Revealing Implicit Assumptions of the Component Substitution Pansharpening Methods

Abstract

The component substitution (CS) pansharpening methods have been developed for almost three decades and have become better understood recently by generalizing them into one framework. However, few studies focus on the statistical assumptions implicit in the CS methods. This paper reveals their implicit statistical assumptions from a Bayesian data fusion framework and suggests best practices for histogram matching of the panchromatic image to the intensity image, a weighted summation of the multispectral images, to better satisfy these assumptions. The purpose of histogram matching was found to make the difference between the high-resolution panchromatic and intensity images as small as possible, as one implicit assumption claims their negligible difference. The statistical relationship between the high-resolution panchromatic and intensity images and the relationship between their corresponding low-resolution images are the same, as long as the low resolution panchromatic image is derived by considering the modulation transfer functions of the multispectral sensors. Hence, the histogram-matching equation should be derived from the low-resolution panchromatic and intensity images, but not derived from the high-resolution panchromatic and expanded low-resolution intensity images. Experiments using three example CS methods, each using the two different histogram-matching equations, was conducted on the four-band QuickBird and eight-band WorldView-2 top-of-atmosphere reflectance data. The results verified the best practices and showed that the histogram-matching equation derived from the high-resolution panchromatic and expanded low-resolution intensity images provides more-blurred histogram-matched panchromatic image and, hence less-sharpened pansharpened images than that derived from the low-resolution image pair. The usefulness of the assumptions revealed in this study for method developers is discussed. For example, the CS methods can be improved by satisfying the assumptions better, e.g., classifying the images into homogenous areas before pansharpening, and by changing the assumptions to be more general to address their deficiencies.

Multispectral Pansharpening with Radiative Transfer-Based Detail-Injection Modeling for Preserving Changes in Vegetation Cover

“…in which µ and σ denote the mean and square root of variance, respectively, and P L is a low-pass version of P having the same spatial frequency content as I [11,12]. In GS spectral sharpening, the fusion process is described by (1), with the injection gains spatially uniform for each band and thus denoted as {g k } k=1,...,N .…”

“…The two methods with path-radiance correction are labeled as CSw/PRC (20) and MRAw/PRC (22). The two versions without path-radiance correction, CSw/oPRC and MRAw/oPRC, are given by (9) with MMSE intensity (5) and by (12), respectively. All spatial filters are separable Gaussian with the amplitude at Nyquist equal to 0.25 [9].…”

Multispectral Pansharpening with Radiative Transfer-Based Detail-Injection Modeling for Preserving Changes in Vegetation Cover

“…in which µ and σ denote mean and square root of variance, respectively, and P L is a lowpass version of P having the same spatial frequency content as I [9,35]. In GS spectral sharpening, the fusion process is described by (1), with the injection gains are spatially uniform for each band, and thus denoted as {g k } k=1,...,N .…”

Guided Image Filtering-Based Pan-Sharpening Method: A Case Study of GaoFen-2 Imagery

“…Five state-of-the-art pan-sharpening methods, including Gram-Schmidt transformation [30] and NND pan-sharpening [17] from the ENVI software, the University of New Brunswick method [14] from the PCI Geomatica software, the adaptive GS (GSA) method [12], and the GD method [31] were selected for comparisons. These approaches are either integrated into commercial software or are newly developed, and have all been shown to be efficient for fusing remote sensing images.…”

“…In this study, the default values of the parameters were utilized across all the experiments. (4) University of New Brunswick method (UNB) [14]: The UNB pan-sharpening method first equalizes the histogram of the MS image and Pan image. Then, the spectral bands of the MS image, that are covered by the Pan band, are employed to produce a new synthetic image using the least squares technique.…”