Solving Jigsaw Puzzles By the Graph Connection Laplacian

We propose a novel mathematical framework to address the problem of automatically solving large jigsaw puzzles. This problem assumes a large image, which is cut into equal square pieces that are arbitrarily rotated and shuffled, and asks to recover the original image given the transformed pieces. The main contribution of this work is a method for recovering the rotations of the pieces when both shuffles and rotations are unknown. A major challenge of this procedure is estimating the graph connection Laplacian without the knowledge of shuffles. We guarantee some robustness of the latter estimate to measurement errors. A careful combination of our proposed method for estimating rotations with any existing method for estimating shuffles results in a practical solution for the jigsaw puzzle problem. Numerical experiments demonstrate the competitive accuracy of this solution, its robustness to corruption and its computational advantage for large puzzles

Image Reconstruction from Bag-of-Visual-Words

The objective of this work is to reconstruct an original image from Bag-of-Visual-Words (BoVW). Image reconstruction from features can be a means of identifying the characteristics of features. Additionally, it enables us to generate novel images via features. Although BoVW is the de facto standard feature for image recognition and retrieval, successful image reconstruction from BoVW has not been reported yet. What complicates this task is that BoVW lacks the spatial information for including visual words. As described in this paper, to estimate an original arrangement, we propose an evaluation function that incorporates the naturalness of local adjacency and the global position, with a method to obtain related parameters using an external image database. To evaluate the performance of our method, we reconstruct images of objects of 101 kinds. Additionally, we apply our method to analyze object classifiers and to generate novel images via BoVW

Measures of Similarity between Qualitative Descriptions of Shape, Colour and Size Applied to Mosaic Assembling

A computational approach for obtaining a similarity measure between qualitative descriptions of shape, colour and size of objects within digital images is presented. According to the definition of the qualitative features, the similarity values determined are based on conceptual neighbourhood diagrams or interval distances. An approximate matching algorithm between object descriptions is defined and applied to tile mosaic assembling and results of previous approaches are improved.This work has been partially supported by Universitat Jaume I (Fons del Pla Estratégic de 2011/2012), by the Zentrale Forschungsförderung der Universität Bremen under the project name “Providing human-understandable qualitative and semantic descriptions”, and by the Spanish Ministry of Science and Innovation under project ARTEMISA (TIN2009-14378-C02-01)

Improved shape-signature and matching methods for model-based robotic vision

Researchers describe new techniques for curve matching and model-based object recognition, which are based on the notion of shape-signature. The signature which researchers use is an approximation of pointwise curvature. Described here is curve matching algorithm which generalizes a previous algorithm which was developed using this signature, allowing improvement and generalization of a previous model-based object recognition scheme. The results and the experiments described relate to 2-D images. However, natural extensions to the 3-D case exist and are being developed