NMPE: A normalized metric for measuring generalized spatial distortion of multispectral panshapening fusion

Abstract

Adaptivity is important in remote sensing image fusion because of the data-intensive and mass-driven processing platforms that call for reliable evaluation metrics to assess the runtime fusion procedure. Spatial distortion, including poor detail, visual disorder, or over-injection, has not been measured as effectively as in the spectral domain. A new metric, namely normalized mean potential energy (NMPE), is proposed in this paper to check the generalized spatial distortion of fused images by calculating the potential energy of marginal filtering distributions using information of high-order Markov random fields. NMPE is defined based on the GFoE model, which is a new high-order model that we built for remote sensing image applications. To incorporate the evaluation experience of human vision system into the GFoE model, the real zero-mean Gabor filters with multiple directions and scales are used as feature extractors, and the Gaussian scale mixture model as the expert function. The model parameters are trained from 200 images of the Berkeley segmentation dataset. Poor detail in a fused image tends to result in small NMPE evaluation with respect to small Gabor scales. Our observation shows that scale invariance exists only for “good” details, so we use large scales of Gabor functions to detect visual disorder. Over-injection is checked when the fused NMPE is much higher than 1. In the experimental procedure, satellite images from Quickbird, LandSat-7, and SPOT-5 were put to fusion with five popular methods to produce different images for visual and digital comparison. It can be concluded from the experiment that NMPE is in line with our subjective judgment to measure the pansharpening quality in terms of enhanced detail, visual distortion, and over-injection.