Optical Flow via Bilinear Spline Matching

Comparing gradient descent path to Newton's method for small steps. Optical flow is the apparent motion of objects across multiple images or frames of video.  It has many applications in computer vision including 3D structure from motion and video super resolution. In this article I illustrate one specific technique for calculating sub-pixel accurate dense optical flow by matching continuous image areas using optimization techniques over bilinear splines.
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Logistic Regression and Optimization Basics

Comparing gradient descent path to Newton's method for small steps. Logistic regression uses a sigmoid (logistic) function to pose binary classification as a curve fitting (regression) problem. It can be a useful technique, but more importantly it provides a good example to illustrate the basics of nonlinear optimization. I’ll show how to solve this problem iteratively with both gradient descent and Newton’s method as well as go over the Wolfe conditions that we’ll satisfy to guarantee fast convergence. These are the prerequisites for the upcoming neural network articles!
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Project: Auto-Soylent

A creamy food flavored beverage. I’m taking a break from the usual lessons to discuss a side project of mine: Auto-Soylent.  The idea of Soylent is to create a single shake that contains all nutrients a person needs.   Auto-Soylent is an application that works with diy.soylent.me to generate recipes automatically from any given ingredients.  Once the math was done, I decided to put my mouth where my money is and mix up a few batches of the computer generated recipe.
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Classification Validation

IconIt’s important to know how well your models are likely to work in the real world. In this article I’ll be discussing basic testing procedures  for classification problems such as generating receiver operating characteristics and confusion matrices as well as performing cross validation. We’ll also take a look at the effect of over-fitting and under-fitting models.
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