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Essential Matrix, Fundamental Matrix

X: A 3D point projected to two cameras.u_i​, u_j: Corresponding image points in the two views.The line joining the two camera centers and X forms the epipolar plane.The intersections of this plane with each image plane form epipolar lines.The key idea: the corresponding point must lie on the epipolar line.Essential Matrix 𝐸 $${\mathbf{u}}_j^{\mathrm{\top }}\mathbf{E}{\mathbf{u}}_i=0$$..

Homography

This figure explains the concept of Homography in computer vision — specifically, how to map one image to another when viewing the same plane in the world from two different viewpoints (i.e., two different camera positions). C and C′ are two camera centers.A 3D point X lies on a plane π.The point projects to image 1 as ui​ and to image 2 as uj​.Because the point lies on the same plane, there's a..

BRIEF (Binary Robust Independent Elementary Features)

BRIEF is not a feature detector—it is a feature descriptor. It describes a keypoint (like one detected using FAST) by encoding intensity comparisons between pairs of pixels in a small image patch.  Binary Descriptor ComputationFor a detected keypoint, take a square patch (e.g. S × S pixels).Pick pairs of points x and y inside this patch.For each pair, compare pixel intensities:  This gives a 1-b..

FAST (Features from Accelerated Segment Test)

It's a fast corner detection method often used in real-time applications due to its speed and simplicity.  To determine if a pixel p is a corner, FAST uses:A circle of 16 pixels around the candidate pixel p.These pixels are tested to see if a segment of N contiguous pixels on the circle are all brighter or all darker than p by a threshold. Select 4 key pixels around p (in this example: pixels 1,..

KAZE

Traditional methods like SIFT/SURF use Gaussian blurring (a linear scale space), which blurs both boundaries and noise equally. This weakens edges. KAZE uses a nonlinear diffusion filter to:- Preserve edges (boundaries)- Suppress noiseThis leads to better keypoint localization, especially around object edges. KAZE constructs a nonlinear scale space using the following equation:\begin{equation}\f..