Removal of Non-Gaussian Jitter Noise for Shape From Focus Through Improved Maximum Correntropy Criterion Kalman Filter

Abstract

Three-dimensional (3D) shape reconstruction from one or multiple observations is a primary problem of computer vision. Shape from Focus (SFF) is a passive optical method that uses multiple twodimensional (2D) images with different focus levels. When obtaining 2D images in each step along the optical axis, mechanical vibrations, referred as jitter noise, occur. SFF techniques are vulnerable to jitter noise that can vary focus values in 2D images. In this paper, new filtering method, which provides high accuracy of 3D shape reconstruction and low computational cost, is proposed. First, jitter noise is modeled as Lévy distribution. This assumption makes it possible to show the influence of proposed filtering method in real environment with non-Gaussian jitter noise. Second, focus curves are modeled as Gaussian function to compare the performance of proposed filtering method with those of the conventional filtering methods. Finally, improved maximum correntropy criterion Kalman filter (IMCC-KF) is designed as a post-processing step, and is applied to the modeled focus curves. The experiments are performed on real and synthetic objects and the results demonstrate the effectiveness of proposed method. INDEX TERMS Focus curve, improved maximum correntropy criterion Kalman filter (IMCC-KF), jitter noise, non-Gaussian distribution, shape from focus (SFF).

A simplified approach using deep neural network for fast and accurate shape from focus

“…These are widely used FMs in SFF. Many authors have utilized them to evaluate their works (Jang et al (2020, b); Yan, Hu, Qian, Qiao, and Zhang (2020b); Mahmood and Lee (2020)). A brief description of these FMs is given below.…”

“…Recently, a new FM based on the analysis of 3D structure tensor of the image sequence is proposed in (Mahmood and Lee (2019)). Furthermore, the removal of jitter from sampled images in SFF using Kalman filter has also been proposed in (Jang et al [2018, 2019, 2020, b]). Ma, Kim, and Shin (2020) proposed a method for depth reconstruction using nonlocal matting Laplacian prior with Markov random field to obtain a reliable depth image with clear edges and fine details.…”

Sampling-Noise Modeling & Removal in Shape From Focus Systems Through Kalman Filter

“…Jang et al in [28] proposed the removal of Jitter noise using Kalman Filter. Since then, many variants of their method have been proposed [29]- [33]. However, all of their methods used scalar-models for Kalman filter (i.e., the system matrix was taken as 1), and ignored the dynamic nature of focus cues.…”

“…It also impacts the practical use of their methods. Also, Jang et al in [28]- [33] considered only symmetric bell-shaped distributions for vibrational noise in translational stage, and their designed measurement model measures only a constant (each step position k). However, in such case taking the mean of the measurement values on every step position k can provide the similar results.…”

A Small and High-Speed Driving Mechanism for 3D Shape Measurement in Monocular Endoscopy

“…It worked well for laparoscopy due to the camera location outside the patient’s body, but there might have been a problem with the device size for endoscopy application. To improve SFF accuracy and stability, many software algorithms have addressed noise reduction [ 16 , 17 , 18 ] and point-spread-function optical modeling [ 19 ]. In addition, SFF hardware imagers have been proposed [ 20 , 21 ], but have not been introduced for endoscopy.…”