A new framework of quantifying differences between images by matching gradient fields and its application to image blending

This paper presents a new method for quantifying the differences between images. The proposed model is based on matching the gradient fields of two images. We first define new image spaces in which images are considered equivalent under a similarity group actions and the difference between two image classes is then defined by employing the Cauchy-Schwarz inequality to the gradient fields. The advantage of our approach is that images are identified by their relative contrasts and thus is scale free. Using this approach, we are able to achieve image blending in a novel way. By modifying the group actions, we extend our basic model to more general equivalence classes. The variational problems and the corresponding Euler-Lagrange equations associated to these models are proposed and the gradient descent time dependent partial differential equations are derived. Fast and efficient solvers employing the Additive Operator Splitting scheme are also presented. We tested our models on simulation images as well as real brain MRI and PET images from normal control subjects.