Computational Reconstruction of Integral Imaging for Accurate Depth Estimation Using Non-Uniform Pitches

Integral imaging is a promising technology for passive three-dimensional (3D) scene acquisition and display, providing full parallax and continuous viewpoints without the need for specialized viewing glasses. However, in volumetric computational reconstruction (VCR), depth estimation accuracy is basically constrained by shifting pixel quantization errors arising from the discrete pixelation of elemental images. Although non-uniform VCR (NVCR) can reduce these errors through localized rounding, shifting pixel quantization errors may not be reduced to exactly zero. In this paper, we propose a computational reconstruction method for integral imaging that completely eliminates shifting pixel quantization errors while preserving uniform depth resolution across multiple target depths. The proposed method uses a least common multiple (LCM) search based on the respective optimum pitch bases of multiple target planes to calculate a unified optimum pitch. Simultaneously, the physical layout of the camera array is structured non-uniformly using a Latin-square distribution of subarrays governed by the approximate squared-multiple rule. This layout maintains a constant depth resolution limit across the entire distance range and avoids the quadratic degradation of depth resolution observed at farther distances. Through mathematical analysis and computational simulations, we demonstrate that the proposed non-uniform pitch method achieves exact depth recovery with a mean squared error of zero (MSE = 0) at all target depths and produces sharp, high-intensity peak sidelobe ratio (PSR) responses. This approach holds significant potential for advanced sensing applications, such as autonomous vehicles, digital twins, and industrial robotics.