# Affine region detectors

## What is being detected?

Affine region is basically any region of the image that is stable under affine transformations. It can be edges under affinity conditions, corners (small patch of an image) or any other stable features.

## Available detectors

At the moment, the following detectors are implemented

• Harris detector
• Hessian detector

## Algorithm steps

### Harris and Hessian

Both are derived from a concept called Moravec window. Lets have a look at the image below: Moravec window corner case

As can be noticed, moving the yellow window in any direction will cause very big change in intensity. Now, lets have a look at the edge case: Moravec window edge case

In this case, intensity change will happen only when moving in particular direction.

This is the key concept in understanding how the two corner detectors work.

The algorithms have the same structure:

1. Compute image derivatives
2. Compute Weighted sum
3. Compute response
4. Threshold (optional)

Harris and Hessian differ in what derivatives they compute. Harris computes the following derivatives:

`HarrisMatrix = [(dx)^2, dxdy], [dxdy, (dy)^2]`

(note that `d(x^2)` and `(dy^2)` are numerical powers, not gradient again).

The three distinct terms of a matrix can be separated into three images, to simplify implementation. Hessian, on the other hand, computes second order derivatives:

`HessianMatrix = [dxdx, dxdy][dxdy, dydy]`

Weighted sum is the same for both. Usually Gaussian blur matrix is used as weights, because corners should have hill like curvature in gradients, and other weights might be noisy. Basically overlay weights matrix over a corner, compute sum of `s[i,j]=image[x + i, y + j] * weights[i, j]` for `i, j` from zero to weight matrix dimensions, then move the window and compute again until all of the image is covered.

Response computation is a matter of choice. Given the general form of both matrices above

`[a, b][c, d]`

One of the response functions is

`response = det - k * trace^2 = a * c - b * d - k * (a + d)^2`

`k` is called discrimination constant. Usual values are `0.04` - `0.06`.

The other is simply determinant

`response = det = a * c - b * d`

Thresholding is optional, but without it the result will be extremely noisy. For complex images, like the ones of outdoors, for Harris it will be in order of 100000000 and for Hessian will be in order of 10000. For simpler images values in order of 100s and 1000s should be enough. The numbers assume `uint8_t` gray image.

To get deeper explanation please refer to following paper:

Harris, Christopher G., and Mike Stephens. “A combined corner and edge detector.” In Alvey vision conference, vol. 15, no. 50, pp. 10-5244. 1988.

Mikolajczyk, Krystian, and Cordelia Schmid. “An affine invariant interest point detector.” In European conference on computer vision, pp. 128-142. Springer, Berlin, Heidelberg, 2002.

Mikolajczyk, Krystian, Tinne Tuytelaars, Cordelia Schmid, Andrew Zisserman, Jiri Matas, Frederik Schaffalitzky, Timor Kadir, and Luc Van Gool. “A comparison of affine region detectors.” International journal of computer vision 65, no. 1-2 (2005): 43-72.