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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. 

Integral imaging (InIm) is useful for passive ranging and 3D visualization of partially-occluded objects. We consider 3D object localization within a scene and in occlusions. 2D localization can be achieved using machine learning and non-machine learning-based techniques. These techniques aim to provide a 2D bounding box around each one of the objects of interest. A recent study uses InIm for the 3D reconstruction of the scene with occlusions and utilizes mutual information (MI) between the bounding box in this 3D reconstructed scene and the corresponding bounding box in the central elemental image to achieve passive depth estimation of partially occluded objects. Here, we improve upon this InIm method by using Bayesian optimization to minimize the number of required 3D scene reconstructions. We evaluate the performance of the proposed approach by analyzing different kernel functions, acquisition functions, and parameter estimation algorithms for Bayesian optimization-based inference for simultaneous depth estimation of objects and occlusion. In our optical experiments, mutual-information-based depth estimation with Bayesian optimization achieves depth estimation with a handful of 3D reconstructions. To the best of our knowledge, this is the first report to use Bayesian optimization for mutual information-based InIm depth estimation. 

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. 

In this paper, we have used the angular spectrum propagation method and numerical simulations of a single random phase encoding (SRPE) based lensless imaging system, with the goal of quantifying the spatial resolution of the system and assessing its dependence on the physical parameters of the system. Our compact SRPE imaging system consists of a laser diode that illuminates a sample placed on a microscope glass slide, a diffuser that spatially modulates the optical field transmitting through the input object, and an image sensor that captures the intensity of the modulated field. We have considered two-point source apertures as the input object and analyzed the propagated optical field captured by the image sensor. The captured output intensity patterns acquired at each lateral separation between the input point sources were analyzed using a correlation between the captured output pattern for the overlapping point-sources, and the captured output intensity for the separated point sources. The lateral resolution of the system was calculated by finding the lateral separation values of the point sources for which the correlation falls below a threshold value of 35% which is a value chosen in accordance with the Abbe diffraction limit of an equivalent lens-based system. A direct comparison between the SRPE lensless imaging system and an equivalent lens-based imaging system with similar system parameters shows that despite being lensless, the performance of the SRPE system does not suffer as compared to lens-based imaging systems in terms of lateral resolution. We have also investigated how this resolution is affected as the parameters of the lensless imaging system are varied. The results show that SRPE lensless imaging system shows robustness to object to diffuser-to-sensor distance, pixel size of the image sensor, and the number of pixels of the image sensor. To the best of our knowledge, this is the first work to investigate a lensless imaging system’s lateral resolution, robustness to multiple physical parameters of the system, and comparison to lens-based imaging systems.