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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.