An Evaluation of the Constant Image Brightness Assumption and its Correction by Dynamic Histogram Warping

The constant image brightness (CIB) assumption assumes that the intensities of corresponding points (or planar patches) in two (or more) images are equal. This assumption is central to bodies of work in optical ow estimation, motion and structure, stereo and recognition based on color histograms. However, surprisingly little work has been performed to support this assumption, despite the fact the many of these algorithms are very sensitive to deviations from CIB. While it is commonly believed that the image brightness assumption is false, it is usually assumed that this deviation can be modelled by a simple global spatially-invariant additive constant and/or a global spatially-invariant scaling of the image intensities (contrast). An examination of the images contained in the SRI JISCT stereo database revealed that the constant image brightness assumption is indeed often false. Moreover, the simple additive and linear models do not adequately represent the observed deviations. A comprehensive physical model of the observed deviations is di cult to develop. However, many potential sources of deviations might be represented by a non-linear monotonically increasing function of intensities. Under these conditions, we believe that an expansion/contraction matching of the intensity histograms represents the best method to both measure the degree of validity of constant image brightness assumption and correct for it. The dynamic histogram warping (DHW) is performed via dynamic programming and is closely related to histogram speci cation. However, while histogram speci cation produces good matches, the local matching of cumulative histograms introduces artifacts (spikes in the matched histograms) because matching errors propogate and accumulate and must periodically be corrected. This problem does not occur with dynamic histogram warping, in which a global minimum is found. Experimental results show that image histograms are closely matched after DHW. A further reason for this is that while histogram speci cation only modi es one histogram DHW can modify both histograms simulatenously. This is especially useful when expansion of an intensity bin of one histogram is not possible but a corresponding compression of the other histogram is. DHW is also capable of removing simple constant additive and multiplicative biases without derivative operations, thereby avoiding ampli cation of high frequency noise.