Resolution loss without imaging blur

Abstract

Image recovery under noise is widely studied. However, there is little emphasis on performance as a function of object size. In this work we analyze the probability of recovery as a function of object spatial frequency. The analysis uses a physical model for the acquired signal and noise, and also accounts for potential postacquisition noise filtering. Linear-systems analysis yields an effective cutoff frequency, which is induced by noise, despite having no optical blur in the imaging model. This means that a low signal-to-noise ratio (SNR) in images causes resolution loss, similar to image blur. We further consider the effect on SNR of pointwise image formation models, such as added specular or indirect reflections, additive scattering, radiance attenuation in haze, and flash photography. The result is a tool that assesses the ability to recover (within a desirable success rate) an object or feature having a certain size, distance from the camera, and radiance difference from its nearby background, per attenuation coefficient of the medium. The bounds rely on the camera specifications.

Cutoff due to pointwise degradations in color images

“…The analysis is irrespective of a potential human in the process. This paper generalizes a prior study on limits in monochrome images [2]. The analysis in our study accounts for inherent detector noise, as well as potential noise filtering, which is optimally derived for each color channel.…”

“…Many imaging problems are characterized by pointwise image formation models [1,2]. These models treat each pixel independent of its surroundings, unlike effects such as optical blur.…”

“…Even in such pointwise problems, which lack optical blur, noise degrades the effective resolution (see Fig. 1), as shown in [2]. However, the analysis in [2] applies to single-channel, monochrome sensors.…”

“…The pointwise model applies to a wide range of problems. For example, t c x can be a distance-dependent atmospheric transmittance [1,2]. Then, a c x accounts for path radiance (airlight) [10].…”

“…In addition, n c x accounts for random noise. The c dependency generalizes the monochrome model given in [2]. We aim to assess resolution limits in color imaging systems.…”