The Three-Dimensional Interpretation of a Class of Simple Line-Drawings

We provide a theory of the three-dimensional interpretation of a class of line-drawings called p-images, which are interpreted by the human vision system as parallelepipeds ("boxes"). Despite their simplicity, p-images raise a number of interesting vision questions: *Why are p-images seen as three-dimensional objects? Why not just as flatimages? *What are the dimensions and pose of the perceived objects? *Why are some p-images interpreted as rectangular boxes, while others are seen as skewed, even though there is no obvious distinction between the images? *When p-images are rotated in three dimensions, why are the image-sequences perceived as distorting objects---even though structure-from-motion would predict that rigid objects would be seen? *Why are some three-dimensional parallelepipeds seen as radically different when viewed from different viewpoints? We show that these and related questions can be answered with the help of a single mathematical result and an associated perceptual principle. An interesting special case arises when there are right angles in the p-image. This case represents a singularity in the equations and is mystifying from the vision point of view. It would seem that (at least in this case) the vision system does not follow the ordinary rules of geometry but operates in accordance with other (and as yet unknown) principles.

Robust and Efficient 3D Recognition by Alignment

Alignment is a prevalent approach for recognizing 3D objects in 2D images. A major problem with current implementations is how to robustly handle errors that propagate from uncertainties in the locations of image features. This thesis gives a technique for bounding these errors. The technique makes use of a new solution to the problem of recovering 3D pose from three matching point pairs under weak-perspective projection. Furthermore, the error bounds are used to demonstrate that using line segments for features instead of points significantly reduces the false positive rate, to the extent that alignment can remain reliable even in cluttered scenes.