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 athematical 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:

  1. Multiview stereo 3D reconstruction, camera estimation and recognition using curves and surfaces: modeling the dynamic and geometric phenomena (possibly high dimensional) that take place in 3-space at the human scale, mainly using multiple images of the same scene (as acquired by a camera in different positions, systems of multiple cameras, or video). My interests is in devising robust, precise and automatic methods for tackling problems in this area. In order to meet such requirements, I explore the use of grouped primitives such as curves and their differential geometry as the basis for the methods, complementing interest points and other approaches. The computational end-goal is a system based on video sequences, that would work for any type of scene geometry, without need for calibration or textured regions, being able to identify not only the 3D structure of objects, but also their dynamics, camera position, the reflectance properties, and lighting conditions.
  2. Geometric Machine Learning/Manifold Learning: the understanding of typically high-dimensional patterns or manifolds from images, for applications such as robust recognition, tracking, occlusion completion, through Diffusion Maps, digital exterior calculus, and other general or specialized manifestations of differential geometry somewhat related to Hodge Theory, using principles from Pattern Theory. For instance, I have been applying this to the 3D modeling of ocean waves from multiple videos.
    • Collaborators: Francisco Duarte Moura Neto (Ph.D. Berkeley), a mathematician working on inverse problems, my colleague at UERJ. He is my primary and close collaborator in this front. Check out his book on Inverse Problems. We are finishing up a book on Diffusion Maps.

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 cycle on a manifold is a mix of the cohomology classes of subvarieties, on the projective case. 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. Is your brain is hypothesizing a global light source, and both bars can't be 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. Some curious illusions: convex concave crater illusion, and the hollow-face illusion.