Inverse trigonometric functions

About: Inverse trigonometric functions is a research topic. Over the lifetime, 854 publications have been published within this topic receiving 11141 citations. The topic is also known as: arcus function & antitrigonometric function.

An elliptic phase-shift algorithm for high speed three-dimensional profilometry

Abstract: A high throughput is often required in many machine vision systems, especially on the assembly line in the semiconductor industry. To develop a non-contact three-dimensional dense surface reconstruction system for real-time surface inspection and metrology applications, in this work, we project sinusoidal patterns onto the inspected objects and propose a high speed phase-shift algorithm. First, we use an illumination-reflectivity-focus (IRF) model to investigate the factors in image formation for phase-measuring profilometry. Second, by visualizing and analyzing the characteristic intensity locus projected onto the intensity space, we build a two-dimensional phase map to store the phase information for each point in the intensity space. Third, we develop an efficient elliptic phase-shift algorithm (E-PSA) for high speed surface profilometry. In this method, instead of calculating the time-consuming inverse trigonometric function, we only need to normalize the measured image intensities and then index the built two-dimensional phase map during real-time phase reconstruction. Finally, experimental results show that it is about two times faster than conventional phase-shift algorithm.

Understanding Calculus: A User's Guide

Abstract: Author's Message to the Reader Acknowledgments Lines Parabolas, Ellipses, Hyperbolas Differentiation Differentiation Formulas The Chain Rule Trigonometric Functions Exponential Functions and Logarithms Inverse Functions Derivatives and Graphs Following the Tangent Line The Indefinite Integral The Definite Integral Work, Volume, and Force Parametric Equations Change of Variable Integrating Rational Functions Integration By Parts Trigonometric Integrals Trigonometric Substitution Numerical Integration Limits At Sequences Improper Integrals Series Power Series Taylor Polynomials Taylor Series Separable Differential Equations First-Order Linear Equations Homogeneous Second-Order Linear Equations Nonhomogeneous Second-Order Equations Answers Index About the Author.

Multiclass Classification Using Arctangent Activation Function and Its Variations

Abstract: Deep learning have been applied in life changing areas. Wide range of areas shows how successful deep learning is. There are several reasons why deep neural networks works well. The most importantly, activation functions since they are very powerful for solving non-linear problems. For that reason, it became a focus point for artificial intelligence researchers who want to improve the performance of neural networks. Special irrational numbers like pi and the golden ratio are shown up themselves in many areas such as art, geometry, architecture, etc. The wide range of occurrences of the pi and golden ratio inspire us to apply them to activation functions. This document is written for comprehensive explanation and comparison of activation functions which mainly focuses on arc tangent and its' variations defined in the paper. Experimental results are showed that variations which are obtained using irrational numbers pi and golden ratio, and also self-arctan, give promising results. Especially arctan with golden ratio have given better results. Multi-class classification problem was taken consider in the paper.