A Novel Colour Hessian and its Applications

Abstract

The idea of contrast at a pixel, including contrast in colour or higher-dimensional image data, has traditionally been associated with the Structure Tensor, also named the di Zenzo matrix or Harris matrix. This 2 × 2 array encapsulates how colour-channel first-derivatives give rise to change in any spatial direction in x, y. The di Zenzo or Harris matrix Z has been put to use in several different applications. For one, the Spectral Edge method for image fusion uses Z for a putative colour image, along with the Z for higher-dimensional data, to produce an altered RGB image which properly has exactly the same Z as that of high-D data. So e.g. the contrast from RGB + NIR images can be fused such that Z in RGB takes on the same values as Z for 4-D data. As well, Z has been used as the foundation for the Harris interest-point or corner-point detector. However, a competing definition for Z is the 2 × 2 Hessian matrix, formed from second-derivative values rather than first derivatives. In this paper we develop a novel Z which in the first place utilizes the Harris Z, but then goes on to modify Z by adding some information from the Hessian. Moreover, here we consider an extension to a Hessian for colour or higher-D image data which treats colour channels not as simply to be added, but in a colour formulation that generates the Hessian from a colour vector. For image fusion, experiments are carried out on three datasets of 50 images each. Using the modified version of Z that includes Hessian information, results are shown to retain more details and also generate fused images that have smaller CIELAB errors from the original RGB. Using the new Z in corner-detection, the novel colour Hessian produces interest points that are more accurate, and as well generates fewer mistake points.