1. bookVolume 75 (2020): Issue 1 (April 2020)
    Applied Mathematics'19
Journal Details
License
Format
Journal
eISSN
1338-9750
First Published
12 Nov 2012
Publication timeframe
3 times per year
Languages
English
access type Open Access

Efficient 3D Shape Registration by Using Distance Maps and Stochastic Gradient Descent Method

Published Online: 24 Apr 2020
Volume & Issue: Volume 75 (2020) - Issue 1 (April 2020) - Applied Mathematics'19
Page range: 81 - 102
Received: 26 Jun 2019
Journal Details
License
Format
Journal
eISSN
1338-9750
First Published
12 Nov 2012
Publication timeframe
3 times per year
Languages
English
Abstract

This paper presents an efficient 3D shape registration by using distance maps and stochastic gradient descent method. The proposed algorithm aims to find the optimal affine transformation parameters (translation, scaling and rotation) that maps two distance maps to each other. These distance maps represent the shapes as an interface and we apply level sets methods to calculate the signed distance to these interfaces. To maximize the similarity between the two distance maps, we apply sum of squared difference (SSD) optimization and gradient descent methods to minimize it. To address the shortcomings of the standard gradient descent method, i.e., many iterations to compute the minimum, we implemented the stochastic gradient descent method. The outcome of these two methods are compared to show the advantages of using stochastic gradient descent method. In addition, we implement computational optimization’s such as parallelization to speed up the registration process.

Keywords

MSC 2010

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