activity of each shape map is observed by summing it up and plotting it against time. This sum is now called the population activity. Five shapes were used for testing, see figure 53: a rectangle, a circle, a triangle, a cross and a shape consisting of the superposition of the rectangle and the cross, which we now call square board. The 1st column is the centered shape, which was used for learning - for burning the CPF into the shape map. The 2nd column is a translated version of the shape, shifted to the lower right by 5 pixels in each dimension, which represents about 10 to 12 percent of the shape’s width and height. The 3rd column is scaled version of the (centered) shape, made smaller by 6 pixels in each dimension. The 4th column is the (centered) shape with a ‘disturbance’, a straight line extending from the right side of the image center to the upper right. The 5th column contains the shape made of a dotted contour, an input that is hereafter called fragmented. Figure 54 shows the CPF of two shapes.

The ability of a shape map to identify was tested with its own centered, shifted, scaled (smaller), ‘disturbed’ and fragmented shape. The ability to discriminate was tested by placing the other, centered shapes on it.

Figure 53: Shapes used for testing. From top to bottom: rectangle, cross, triangle, circle, square board. The 1st column shows the centered shapes. The 2nd column shows the translated shapes, which were shifted by 5 pixels into both axis directions (shifted to the lower right), which is about 10 to 12 percent of the shape width. The 3rd column is a down-scaled (smaller) version of the (centered) shape. The 4th column shows the (centered) shape with a ‘disturbance’, a straight line extending from the right of the image center to the upper right. The 5th column is a dotted version of the shape, called fragmented.

Figure 55 illustrates the population activity of the shape maps in response to various stimuli. The identification responses are discussed first.

The response to its ‘centered’ shape, called the signature now, is denoted as a thick, solid line: it rises steeply and stays well above the

Figure 54: Contour propagation field (CPF) of the centered rectangle (top) and circle (bottom). An inward-pointing and outward-pointing vector field is present.

response activity for any other identification response. Its amplitude is determined by the length of the shape contour. It may increase or decrease during the propagation process depending on whether contours cancel each other out (e.g. square board) or whether they are only growing (e.g. cross). Part of the fluctuations are due to the aliasing problem (coarse nature of our network).