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In this paper, we present a polarimetric image restoration approach that aims to recover the Stokes parameters and the degree of linear polarization from their corresponding degraded counterparts. The Stokes parameters and the degree of linear polarization are affected due to the degradations present in partial occlusion or turbid media, such as scattering, attenuation, and turbid water. The polarimetric image restoration with corresponding Mueller matrix estimation is performed using polarization-informed deep learning and 3D Integral imaging. An unsupervised image-to-image translation (UNIT) framework is utilized to obtain clean Stokes parameters from the degraded ones. Additionally, a multi-output convolutional neural network (CNN) based branch is used to predict the Mueller matrix estimate along with an estimate of the corresponding residue. The degree of linear polarization with the Mueller matrix estimate generates information regarding the characteristics of the underlying transmission media and the object under consideration. The approach has been evaluated under different environmentally degraded conditions, such as various levels of turbidity and partial occlusion. The 3D integral imaging reduces the effects of degradations in a turbid medium. The performance comparison between 3D and 2D imaging in varying scene conditions is provided. Experimental results suggest that the proposed approach is promising under the scene degradations considered. To the best of our knowledge, this is the first report on polarization-informed deep learning in 3D imaging, which attempts to recover the polarimetric information along with the corresponding Mueller matrix estimate in a degraded environment. 

The two-point source longitudinal resolution of three-dimensional integral imaging depends on several factors including the number of sensors, sensor pixel size, pitch between sensors, and the lens point spread function. We assume the two-point sources to be resolved if their point spread functions can be resolved in any one of the sensors. Previous studies of integral imaging longitudinal resolution either rely on geometrical optics formulation or assume the point spread function to be of sub-pixel size, thus neglecting the effect of the lens. These studies also assume both point sources to be in focus in captured elemental images. More importantly, the previous analysis does not consider the effect of noise. In this manuscript, we use the Gaussian process-based two-point source resolution criterion to overcome these limitations. We compute the circle of confusion to model the out-of-focus blurring effect. The Gaussian process-based two-point source resolution criterion allows us to study the effect of noise on the longitudinal resolution. In the absence of noise, we also present a simple analytical expression for longitudinal resolution which approximately matches the Gaussian process-based formulation. Also, we investigate the dependence of the longitudinal resolution on the parallax of the integral imaging system. We present optical experiments to validate our results. The experiments demonstrate agreement with our Gaussian process-based two-point source resolution criteria. 

We propose polarimetric three-dimensional (3D) integral imaging profilometry and investigate its performance under degraded environmental conditions in terms of the accuracy of object depth acquisition. Integral imaging based profilometry provides depth information by capturing and utilizing multiple perspectives of the observed object. However, the performance of depth map generation may degrade due to light condition, partial occlusions, and object surface material. To improve the accuracy of depth estimation in these conditions, we propose to use polarimetric profilometry. Our experiments indicate that the proposed approach may result in more accurate depth estimation under degraded environmental conditions. We measure a number of metrics to evaluate the performance of the proposed polarimetric profilometry methods for generating the depth map under degraded conditions. Experimental results are presented to evaluate the robustness of the proposed method under degraded environment conditions and compare its performance with conventional integral imaging. To the best of our knowledge, this is the first report on polarimetric 3D integral imaging profilometry, and its performance under degraded environments. 

Integral imaging has proven useful for three-dimensional (3D) object visualization in adverse environmental conditions such as partial occlusion and low light. This paper considers the problem of 3D object tracking. Two-dimensional (2D) object tracking within a scene is an active research area. Several recent algorithms use object detection methods to obtain 2D bounding boxes around objects of interest in each frame. Then, one bounding box can be selected out of many for each object of interest using motion prediction algorithms. Many of these algorithms rely on images obtained using traditional 2D imaging systems. A growing literature demonstrates the advantage of using 3D integral imaging instead of traditional 2D imaging for object detection and visualization in adverse environmental conditions. Integral imaging’s depth sectioning ability has also proven beneficial for object detection and visualization. Integral imaging captures an object’s depth in addition to its 2D spatial position in each frame. A recent study uses integral imaging for the 3D reconstruction of the scene for object classification and utilizes the mutual information between the object’s bounding box in this 3D reconstructed scene and the 2D central perspective to achieve passive depth estimation. We build over this method by using Bayesian optimization to track the object’s depth in as few 3D reconstructions as possible. We study the performance of our approach on laboratory scenes with occluded objects moving in 3D and show that the proposed approach outperforms 2D object tracking. In our experimental setup, mutual information-based depth estimation with Bayesian optimization achieves depth tracking with as few as two 3D reconstructions per frame which corresponds to the theoretical minimum number of 3D reconstructions required for depth estimation. To the best of our knowledge, this is the first report on 3D object tracking using the proposed approach. 

The two-point-source resolution criterion is widely used to quantify the performance of imaging systems. The two main approaches for the computation of the two-point-source resolution are the detection theoretic and visual analyses. The first assumes a shift-invariant system and lacks the ability to incorporate two different point spread functions (PSFs), which may be required in certain situations like computing axial resolution. The latter approach, which includes the Rayleigh criterion, relies on the peak-to-valley ratio and does not properly account for the presence of noise. We present a heuristic generalization of the visual two-point-source resolution criterion using Gaussian processes (GP). This heuristic criterion is applicable to both shift-invariant and shift-variant imaging modalities. This criterion can also incorporate different definitions of resolution expressed in terms of varying peak-to-valley ratios. Our approach implicitly incorporates information about noise statistics such as the variance or signal-to-noise ratio by making assumptions about the spatial correlation of PSFs in the form of kernel functions. Also, it does not rely on an analytic form of the PSF.