Real images can contain geometric distortions as well as photometric degradations. Analysis and characterization of those images without recourse to either restoration or geometric standardization is of great importance for the computer vision community as those two processes are often ill-posed problems. To this end, it is necessary to implement image descriptors that make it possible to identify the original image in a simple way independently of the imaging system and imaging conditions. Ideally, descriptors that capture image characteristics must be invariant to the whole range of geometric distortions and photometric degradations, such as blur, that may affect the image. In this paper, we introduce two new classes of radiometric and/or geometric invariant descriptors. The first class contains two types of radiometric invariant descriptors. The first of these type is based on the Mellin transform and the second one is based on central moments. Both descriptors are invariant to contrast changes and to convolution with any kernel having a symmetric form with respect to the diagonals. The second class contains two subclasses of combined invariant descriptors. The first subclass includes central-moment-based descriptors invariant simultaneously to horizontal and vertical translations, to uniform and anisotropic scaling, to stretching, to convolution, and to contrast changes. The second subclass contains central-complex-moment-based descriptors that are simultaneously invariant to similarity transformation and to contrast changes. We apply these invariant descriptors to the matching of geometric transformed and/or blurred images. Experimental results confirm both the robustness and the effectiveness of the proposed invariants.

In this paper we introduce a new filter to approximate multiple scattering of light rays within a participating media. This filter is derived from the generalized Gaussian distribution GGD. It characterizes the Atmospheric Point Spread Function (APSF) and thus makes it possible to introduce three new approaches. First, it allows us to accurately simulate various weather conditions that induce multiple scattering including fog, haze, rain, etc. Second, it allows us to propose a new method for a cooperative and simultaneous estimation of visual cues, i.e., the identification of weather degradations and the estimation of optical thickness between two images of the same scene acquired under unknown weather conditions. Third, by combining this filter with two new sets of invariant features we recently developed, we obtain invariant features that can be used for the matching of atmospheric degraded images. The first set leads to atmospheric invariant features while the second one simultaneously provides atmospheric and geometric invariance.