Measuring the distance between images

In all appearance-based methods, an important problem is measuring the distance, or similarity, between images. The traditional approach, and so far we do not proposed much more than that, is to compute the distance between images in the image space.

The image space is a space that will contain all possible images of a given size. Each coordinate in the space corresponds to a pixel of the images in the space, a value along that coordinate being the pixel value (this can actually be several values for colour images). An image having 200 by 200 RGB pixels will thus be a point in a 200 * 200 * 3 dimensional space.

Since images are now points in a space that can be defined, we can measure the distance between images in that space. The whole problem is to find the right distance metric, which obviously depends on what the distance function should show.

In this work, we have tried the Euclidean distance as well as the Manhattan distance. Both provide similar results, while the Manhattan distance is faster to compute.

Before Measuring the distance between images (or rather as part of the process), we "un-rotate" the images (see [Lab04] for an explanation).

It is important to notice that we do not extract any kind of feature from the images. Rather, the comparison is at the pixel level, completely sub-symbolic. The reason behind this choice is that we do not want to make any assumption about the environment the robot, which is what usually happens when features are extracted.