Images – A table of pixels, usually of RGB(3D columns – a.k.a a tensor) – can be ravled/unrolled/flattened to a 1D longer array. Sound – long series of numbers(1D array) when digitally recorded(x = time(duration column), y = amplitude of the sound) – usually represented by frequences. Text – partsContinue Reading
Reduce Operator – DownSampling without aliasing: Usually a 5 or 7 tap separable 1D filter like a (1,4,6,4,1) or a (1,6,15,20,15,6,1) filter is used. We need half the number of pixels: An easy example , each odd pixel gets 5 separately filtered by (1,4,6,4,1) filter. Reproducing / Expanding OperatorContinue Reading
The Lucas–Kanade method is a widely used differential method for optical flow estimation. Assumptions – flow is essentially constant in a local neighbourhood – solves the basic optical flow equations for all the pixels in that neighbourhood, by the least squares criterion. motion is linear : When it is non linearContinue Reading
The motion direction of a contour is ambiguous(usually to a combination of left/right with up/down), because the motion component parallel to the line (edge) cannot be inferred based on the visual input. You can only tell the motion locally in the direction perpendicular to the edge(line).Continue Reading
In order to compute Optical Flow there are two assumptions/constraints: Image moves in u(x cord) and v(y cord): The brightness(grayscale)/color consistency is same between the original image I ( x, y,t), and the image in I ( x+u, y+v,t+1). The change in motion is almost zero(smooth), which means that the original IContinue Reading
Radiance (L)- light carried by a ray from a light source. 1 Watt(W) = 1 Joule per second. A radian(r) is a measure of an angle, a steradian/ square radian[(sr) is a measure of a solid angle. e.g. In a cone it’s the amount of the radian area of the cone. IrradianceContinue Reading
The idea behind gradient descent is looking for the global minimum (or local minimum when wrong) of the function, it is done by subtracting the derivative from the initial position, this process is called minimizing the cost function. The way we update the parameters after the gradient descent is done,Continue Reading
A derivative is a sub function that derives from a main function. It describes the rate of change/slope in the main function. The derivative of a constant is 0 because a constant doesn’t change. The derivative of a linear function is a constant. The derivative of the exponential is theContinue Reading
Feature Finding/Correspondence: 1)Detect Features – Find POI’s by a repeatable detector. 2)Find Corresponding Pairs by distinctive descriptors. *In case of panoramic view – stitching – align images The main issues in the process are: 1) Find most of the points of interest on both images, by a repeatable detector. (precision,Continue Reading
In perspective projections – lines project into lines, so lines in one image must project to lines in the other image. In stereo images, any point on the epipolar line must be on the other epipolar line, this constraint allows us to reduce the search for a given point, toContinue Reading