Highlights: Hello and welcome to our new post. Here we are going to talk about Principal Component Analysis (PCA). In the previous post, we learned that we need to apply this method to construct a parametric face model. In order to better understand the whole process let’s remind ourselves what is PCA and how it works. The theoretical explanation of the PCA in this post is based on the YouTube video “3D Scanning & Motion…
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Highlights: Hello and welcome. In the last few years, Deep fake videos become very popular on social media. In this post, we will learn the basic theory behind deep fakes, and more specifically, how we can build a 3D face model and capture a motion in the human face. In this post, we are going to review the YouTube video “3D Scanning & Motion Capture: 8. Parametric Face Models”[1]. So let’s begin! Let’s have a…
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Highlight: Linear least squares is a very powerful algorithm to find the approximate solutions of overdetermined linear systems of linear equations. Those are systems of linear equations that have more equations than unknowns. The solution to this idea is to minimize the sum of squares of errors in the equation. This method was discovered independently by the mathematicians, Carl Friedrich Gauss, and Adrien-Marie Legendre, around the beginning of the 19th century. So, let’s begin with…
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Highlights: In the real-world scenario, models don’t produce linear graphs that often. Most of the time the equation of the model involves higher-order and higher-degree functions. In this post, we will learn how to solve the harder nonlinear equations using a heuristic algorithm of finding the least-squares approximate solution. So let’s begin. Tutorial Overview: Nonlinear Equations Introduction Difficulty Of Solving nonlinear equations Nonlinear Least Squares Optimality condition Gauss-Newton Algorithm Basic Gauss-Newton Algorithm Shortcomings Of The Gauss-Newton Algorithm…
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Highlight: In this post, we will discuss the Principle Component Analysis (PCA). PCA is the bedrock dimensionality reduction technique for probability and statistics. It is commonly used in Data Science and Machine Learning Applications to deal with high-dimensional data that have some statistical distribution. Our goal is to use PCA and uncover the low-dimensional patterns to build models. Before we learn about PCA, we need to understand several steps. First, we will learn about the…
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