Semantic spaces revisited: investigating the performance of auto-annotation and semantic retrieval using semantic spaces

Semantic spaces encode similarity relationships between objects as a function of position in a mathematical space. This paper discusses three different formulations for building semantic spaces which allow the automatic-annotation and semantic retrieval of images. The models discussed in this paper require that the image content be described in the form of a series of visual-terms, rather than as a continuous feature-vector. The paper also discusses how these term-based models compare to the latest state-of-the-art continuous feature models for auto-annotation and retrieval

The Algebraic Approach to Phase Retrieval and Explicit Inversion at the Identifiability Threshold

We study phase retrieval from magnitude measurements of an unknown signal as an algebraic estimation problem. Indeed, phase retrieval from rank-one and more general linear measurements can be treated in an algebraic way. It is verified that a certain number of generic rank-one or generic linear measurements are sufficient to enable signal reconstruction for generic signals, and slightly more generic measurements yield reconstructability for all signals. Our results solve a few open problems stated in the recent literature. Furthermore, we show how the algebraic estimation problem can be solved by a closed-form algebraic estimation technique, termed ideal regression, providing non-asymptotic success guarantees

Automated Generation of Geometric Theorems from Images of Diagrams

We propose an approach to generate geometric theorems from electronic images of diagrams automatically. The approach makes use of techniques of Hough transform to recognize geometric objects and their labels and of numeric verification to mine basic geometric relations. Candidate propositions are generated from the retrieved information by using six strategies and geometric theorems are obtained from the candidates via algebraic computation. Experiments with a preliminary implementation illustrate the effectiveness and efficiency of the proposed approach for generating nontrivial theorems from images of diagrams. This work demonstrates the feasibility of automated discovery of profound geometric knowledge from simple image data and has potential applications in geometric knowledge management and education.Comment: 31 pages. Submitted to Annals of Mathematics and Artificial Intelligence (special issue on Geometric Reasoning