Jean-Michel Morel
morel”at”cmla”dot”ens-cachan”dot”fr
This page is dedicated to the theories that have made my collaborators and me quite busy in the past ten years. They are mainly concerned with all aspects of image processing, analysis, and synthesis. My present efforts concentrate on the Image Processing on Line project.
Profile
Here is a recent short profile of mine, containing also an abridged curriculum vitae.
This is a new concept of publication for image processing. Putting image processing and image analysis algorithms on line allows every researcher to test directly the algorithms on his (her) own images. Some sample images are also proposed on each algorithm site. This project is under construction, but several algorithms are already available here. Each algorithm is described in a web site, which gives the main bibliographic links, and which comments on many experimental results. Each algorithm is also thoroughly described, and a code can be downloaded. Image processing on line is only possible with algorithms which have been mathematically analyzed and rationalized to the point where they do not depend anymore on technical parameters. A publication on line is different from --but can be complementary to-- a journal publication. In this building up phase, the project is internal to the lab, and will not take submissions. If the project gains European support, it will move into becoming a new kind of publication, with an international scientific board. The online algorithms must be elaborated to the point where they are fully autonomous, or depend on at most one user's parameter (typically the scale). Go to IPOL and try a Microtexture synthesis algorithm, a Cartoon + Texture decomposition, a fully autonomous line segment detector, a PDE implementation of the color perception Retinex theory or a fully affine invariant image comparison algorithm, ASIFT. If the project thrives, it will serve the ever growing community of researchers who deal with scientific images, are not image processing specialists, but need to know what can be done rigorously and automatically on their images.
Computational Gestalt Theory
The main question treated in this theory and book is the visual perception of geometric structure. Visual perception can receive (up to a certain limit we cannot yet fix) a fully mathematical treatment. The book is mainly dedicated to one perception principle, the Helmholtz principle. Informally, it states that there is no perception in white noise. A white noise image is an image whose samples are identically distributed independent random variables. The view of a white sheet of paper in daylight gives a fair idea of what white noise is. From this impossibility of seing something on a white sheet, one can derive mathematical techniques and algorithms analyzing digital images and seeing the geometric structures they contain.
Most experiments are performed on digital every day photographs. The line segment detector is an on line example of a fully autonomous image analysis algorithm stemming from this theory.
This textbook on line, with exercises, is about the deep links between linear and non-linear image filtering and partial differential equations. The book starts with a detailed account of the heat equation and its multiple applications in image processing. Then "flat" mathematical morphology, a contrast invariant image analysis theory, is developed. This leads to study several geometric PDE's, which commute with contrast changes and are therefore shape analyzers. In particular, the famous mean curvature motion is detailed and linked to a classic image filter, the median filter. This book is taught at our grand research master, MVA.
Be careful, the download of these slides containing many real and synthetic paintings will be long! Our method to create abstract images starts from principles and techniques proposed by the founders of abstract art, particularly Klee and Kandinsky. Their manifesto was to liberate painting from the imitation of real world objects, and therefore to invent techniques to create new shapes, and new ways to combine them. The sites Algomo1 and Algomo2 show many images created by Alvarez, Gousseau and myself with automatic stochastic algorithms respecting abstract synthesis principles. Some of these images actually try more elaborate multi-scale shape combination principles, leading to new kinds of images and textures.
This book is an application of the computational Gestalt theory (see above). It gives a complete method permitting to decide whether two images contain or not the same shapes. The theory is applied with three different methods to extract invariant features from images: LLD, SIFT, and MSER. It is demonstrated that the a contrario method is a suitable and efficient way to decide whether two shapes look alike "just by chance", or whether the observed similarity cannot be casual.
This recent mathematical theory formalizes natural and artificial irrigation and transportation networks obeying a single principle: the transportation cost (or energy needed) per unit is lowered by a joint transportation. This common sense observation is usually stated as a concave power cost: the per unit transportation cost of a quantity of matter s over a length l has the form f(s)=lsa, where the exponent a satisfies 0=< a =<1. When a =1, this simply is the classic Monge-Kantorovitch optimal transportation theory. When a =0, the solutions are the Steiner optimal graphs. But for 0=< a <1, the optimal solutions are networks with a tree structure, whose roots spread over the irrigating measure, and the branches carry the transported material to the irrigated measure. The most striking natural examples of such networks are the hydrographic networks, draining the water of a continent to the ocean, the trees transporting water and nutrients to the leaves, the lungs and the blood circulation system. The artificial most studied networks obeying a similar law are the human distribution networks (oil pipelines, water, power, communication networks).