<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

This paper presents an efficient 3D shape registration by using distance maps and stochastic gradient descent method. The proposed algorithm aims to find the...

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

Published Online: Apr 24, 2020

Page range: 81 - 102

Received: Jun 26, 2019

DOI: https://doi.org/10.2478/tmmp-2020-0006

Keywords
distance map, stochastic gradient method, registration, parallelization, affine transformation, optimization

© 2020 Polycarp Omondi Okock et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Apr 24, 2020

Page range: 81 - 102

Received: Jun 26, 2019

DOI: https://doi.org/10.2478/tmmp-2020-0006

Keywordsdistance map, stochastic gradient method, registration, parallelization, affine transformation, optimization

© 2020 Polycarp Omondi Okock et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
distance map, stochastic gradient method, registration, parallelization, affine transformation, optimization