In regard to Shape from Focus, one critical factor impacting system application is mechanical vibration of the translational stage causing jitter noise along the optical axis. This noise is not detectable by simply observing the image. However, when focus measures are applied, inaccuracies in the depth occur. In this article, jitter noise and focus curves are modeled by Gaussian distribution and quadratic function, respectively. Then Kalman filter is designed and applied to eliminate this noise in the focus curves, as a post-processing step after the focus measure application. Experiments are implemented with simulated objects and real objects to show usefulness of proposed algorithm.

The consideration of the noise that affects 3D shape recovery is becoming very important for accurate shape reconstruction. In Shape from Focus, when 2D image sequences are obtained, mechanical vibrations, referred as jitter noise, occur randomly along the z‐axis, in each step. To model the noise for real world scenarios, this article uses Lévy distribution for noise profile modeling. Next, focus curves acquired by one of focus measure operators are modeled as Gaussian function to consider the effects of the jitter noise. Finally, since conventional Kalman filter provides good output under Gaussian noise only, a modified Kalman filter, as proposed method, is used to remove the jitter noise. Experiments are carried out using synthetic and real objects to show the effectiveness of the proposed method.

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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).

Recovering three-dimensional (3D) shape of an object from two-dimensional (2D) information is one of the major domains of computer vision applications. Shape from Focus (SFF) is a passive optical technique that reconstructs 3D shape of an object using 2D images with different focus settings. When a 2D image sequence is obtained with constant step size in SFF, mechanical vibrations, referred as jitter noise, occur in each step. Since the jitter noise changes the focus values of 2D images, it causes erroneous recovery of 3D shape. In this paper, a new filtering method for estimating optimal image positions is proposed. First, jitter noise is modeled as Gaussian or speckle function, secondly, the focus curves acquired by one of the focus measure operators are modeled as a quadratic function for application of the filter. Finally, Kalman filter as the proposed method is designed and applied for removing jitter noise. The proposed method is experimented by using image sequences of synthetic and real objects. The performance is evaluated through various metrics to show the effectiveness of the proposed method in terms of reconstruction accuracy and computational complexity. Root Mean Square Error (RMSE), correlation, Peak Signal-to-Noise Ratio (PSNR), and computational time of the proposed method are improved on average by about 48%, 11%, 15%, and 5691%, respectively, compared with conventional filtering methods.