Optical Flow

This post explains my understanding on Aperture Problem in Optical Flow and Lukas-Kanade method which is one of approaches to solve the problem. 

First, Optical Flow is a one way to estimate motion flow by analyzing pixel images of continous frames. Assuming Bright Constancy which leads to Gradient Constancy, one can define a line in the (u, v) space where u, v stand for dx / dt , dy / dt. But we should solve exact (u,v) the motion vector for each pixel, not a line.

class slide about Brightness Constancy and Gradient Constancy

The line implies the Apeture Problem which means multiple motion vectors can be an answer to our equation. (Gradient Constancy). So we need regularizer. Before going on, you must understand Aperture Problem is that each motion sensor or directional selectivity (DS) neuron in the visual system is sensitive or responsive only to events that take place within the small part of its own receptive field. https://stoomey.wordpress.com/2008/04/18/20/ In this case, I think "motion sensor" is the Gradient Constancy equation which look on its pixel value only.

 

Aperture Problem, no matter which motion flow(A, B, C) it is the motion sensor thinks it is same. (maybe as B)

Therefore to solve Aperture Problem in Optical flow you can add regularizer factor as below, or

See what does Ereg do

Assume constant optical flow for neighborhood pixels and get multiple Gradient Constancy equations. And solve least square problem which is quite intuitive overall. 

Lukas-Kanade method