A unified framework for 3D reconstruction

Abstract

3D reconstruction is a branch of computer vision with a broad range of applications like computer aided design, animation, medicine and many others. In this talk we use continuous linear functionals for characterizing different kinds of 3D data. These problems can be tackled in the framework of Reproducing Kernel Hilbert Spaces and regularization of inverse problems. It can be said that 3D reconstruction is the general problem of estimating or finding functional dependencies from a three-dimensional data set. The origin of these data covers a wide range that includes tomography, surface reconstruction from point clouds or image and signal processing. Usually the problem of reconstruction has a very close relationship with scientific visualization and computer graphics. Reconstruction and generalized interpolationIn the same way we need data structures for representing data into a computer we also need a mathematical structure to represent different kinds of data. This can be done using the concept of functional on a Hilbert Space and some results from approximation theory [1]. If X is a function space, i.e. a space whose elements are functions then a real function R X → φ :on X is called a functional [3]. Our setting is a real Hilbert space, X =H, whose inner product is written