Optimal depth estimation using modified Kalman filter in the presence of non-Gaussian jitter noise

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.