A Statistical View on Synthetic Aperture Imaging for Occlusion Removal

Abstract

Synthetic apertures find applications in many fields, such as radar, radio telescopes, microscopy, sonar, ultrasound, LiDAR, and optical imaging. They approximate the signal of a single hypothetical wide aperture sensor with either an array of static small aperture sensors or a single moving small aperture sensor. Common sense in synthetic aperture sampling is that a dense sampling pattern within a wide aperture is required to reconstruct a clear signal. In this article we show that there exists practical limits to both, synthetic aperture size and number of samples for the application of occlusion removal. This leads to an understanding on how to design synthetic aperture sampling patterns and sensors in a most optimal and practically efficient way. We apply our findings to airborne optical sectioning which uses camera drones and synthetic aperture imaging to computationally remove occluding vegetation or trees for inspecting ground surfaces.

Thermal Airborne Optical Sectioning

“…Figure 1d,e illustrates that the results can be improved by capturing and combining more samples (up to 50) over a wider synthetic aperture. However, we have previously shown that there exist limits on the synthetic aperture size and number of samples which depend on the average projected size and disparity of occluders on the image sensor [23]. Relatively small apertures with a relatively low number of samples already lead to optimal results, while larger apertures and additional samples do not provide improvements.…”

“…Figure 1e does not show additional unoccluded features on the target, but only a stronger blur that results from more (slightly misaligned) images being integrated. More details on the statistical theory of SA sampling can be found in [23].…”

“…In [23] we derive a statistical model that reveals practical limits to both synthetic aperture size and number of samples for the application of occlusion removal. This leads to an understanding on how to design synthetic aperture sampling patterns and sensors in a most optimal and practically efficient way.…”

Fast Automatic Visibility Optimization for Thermal Synthetic Aperture Visualization

“…Consequently, objects above and below the focal plane (e.g., occluders) are suppressed while objects on the focal plane are amplified and become more visible. See [3] and [2] for more details on the image integration process and the statistical principles and of AOS.…”

“…This principle has been used for radar, telescopes, microscopes, sonar, ultrasound, laser, and optical imaging [1]. With Airborne Optical Sectioning (AOS) [2], [3], [4], we have introduced a synthetic aperture imaging technique that captures an unstructured light field with an aircraft. Color and thermal images recorded within the shape of a wide (possibly hundreds to thousands of square meters) synthetic aperture area above forest are combined computationally to remove occluders, such as trees and other vegetation.…”