Ricardo Fabbri

Research statement

My research is moved by the desire for a scientific and deeply conceptual theory of the principles behind the visual world. While biology provides reference visual systems, my focus is to devise scientific and mathematical theories with large-scale, realistic and useful computer systems. Without a working computational model, can we claim to understand anything completely? Computer systems are theories made alive; they incorporate physical contexts against which the principles of a theory can be checked, generalized and improved. The mathematical theory in my research is based on differential geometry for modeling general structures from multiple images and for machine learning – a "geometrization" of computer vision (vaguely speaking). I have focused on two lines of research:

Current focus: Mathematics. I will be prioritizing mathematics and geometry for the next couple of years, in the broad sense of extracting deep concepts to produce better algorithms and theories for the visual world. My primary interest is in differential geometry, both in the traditional and discrete/probabilistic/graphical manifestations in fields such as diffusion maps, spectral graph theory, and manifold learning.

Selected Publications

Teaching

PhD Students and Notable Msc Students

Current Past

Interests

Other areas I have interests in: automated analysis of biological images, complex networks, singularity theory, pattern recognition, machine learning, design of algorithms (using geometry or for solving geometry problems), theory of computation, applied distributed systems, 2D and 3D shape and image databases, open source software. I also research other topics: the zeros of the Riemann zeta function, the curious fact that any even number seems to be the sum of two primes, whether there is a chance P could really be NP, whether solutions to 3D Navier-Stokes always exist and are smooth, and whether every Hodge class on a complex projective manifold is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of the manifold. These will likely be solved by the time computers start seeing, so they might be useful intermediate steps :)

Software

Research and study material

Email

my email address in Zapfino

Links

Curiosities

Do the vertical borders of this page look strange to you? They are exactly the same gradients, reflected vertically. On their own, they should look convex or concave. But your brain is hypothesizing a global light source, and both bars can't be both convex and consistent with the same light source. There are also biases in direction - the brain tends to favor certain directions for the light source over others. As you might know, this is known as the convex concave crater illusion, and is related to the hollow-face illusion.