Computer Vision: Harris Corner Detector

Identifying key characteristics (features) in an image to represent it concisely.

Features that are repeatable (appear consistently across different views), salient (distinctive), compact (take up little space), and local (localized to a small area).

Identifying points in an image where there are two or more significant gradient directions.

A method for detecting corners using a combined approach of corner and edge detection.

Adjusting the position and orientation of two images so they match up.

Using multiple views to create a model of a 3D object.

Following the movements of objects or elements within an image sequence.

Using computer vision to help robots understand their environment and move around.

Categorizing or filing images for efficient finding.

Identifying corners in an image is based on detecting significant intensity changes from small window shifts in all directions.

E(u, v) = sum of w(x,y) * [I(x+u, y+v) - I(x, y)]^2 for all x, y in the window, where I is image intensity, u and v are shift amounts and w(x,y) is a window function.

A function defining the area (window) to check for intensity changes around a pixel. It can be a uniform square-shaped area, or a smoothed Gaussian shape.

The brightness value at a specific point in an image (x, y).

The amount of horizontal and vertical displacement applied to the window to calculate the intensity change.

A measure of the change in intensity of a window around a point when the window is shifted horizontally by u pixels and vertically by v pixels.

A matrix used to approximate the shape of a surface (E(u,v)) locally, computed by summing weighted intensity changes around a point for different shifts.

Measure of change in intensity as a window is shifted (u,v).

When gradients of intensity are mostly horizontal or vertical in the image, M is diagonal.

Values indicating the magnitudes of change in intensity along different shift directions in M.

Locate locations where both eigenvalues (λ) in the matrix (M) are high.

E(u,v) = sum of w(x,y) ✕ [ I(x+u, y+v) - I(x,y) ]^2 . This measures how pixel intensity changes when shifting by (u,v). w(x,y) is a window function weighting the contribution of each pixel.

Approximates E(u,v) using a quadratic function centered at (0,0).

A matrix calculated from image derivatives. Crucial for corner detection.

Horizontal (u) and vertical (v) displacement values for analyzing intensity changes.

Measure of the change in intensity in a window when shifted (u, v).

Measures change in window w(x,y) appearance due to shift [u,v] by calculating the squared difference of intensity values.

A second-order Taylor expansion used to approximate a function (E(u,v)) near a specific point (0,0).

Partial derivative of E with respect to u, twice, Evaluated at that specific value u and v, used in second-order Taylor expansion.

Partial derivative of E w.r.t u and then v part. Second order Taylor expansion calculation required.

The value of the function at point (0, 0). Specific to the function E.

A method of approximating a function by expressing it as an infinite sum, especially around certain points, useful to approximate function values.

The equation of an ellipse in terms of eigenvalues and image coordinates: λ1u^2 + λ2v^2 = K

Matrix M is transformed into a form where its components are aligned along a 2D coordinate system, using a change of basis matrix R.

Eigenvalues determine the lengths of the ellipse's axes.

Matrix R determines the orientation of the ellipse.

Image point likely to be an edge.

Image point likely to be a region or flat area

Image point likely to be a corner or fast-changing point.

Image point likely to be a flat or constant region.