In this paper, we address the problem of computing an intrinsic decomposition of the colors of a surface into an albedo and a shading term. The surface is reconstructed from a single or multiple RGB-D images of a static scene obtained from different views. We thereby extend and improve existing works in the area of intrinsic image decomposition. In a variational framework, we formulate the problem as a minimization of an energy composed of two terms: a data term and a regularity term. The first term is related to the image formation process and expresses the relation between the albedo, the surface normals, and the incident illumination. We use an affine shading model, a combination of a Lambertian model, and an ambient lighting term. This model is relevant for Lambertian surfaces. When available, multiple views can be used to handle view-dependent non-Lambertian reflections. The second term contains an efficient combination of l₂ and l₁-regularizers on the illumination vector field and albedo respectively. Unlike most previous approaches, especially Retinex-like techniques, these terms do not depend on the image gradient or texture, thus reducing the mixing shading/reflectance artifacts and leading to better results. The obtained non-linear optimization problem is efficiently solved using a cyclic block coordinate descent algorithm. Our method outperforms a range of state-of-the-art algorithms on a popular benchmark dataset.

The bound state solution of the Feynman propagator with the deformed generalized Schiöberg potential is determined using an approximation of the centrifugal term. The energy eigenvalue expression is computed using Duru–Kleinert space–time transformation for both positive and negative deformation parameters of diatomic molecules. Besides, the rotation–vibration energy eigenvalues are numerically calculated for some diatomic molecules and compared with those given in the literature. The obtained results are in agreement with those given by state-of-the-art approximate and numerical methods.

In this paper, we address a complex image registration issue arising while the dependencies between intensities of images to be registered are not spatially homogeneous. Such a situation is frequently encountered in medical imaging when a pathology present in one of the images modifies locally intensity dependencies observed on normal tissues. Usual image registration models, which are based on a single global intensity similarity criterion, fail to register such images, as they are blind to local deviations of intensity dependencies. Such a limitation is also encountered in contrast-enhanced images where there exist multiple pixel classes having different properties of contrast agent absorption. In this paper, we propose a new model in which the similarity criterion is adapted locally to images by classification of image intensity dependencies. Defined in a Bayesian framework, the similarity criterion is a mixture of probability distributions describing dependencies on two classes. The model also includes a class map which locates pixels of the two classes and weighs the two mixture components. The registration problem is formulated both as an energy minimization problem and as a maximum a posteriori estimation problem. It is solved using a gradient descent algorithm. In the problem formulation and resolution, the image deformation and the class map are estimated simultaneously, leading to an original combination of registration and classification that we call image classifying registration. Whenever sufficient information about class location is available in applications, the registration can also be performed on its own by fixing a given class map. Finally, we illustrate the interest of our model on two real applications from medical imaging: template-based segmentation of contrast-enhanced images and lesion detection in mammograms. We also conduct an evaluation of our model on simulated medical data and show its ability to take into account spatial variations of intensity dependencies while keeping a good registration accuracy.

In this paper, we present analytic solutions of the Feynman propagator with the Rosen–Morse potential. To this end, an approximation of the centrifugal potential for any l state is used and nonlinear space–time transformations in the radial path integral are applied. A transformation formula that relates the original path integral to the Green function of a new quantum soluble system is derived. Explicit expressions of the bound state energy spectra and the eigenfunctions are obtained and compared to those of Schrödinger formalism. The Eckart potential is also treated as a special case.