Removal of Jitter Noise in Image Focus based 3D Shape Recovery

Abstract

Recovering the shape of an object is an active research area in computer vision. In order to obtain shape, many optical shape recovery methods available in the literature have been proposed. These methods are divided into active and passive methods. Shape from Focus (SFF) is one of the passive methods for shape recovery of an object that uses multiple images with different focus values. In this method, a translational stage in a microscope moves with a constant step size along the optical axis to obtain stack of 2D images. Focus measure operator (such as Sum of Modified Laplacian (SML)) is then applied to each image frame for acquiring the focus values. Finally, depth map is obtained by finding the image frame that maximizes the focus value of each pixel along the optical axis. This method is called SFF.TR. Many SFF techniques available in the literature have been proposed to acquire more improved depth map. As one of the critical problems for 3D shape reconstruction, noise that has been researched is mainly limited to image noise. To remove this type of noise, various filtering techniques available in the literature have been proposed. However, when 2D image sequences are obtained in SFF, mechanical vibration of the translational stage causing jitter noise which is different from image noise along the optical axis as one critical factor impacting system application in regard to SFF occurs. This noise is not detectable by simply observing the image. However, when focus measures are applied, inaccuracies in the depth occur due to changed focus values of the image sequence. In this thesis, new optimized sampling step size which provides improved depth map in the presence of jitter noise is proposed. the noise is modeled by using Newton's second law and principle of rack and pinion gear for theoretical demonstration. Focus curves are modeled as quadratic function to evaluate the performance of proposed sampling step size. Moreover, to remove the jitter noise, jitter noise is modeled by Gaussian distribution and focus curves are modeled by quadratic function or Gaussian distribution. Then filters are designed and applied as a post-processing step after the focus measure application. A Low pass filter (LPF) can be utilized to filter jitter noise, but, the results are not very accurate. The LPF also introduces a depth lag in all the pixels. So, in this thesis, Kalman filter and Bayes filter are used. Kalman filter is statistically stable and accurate, as it is an optimal estimator, which uses a series of measurements observed over time, containing statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone. Bayes filter estimates the unknown probability density function recursively and obtains an estimate of unknown variable which has the highest probability. Experiments are implemented with simulated objects and real objects to show effectiveness of proposed methods.