IEICE TRANSACTIONS on Fundamentals
Deep Unrolling of Non-Linear Diffusion with Extended Morphological Laplacian
Summary :
This paper presents a deep network based on unrolling the diffusion process with the morphological Laplacian. The diffusion process is an iterative algorithm that can solve the diffusion equation and represents time evolution with Laplacian. The diffusion process is applied to smoothing of images and has been extended with non-linear operators for various image processing tasks. In this study, we introduce the morphological Laplacian to the basic diffusion process and unwrap to deep networks. The morphological filters are non-linear operators with parameters that are referred to as structuring elements. The discrete Laplacian can be approximated with the morphological filters without multiplications. Owing to the non-linearity of the morphological filter with trainable structuring elements, the training uses error back propagation and the network of the morphology can be adapted to specific image processing applications. We introduce two extensions of the morphological Laplacian for deep networks. Since the morphological filters are realized with addition, max, and min, the error caused by the limited bit-length is not amplified. Consequently, the morphological parts of the network are implemented in unsigned 8-bit integer with single instruction multiple data set (SIMD) to achieve fast computation on small devices. We applied the proposed network to image completion and Gaussian denoising. The results and computational time are compared with other denoising algorithm and deep networks.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E106-A No.11 pp.1395-1405
- Publication Date
- 2023/11/01
- Publicized
- 2023/07/21
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2023SMP0004
- Type of Manuscript
- Special Section PAPER (Special Section on Smart Multimedia & Communication Systems)
- Category
- Image
Authors
Gouki OKADA
Chiba Institute of Technology
Makoto NAKASHIZUKA
Chiba Institute of Technology
Keyword
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Gouki OKADA, Makoto NAKASHIZUKA, "Deep Unrolling of Non-Linear Diffusion with Extended Morphological Laplacian" in IEICE TRANSACTIONS on Fundamentals,
vol. E106-A, no. 11, pp. 1395-1405, November 2023, doi: 10.1587/transfun.2023SMP0004.
Abstract: This paper presents a deep network based on unrolling the diffusion process with the morphological Laplacian. The diffusion process is an iterative algorithm that can solve the diffusion equation and represents time evolution with Laplacian. The diffusion process is applied to smoothing of images and has been extended with non-linear operators for various image processing tasks. In this study, we introduce the morphological Laplacian to the basic diffusion process and unwrap to deep networks. The morphological filters are non-linear operators with parameters that are referred to as structuring elements. The discrete Laplacian can be approximated with the morphological filters without multiplications. Owing to the non-linearity of the morphological filter with trainable structuring elements, the training uses error back propagation and the network of the morphology can be adapted to specific image processing applications. We introduce two extensions of the morphological Laplacian for deep networks. Since the morphological filters are realized with addition, max, and min, the error caused by the limited bit-length is not amplified. Consequently, the morphological parts of the network are implemented in unsigned 8-bit integer with single instruction multiple data set (SIMD) to achieve fast computation on small devices. We applied the proposed network to image completion and Gaussian denoising. The results and computational time are compared with other denoising algorithm and deep networks.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2023SMP0004/_p
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@ARTICLE{e106-a_11_1395,
author={Gouki OKADA, Makoto NAKASHIZUKA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Deep Unrolling of Non-Linear Diffusion with Extended Morphological Laplacian},
year={2023},
volume={E106-A},
number={11},
pages={1395-1405},
abstract={This paper presents a deep network based on unrolling the diffusion process with the morphological Laplacian. The diffusion process is an iterative algorithm that can solve the diffusion equation and represents time evolution with Laplacian. The diffusion process is applied to smoothing of images and has been extended with non-linear operators for various image processing tasks. In this study, we introduce the morphological Laplacian to the basic diffusion process and unwrap to deep networks. The morphological filters are non-linear operators with parameters that are referred to as structuring elements. The discrete Laplacian can be approximated with the morphological filters without multiplications. Owing to the non-linearity of the morphological filter with trainable structuring elements, the training uses error back propagation and the network of the morphology can be adapted to specific image processing applications. We introduce two extensions of the morphological Laplacian for deep networks. Since the morphological filters are realized with addition, max, and min, the error caused by the limited bit-length is not amplified. Consequently, the morphological parts of the network are implemented in unsigned 8-bit integer with single instruction multiple data set (SIMD) to achieve fast computation on small devices. We applied the proposed network to image completion and Gaussian denoising. The results and computational time are compared with other denoising algorithm and deep networks.},
keywords={},
doi={10.1587/transfun.2023SMP0004},
ISSN={1745-1337},
month={November},}
Copy
TY - JOUR
TI - Deep Unrolling of Non-Linear Diffusion with Extended Morphological Laplacian
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1395
EP - 1405
AU - Gouki OKADA
AU - Makoto NAKASHIZUKA
PY - 2023
DO - 10.1587/transfun.2023SMP0004
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E106-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2023
AB - This paper presents a deep network based on unrolling the diffusion process with the morphological Laplacian. The diffusion process is an iterative algorithm that can solve the diffusion equation and represents time evolution with Laplacian. The diffusion process is applied to smoothing of images and has been extended with non-linear operators for various image processing tasks. In this study, we introduce the morphological Laplacian to the basic diffusion process and unwrap to deep networks. The morphological filters are non-linear operators with parameters that are referred to as structuring elements. The discrete Laplacian can be approximated with the morphological filters without multiplications. Owing to the non-linearity of the morphological filter with trainable structuring elements, the training uses error back propagation and the network of the morphology can be adapted to specific image processing applications. We introduce two extensions of the morphological Laplacian for deep networks. Since the morphological filters are realized with addition, max, and min, the error caused by the limited bit-length is not amplified. Consequently, the morphological parts of the network are implemented in unsigned 8-bit integer with single instruction multiple data set (SIMD) to achieve fast computation on small devices. We applied the proposed network to image completion and Gaussian denoising. The results and computational time are compared with other denoising algorithm and deep networks.
ER -
English
