The Logarithmic Image Processing (LIP) approach is a mathematical framework, introduced in the middle of the 1980's, based on abstract linear mathematics which provides a set of specific algebraic and functional operations that can be applied to the processing of intensity images valued in a bounded range. The LIP approach has been proved to be physically justified in the setting of transmitted and reflected light imaging, and to be consistent with several laws and characteristics of the human brightness perception. Successful application examples have also been reported in several image processing areas, e.g., image enhancement, image filtering, image restoration, three-dimensional image reconstruction, edge detection and image segmentation.

The Color Logarithmic Image Processing (CoLIP) is a recently introduced (2011) extension of the LIP mathematical framework based on abstract linear mathematics which provides a set of specific algebraic and functional operations that can be applied to the processing of color images valued in a bounded range. The CoLIP approach has been proved to be psycho-physically consistent with several laws and characteristics of the human color perception. A first successful application example has been recently reported on the white balance correction in color images.

 

The General Adaptive Neighborhood Image Processing (GANIP) is a mathematical framework, introduced in the middle of the 2000's, and based on based on abstract linear mathematics and generalized topology, for adaptive processing and analysis of gray-tone images. An intensity image is represented with a set of local neighborhoods defined for each pixel of the image to be studied. Those so-called General Adaptive Neighborhoods (GANs) are simultaneously adaptive with the spatial structures, the analyzing scales and the physical settings of the image to be addressed and/or the human visual system. The GANs are then used as adaptive operational windows for local image transformations (morphological filters, rank/order filters, ...) and for local image analysis (local descriptors, ...). Successful application examples have also been reported in several image processing areas, e.g., image enhancement, image filtering, image restoration, image focus measurement, edge detection and image segmentation.

The Integral Geometric Image Analysis of Spatial Patterns (IGIASP) is a recently developed (2008) research topic. It aims at modeling and analyzing spatial structures within binary or gray-tone images. The concepts and tools are based on: - integral geometry (e.g., Cauchy-Crofton formulas or Minkowski functionals: area, perimeter and connectivity number for 2D fields; volume, surface area, mean breadth and connectivity number for 3D fields), - mathematical morphology (e.g., openings and closures, skeletons, watersheds, granulometry) and - geometric measure theory (e.g., Minkowski content and Weyl-Steiner formulas). Successful application examples have been reported in gray tone image characterization.