Toward Guaranteed Illumination Models for Non-Convex Objects
This addresses illumination modeling for non-convex objects in computer vision, offering a theoretical advance over existing average-case methods.
The paper tackles the challenge of illumination variation in object detection by developing convex cone models with worst-case performance guarantees for non-convex Lambertian objects, achieving a verification test that guarantees acceptance of well-approximated images and rejection of poorly approximated ones, with complexity reduced via dimensionality reduction.
Illumination variation remains a central challenge in object detection and recognition. Existing analyses of illumination variation typically pertain to convex, Lambertian objects, and guarantee quality of approximation in an average case sense. We show that it is possible to build V(vertex)-description convex cone models with worst-case performance guarantees, for non-convex Lambertian objects. Namely, a natural verification test based on the angle to the constructed cone guarantees to accept any image which is sufficiently well-approximated by an image of the object under some admissible lighting condition, and guarantees to reject any image that does not have a sufficiently good approximation. The cone models are generated by sampling point illuminations with sufficient density, which follows from a new perturbation bound for point images in the Lambertian model. As the number of point images required for guaranteed verification may be large, we introduce a new formulation for cone preserving dimensionality reduction, which leverages tools from sparse and low-rank decomposition to reduce the complexity, while controlling the approximation error with respect to the original cone.