I’m reading the paper Shape Context: A new descriptor for shape matching and object orientation. In section 3 it reads:
For a point P on the shape, we compute a coarse histogram of the relative coordinates of the remaining N-1 points. This histogram is defined to be the shape context of P. The reference orientation for the coordinate system can be absolute or relative to a given axis. In this paper we will assume and absolute reference orientation, i.e. angles measured relative to the positive x-axis. The descriptor should be more sensitive to differences in nearby pixels. We thus propose the use of log-polar coordinate system.
What is a coarse histogram? I’m familiar with the color histogram of an image, which has all the colors in the image as the x-axis and the y-axis are the number of pixels of that color. That’s obviously not the sort of histogram they are talking about. After all, you can’t make a histogram like that relative to a point.
What’s the x-axis and y-axis of the proposed histogram?
In the description of Figure 1, you can see items e, f, and g. These are the what the paper calls coarse histograms. Further below your quoted text, the histogram axes are defined as
In Figure 1, you can see log r for the y-axis and theta for the x-axis. Given that they are plotting 12 and 5, is probably why they use the word ‘coarse’, there’s not that many samples.