Lecture 7: Object Detection

Question 1

What is the structure tensor, how is it computed in 2D/3D and what do the eigenvalues of the structure tensor tell us about the local image structure?

Answer 1

The structure tensor is a matrix derived from the intensity gradient of the image (2x2 for 2D images and 3x3 for volumetric images)

The eigenvectors and the associated eigenvalues determine the direction and values of the largest changes of the intensity in the given image region or object.

Question 2

How does the Harris-Stevens corner detector work?

Answer 2

The Harris-Stevens detector derives a criterion for a corner based on the obtained eigenvalues of the structure tensor.

Procedure:

1. Filter the image with a Gaussian for noise suppression.
2. Compute image gradient in the x and y direction for all pixels (convolution with a derivative approximation kernel).
3. Compute the structure tensor for each pixel and evaluate the corner criterion .
4. Chose the best candidates by thresholding the response function and performing a non-maximum suppression.

Question 3

How does template matching work?

Answer 3

The image correlation operator can be exploited to find matches of a sub-image in the original image.

● Slide query patch over the image and compute correlation at each location.
● The image correlation operator can be exploited to find matches of a sub-image in the original image:
● Locations with maximum correlation represent the best match.
● However, correlation is sensitive to amplitude changes.

• Compute normalized cross-correlation between original image and two different templates.
• Templates: Cropped snippet of a real cell or synthetic template that roughly matches the appearance of the objects.