3D visualization in turbid water using optimal photon counting and a GAT-based peplography method

Peplography is a three-dimensional (3D) approach for the visualization of targets in environments characterized by heavy scattering. It detects ballistic photons and subsequently generates a 3D image using integral imaging, where the expected number of ballistic photons is set arbitrarily. However, it affects the robustness of the method and accuracy in the analysis of results. Therefore, we propose a method to determine the optimal number of ballistic photons based on the maximum entropy of the photon counting image. Because accuracy in visualizing 3D targets may be compromised due to extraneous photons and fluctuations in photon intensity, we also address this challenge by integrating the generalized Anscombe transformation (GAT) with the conventional peplography technique. The noise caused by an image sensor during image acquisition can be modeled as a Poisson–Gaussian noise, and the photon counting process can be modeled as a Poisson process. Addressing such noise indirectly involves applying the GAT to the reconstructed image to stabilize its variance, denoising the stabilized data with a Gaussian denoising algorithm (i.e., non-local means filtering), and subsequently applying an exact unbiased inverse GAT to the denoised data. Experimental validation is conducted through experiments, with comparisons to conventional peplography, wavelet peplography, and a few standard dehazing and machine learning methods. Various image quality metrics such as correlation, structural similarity, the peak signal-to-noise ratio, and the natural image quality evaluator are used to demonstrate the superiority of the proposed method over conventional ones.