In this paper we describe a new method for jigsaw puzzle solving. The main steps of the method are local shape analysis followed by global assembly. Local shape analysis is based on an approximate string matching procedure that detects corresponding partial boundaries of pairs of puzzle pieces. In the assembly phase, ambiguities that may result from local shape matching are resolved using a best-first tree search procedure with backtracking. The method takes real images of puzzle pieces as input data. It has been completely implemented and successfully tested on a number of puzzles.

Jigsaw Puzzle Solving Using Approximate String Matching and Best-First Search

Finding rotational symmetries by cyclic string matching

In this paper we describe a system that is able to acquire models of 2D shapes from cluttered scenes. The input of the system is a sequence of images, each of which shows an unknown number of overlapping unknown 2D objects. The system identifies matching partial shapes across different images and combines them into complete 2D shape models, thus giving a complete interpretation of the input scenes. The identification of partial shapes is based on string matching, whereas a graph search procedure is used for shape model generation. The system has been fully implemented and tested on images containing parts of a jigsaw puzzle.

Acquisition of 2D Shape Models from Scenes with Overlapping Objects using String Matching

A class of VLSI architectures is proposed for the computationally intensive task of polygon recognition in 3-D space. They make use of a set of local shape descriptors for polygons that are invariant under affine transformations. The recognition procedure is based on the matching of edge length ratios using a simplified version of the dynamic programming procedure commonly used for string matching. The matching procedure also copes with partial occlusion of polygons. The architectures are systolic and fully utilize the principles of pipelining and parallelism in order to obtain high speed and throughput. A prototype VLSI chip implementing one of the proposed architectures is currently being built. >

VLSI architectures for polygon recognition

Object recognition is imperative in industry automation since it empowers robots with the perceptual capability of understanding the three-dimensional(3-D) environment by means of sensory devices. Considering object recognition as a mapping between object models and a partial description of an object, this paper introduces a three-phase filtering method that eliminates candidate models when their differences with the object show up. Throughout the process, a view-insensitive modeling method, namely localized surface parameters, is employed.

Surface matching is carried out in the first phase to match models with the object by comparing their localized surface descriptions. A model is a candidate of the object only if every object surface matches locally with at least one of the model surfaces. Since the topological relationship between surfaces specifies the global shape of the object and models, it is then checked in the next phase with local coordinate systems to make sure that a candidate model has the identical structure as the object.

Because the information of an object cannot be complete in a single viewing direction, the first two conditions can only determine if a candidate has the same portion as the object. The selected model may still be bigger than the object. To avoid the part-to-whole confusion, in the third phase, a back projection from candidate models is performed to ensure that no unmatched model features become visible when a model is virtually brought to the object‘s orientation.

In case multiple models are selected as a result of the insufficient information, disambiguating features and their visible directions are derived to verify the expected feature. In addition to the view independent object recognition under even ambiguous situations, the filtering method has a low computational complexity upper bounded byO(m^2n^2) and lower bounded by O(mn), where m and n are the numbers of model and object features. The three-phase object recognition has been exercised with real and synthesized range images. Experiment results are given in the paper.

Feature Mapping and View Planning with Localized Surface Parameters

The recognition of polygons in 3-D space is an important task in robot vision. Two particular problems are addressed in the paper. First a new set of local shape descriptors for polygons are proposed that are invariant under affine transformation. Furthermore, they are complete in the sense that they allow the reconstruction of any polygon in 3-D space from three consecutive vertices. The second problem discussed in this paper is the recognition of 2-D polygonal objects under affine transformation and the presence of partial occlusion. A recognition procedure that is based on the matching of edge length ratios is introduced using a simplified version of the standard dynamic programming procedure commonly employed for string matching. The algorithm is conceptually very simple, easy to implement and has a low computational complexity. It is in a set of experiments that the method is reliable and robust. >

T. Glauser

Papers

Viewpoint independent representation and recognition of polygonal faces in 3-D