Abstract
Image interpolation and denoising are important techniques in image processing. These methods are inherent to digital image acquisition as most digital cameras are composed of a 2D grid of heterogeneous imaging sensors. Current polarization imaging employ four different pixelated polarization filters, commonly referred to as division of focal plane polarization sensors. The sensors capture only partial information of the true scene, leading to a loss of spatial resolution as well as inaccuracy of the captured polarization information. Interpolation is a standard technique to recover the missing information and increase the accuracy of the captured polarization information. Here we focus specifically on Gaussian process regression as a way to perform a statistical image interpolation, where estimates of sensor noise are used to improve the accuracy of the estimated pixel information. We further exploit the inherent grid structure of this data to create a fast exact algorithm that operates in ����(N(3/2)) (vs. the naive ���� (N³)), thus making the Gaussian process method computationally tractable for image data. This modeling advance and the enabling computational advance combine to produce significant improvements over previously published interpolation methods for polarimeters, which is most pronounced in cases of low signal-to-noise ratio (SNR). We provide the comprehensive mathematical model as well as experimental results of the GP interpolation performance for division of focal plane polarimeter.
Highlights
Solid state imaging sensors, namely CMOS and CCD cameras, capture two of the three fundamental properties of light: intensity and color
We show that GP-grid allows for improved accuracy results for division of focal plane polarimeter compared to other commonly-used interpolation methods
The time complexity presented for all algorithms is for a single calculation of the negative log marginal likelihood (NLML) and its derivatives, which are the needed calculations in GP learning
Summary
Namely CMOS and CCD cameras, capture two of the three fundamental properties of light: intensity and color. In order to recover the loss of spatial resolution in color sensors and improve the accuracy of the captured color information, various image interpolation algorithms have been developed in the last 30 years. The second contribution of this work is to utilize the actual noise statistics of the data acquisition system, which fits naturally into the GP framework With these advances, it is possible to significantly improve both the interpolation and denoising performance over current methods. The GP statistical inference is able learn the properties of the data and incorporates an estimation of the sensor noise in order to increase the accuracy of the polarization information and improve spatial resolution
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