Color in Computer Vision: Fundamentals and Applications

Chapter 6: Derivative-Based Photometric Invariance

With contributions by Rein van den Boomgaard and Arnold W. M. Smeulders

Image derivatives are essential to describe the local structure in images. First-order derivatives reveal information about the location of edges in images or the speed of objects in videos. Second-order derivatives of images allow us to identify corners in images and object acceleration in videos. Being essential operations, image derivatives are applied in the vast majority of computer vision applications, including basic operations such as edge detection, feature extraction, and optical flow and more complex applications such as shape from shading, image segmentation, and object detection.

A problem in classical derivative-based computer vision, which is based only on luminance or RGB, is that derivatives describe both scene incidental edges such as shadow and specularity transitions, as well as relevant material transitions. ¹For example, luminance-based optical flow estimation is flawed by moving shadows or RGB-based object segmentations fails in the presence of specularities. These problems can be solved by extending the photometric invariance theory described in Chapter 4 to the computation of image derivatives. The differential structure of images could then be split up into separate parts according to their invariance. For example, image derivatives could be derived to be invariant to shading, specularities, and illuminant changes. In Figure 6.1, an ...