Todd A. Cass

Polynomial-Time Geometric Matching for Object Recognition

This paper considers the task of recognition and position determination, by computer, of a 2D or 3D object where the input is a single 2D brightness image, and a model of the object is known a priori. The primary contribution of this paper is a novel formulation and methods for local geometric feature matching. This formulation is based on analyzing geometric constraints on transformations of the model features which geometrically align it with a substantial subset of image features. Specifically, the formulation and algorithms for geometric feature matching presented here provide a guaranteed method for finding all feasible interpretations of the data in terms of the model. This method is robust to measurement uncertainty in the data features and to the presence of spurious scene features, and its time and space requirements are only polynomial in the size of the feature sets. This formulation provides insight into the fundamental nature of the matching problem, and the algorithms commonly used in computer vision for solving it.

Robust affine structure matching for 3D object recognition

We consider model-based object localization based on local geometric feature matching between the model and the image data. The method is based on geometric constraint analysis, working in transformation space. We present a formal method which guarantees finding all feasible matchings in polynomial time. From there we develop more computationally feasible algorithms based on conservative approximations of the formal method. Additionally, our formalism relates object localization, affine model indexing, and structure from multiple views to one another.

Scribbler: a tool for searching digital ink

Scribbler is a tool that enables users to search untranslated digital ink for target patterns such as words, symbols and simple sketches. By matching the raw stroke data instead of performing traditional handwriting recognition, Scribbler allows users to write quickly and naturally without being constrained to a particular writing style or a limited set of dictionary terms. This paper gives a brief description of the current implementation of Scribbler and discusses the results of a controlled experiment run to evaluate the matching engine’s effectiveness.

Analytical methods for uncalibrated stereo and motion reconstruction

We present a new approach to relative stereo and motion reconstruction from a discrete set of point correspondences in completely uncalibrated pairs of images. This approach also yields new projective invariants, and we present some applications to object recognition. Finally, we introduce a new approach to camera self-calibration from two images which allows full metric reconstruction up to some unknown scale factor. We have implemented the proposed methods and present examples using real images.

Robust geometric matching for 3D object recognition

This paper considers a model-based approach to identifying and locating known 3D objects in 2D images of a scene containing them via geometric feature matching of model and image data represented in terms of local geometric features. The problems of finding feature correspondences in the presence of geometric uncertainty, missing, and spurious data features are explicitly handled. The fundamentally geometric and combinatorial elements of the feature matching problem are made explicit, and a formulation based on computational geometry is used to achieve a polynomial-time matching approach for which the author can guarantee completeness and correctness. This paper deals primarily with the case of planar objects undergoing full 3D motion and scaled-orthographic projection.

Robust Affine Structure Matching for 3D Object Recognition

This paper considers a model-based approach to identifying and locating known 3D objects from 2D images. The method is based on geometric feature matching of the model and image data, where both are represented in terms of local geometric features. This paper extends and refines previous work on feature matching using transformation constraint methods by detailing the case of full 3D objects represented as point features and developing geometric algorithms based on conservative approximations to the previously presented general algorithm which are much more computationally feasible.