Basics of Computer Vision - Part 1
My Recent Studies 1.1
My learning process this month usually involves understanding of the basic concepts of computer vision. For this, I followed the "Introduction to Computer Vision" course prepared by Aaron Bobick and Dr. Arpin Chuvkarvarde. Some basic concepts I learned during this time are; epipolar geometry, homography, essential matrix, fundamental matrix, logic of “Ransac” algorithm and optical flow.
Let’s See What Did I Understood From Epipolar Geometry
Epipolar geometry describes the geometric relationship between pairs of images taken from two different angles of an object or a scene (Bobick & Chuvkarvarde, 2015). The relationship between the two images below is expressed in epipolar geometry and the lines you see correspond to the epipolar lines.
There are two different methods for capturing epipolar geometry. These are the “essential” matrix and “fundamental” matrix. Thanks to these calculations, we can find the 3D locations of the points, and this allows us to reconstruct some three-dimensional structures.
Essential matrix works on images taken from a calibrated camera. The image below represents the geometric expression of the essential matrix.
Geometric to Algebraic
Now we have to transform the geometric expression to algebraic expression, otherwise it will be very difficult to express this expression in software.
To put it simply, below picture says the location of x in the prime scene is translated with the vector T by applying the rotation of the X in the non-prime scene.
Let’s see what that actually mean;
The E from the above equation represents the essential matrix.
Let’s Turn Back to The Epipolar Lines
If the above equation is true then this equation works for every point on these rays. This gives us the epipolar line.
So finally we may say Epipolar lines means,
If a point is given in the picture, there must be a line on which the point lies on in the other picture.(Bobick & Chuvkarvarde, 2015).
Essential Matrix vs Fundamental Matrix (Very Shortly)
If these image sources are calibrated, these relationships are captured using Essential Matrix.
If it is not calibrated, this relationship is captured with the fundamental Matrix. Fundamental matrix eliminates the need for intrinsic and extrinsic parameters.
Tebrikler / Congrats!
Resources
1. Bobick A, Chuvkarvarde, A. 2015. Introduction to Computer Vision. Retrieved on October 2021 from https://classroom.udacity.com/courses/ud810/lessons/2947778633/concepts/29434086250923
