A new and efficient method for incorporating the spatiality into difference-based change detection (CD) algorithms is introduced in this paper. It uses the spatial derivatives of image pixels to extract spatial relations among them. Based on this methodology, the performances of two famous difference-based CD methods, conventional polynomial regression (CPR) and multivariate alteration detection (MAD), are improved and called modified polynomial regression (MPR) and spatial multivariate alteration detection (SMAD), respectively. Various quantitative and qualitative evaluations have shown the superiority of MPR over CPR and SMAD over MAD. Also, the superiority of SMAD over all mentioned CD algorithms is shown. Moreover, it has been proved that both proposed methods enjoy the affine invariance property.