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The ability to determine an object's position accurately and quickly is important in many robotics tasks.Monocular scene analysis based on perspective projection can be successfully used to solve this problem if a-priori knowledge on objects is available. In this paper analytic procedures for perspective inversion of quadrics of revolution — in particular for spheres, cones and cylinders — are presented. Preliminary experimental results on real images of a test object are provided, with the main goal to test the procedures accuracy and the suitability of the available low-level processing. 1 INTRODUCTION Monocular computer vision is one of the most challenging approaches for 3D scene analysis. The basicidea of monocular vision is to understand in which situations and under which conditions a single 2D imagecan provide enough information for a 3D interpretation of the scene. A set of paradigms, known as "shape from X" , has been developed within this reference, such as shape from shading, shape from texture and shapefrom contours.Among the methodologies of monocular computer vision, perspective inversion as a tool to infer 3Dinformation from 2D data plays a very important role, especially for its consolidated mathematical foundationsand for its large applicability [4,5,7,2,6,8]. Independently of the kind of application, the basic problem ofperspective inversion is to recover the 3D orientation of some scene elements, referred to as primitives, startingfrom their 2D projection in the image plane, exploiting model knowledge to get the necessary constraints.Within industrial robotics, applications like object recognition and manipulation are good examples ofsituations in which a lot of information (often in the form of CAD models) is available both on the objectsand on the environment structure. Anyway, at present other new applications are emerging that seem as wellsuitable for the perspective inversion approach, like the auto-positioning and the landmark-based navigationof autonomous mobile robots.This paper presents some mathematical procedures which allow to compute the perspective inversion ofquadnics of revolution, obtaining completely analytic solutions. |
