An orientation map assigns a direction to every region in an image at a certain scale, summarizing the dominant orientation of edges within that region. Many mathematically sound methods have been developed to produce such maps. The work described here is almost just a thought experiment, to see how well it would be possible to perform this task without a model, and at as fine a scale as possible. (relevant chapter, pdf)

First, a robot experiments with tapping objects placed in front of it, and segments them based on motion. By sampling the appearance of these objects around their boundaries, the robot collects data about how appearance maps to edge direction. This information is accumulated over time. Figure 1 shows the angles assigned to the most common patches seen by the robot. Patches are small (4 by 4 pixels) and quantized to be binary for simplicity.

Figure 1: the patches the robot sees, ranked by frequency. Each red line corresponds to the angle automatically assigned to the patch around it.

Once the relationship between appearance and direction is quantified, it is converted into a look-up table and applied to the images the robot sees. This assumes that appearance information learned from the boundaries of specific objects can usefully be applied to other situations. Experimentally, this proved to be true. An example look-up table for 4 by 4 binary patches (a very practical size) is available as a table (orient.txt) or distilled into an image for ease of use:

(download as png, ppm, bmp, or plain text)

To understand the table, begin with a patch you wish to assign a direction to -- for example, the following:

The table can be conveniently compressed into an image (png, ppm, bmp) if we are willing to be selective about the information we keep. The above image can be converted back to the important columns of the table with code like the following (fill in your own pixel access stuff):

for (int i=0; i<65536; i++)
{
  int column = i%256;
  int row = i/256;

  PIXEL& pix = GETPIXEL(column,row);

  float angle = pix.RED/100.0-1;
  float mag =  pix.GREEN/255.0;
  float freq = pix.BLUE;
  printf("%d %g %g %g\n", i, angle, mag, freq);
}