Christian Beecks

Signature Quadratic Form Distance

The Signature Quadratic Form Distance is an adaptive similarity measure for flexible content-based feature representations of multimedia data. In this paper, we present a deep survey of the mathematical foundation of this similarity measure which encompasses the classic Quadratic Form Distance defined only for the comparison between two feature histograms of the same length and structure. Moreover, we give the benefits of the Signature Quadratic Form Distance and experimental evaluation on numerous real-world databases.

A comparative study of similarity measures for content-based multimedia retrieval

Determining similarities among data objects is a core task of content-based multimedia retrieval systems. Approximating data object contents via flexible feature representations, such as feature signatures, multimedia retrieval systems frequently determine similarities among data objects by applying distance functions. In this paper, we compare major state-of-the-art similarity measures applicable to flexible feature signatures with respect to their qualities of effectiveness and efficiency. Furthermore, we study the behavior of the similarity measures by discussing their properties. Our findings can be used in guiding the development of content-based retrieval applications for numerous domains.

Signature quadratic form distances for content-based similarity

Determining similarity is a fundamental task in querying multimedia databases in a content-based way. For this challenging task, there exist numerous similarity models which measure the similarity among objects by using their contents. In order to cope with voluminous multimedia data, similarity models are supposed to be both effective and efficient. To this end, we introduce the Signature Quadratic Form Distance measure which allows efficient similarity computations based on flexible feature representations. Our new approach bridges the gap between the well-known concept of Quadratic Form Distances and feature signatures. Experimentation indicates that our similarity measure is able to compete with state-of-the-art similarity models regarding effectiveness of content-based similarity search. Moreover, our Signature Quadratic Form Distance outperforms the established Earth Movers Distance in efficiency: we obtain a speed-up factor of greater than 50.

Signature matching distance for content-based image retrieval

We propose a simple yet effective approach to content-based image retrieval: the signature matching distance. While recent approaches to content-based image retrieval utilize the bag-of-visual-words model, where image descriptors are matched through a common visual vocabulary, signature-based approaches use a distance between signatures, i.e. between image-specific bags of locally aggregated descriptors, in order to quantify image dissimilarity. In this paper, we focus on the signature-based approach to content-based image retrieval and propose a novel distance function, the signature matching distance. This distance matches coincident visual properties of images based on their signatures. In particular, by investigating different descriptor matching strategies and their suitability to match signatures, we show that our approach is able to outperform other signature-based approaches to content-based image retrieval. Moreover, in combination with a simple color and texture-based image descriptor, our approach is able to compete with the majority of bag-of-visual-words approaches.

Indexing the signature quadratic form distance for efficient content-based multimedia retrieval

The Signature Quadratic Form Distance has been introduced as an adaptive similarity measure coping with flexible content representations of various multimedia data. Although the Signature Quadratic Form Distance has shown good retrieval performance with respect to their qualities of effectiveness and efficiency, its applicability to index structures remains a challenging issue due to its dynamic nature. In this paper, we investigate the indexability of the Signature Quadratic Form Distance regarding metric access methods. We show how the distances inherent parameters determine the indexability and analyze the relationship between effectiveness and efficiency on numerous image databases.

Modeling image similarity by Gaussian mixture models and the Signature Quadratic Form Distance

Modeling image similarity for browsing and searching in voluminous image databases is a challenging task of nearly all content-based image retrieval systems. One promising way of defining image similarity consists in applying distance-based similarity measures on compact image representations. Beyond feature histograms and feature signatures, more general feature representations are mixture models of which the Gaussian mixture model is the most prominent one. This feature representation can be compared by employing approximations of the Kullback-Leibler Divergence. Although several of those approximations have been successfully applied to model image similarity, their applicability to mixture models based on high-dimensional feature descriptors is questionable. In this paper, we thus introduce the Signature Quadratic Form Distance to measure the distance between two Gaussian mixture models of high-dimensional feature descriptors. We show the analytical computation of the proposed Gaussian Quadratic Form Distance and evaluate its retrieval performance by making use of different benchmark image databases.

Ptolemaic indexing of the signature quadratic form distance

The signature quadratic form distance has been introduced as an adaptive similarity measure coping with flexible content representations of multimedia data. While this distance has shown high retrieval quality, its high computational complexity underscores the need for efficient search methods. Recent research has shown that a huge improvement in search efficiency is achieved when using metric indexing. In this paper, we analyze the applicability of Ptolemaic indexing to the signature quadratic form distance. We show that it is a Ptolemaic metric and present an application of Ptolemaic pivot tables to image databases, resolving queries nearly four times as fast as the state-of-the-art metric solution, and up to 300 times as fast as sequential scan.

On stability of signature-based similarity measures for content-based image retrieval

Retrieving similar images from large image databases is a challenging task for today’s content-based retrieval systems. Aiming at high retrieval performance, these systems frequently capture the user’s notion of similarity through expressive image models and adaptive similarity measures. On the query side, image models can significantly differ in quality compared to those stored on the database side. Thus, similarity measures have to be robust against these individual quality changes in order to maintain high retrieval performance. In this paper, we investigate the robustness of the family of signature-based similarity measures in the context of content-based image retrieval. To this end, we introduce the generic concept of average precision stability, which measures the stability of a similarity measure with respect to changes in quality between the query and database side. In addition to the mathematical definition of average precision stability, we include a performance evaluation of the major signature-based similarity measures focusing on their stability with respect to querying image databases by examples of varying quality. Our performance evaluation on recent benchmark image databases reveals that the highest retrieval performance does not necessarily coincide with the highest stability.

3D Image Browsing on Mobile Devices

We present an intuitive user interface for the exploration of images on mobile multi-touch devices. Our interface uses a novel cylindrical 3D visualization of visually sorted images as well as touch gestures and tilting operations to support mobile users in interactive browsing of images by providing convenient navigation/interaction and intuitive visualization capabilities.

Efficient Filter Approximation Using the Earth Mover's Distance in Very Large Multimedia Databases with Feature Signatures

The Earth Movers Distance, proposed in computer vision as a distance-based similarity model reflecting the human perceptual similarity, has been widely utilized in numerous domains for similarity search applicable on both feature histograms and signatures. While efficiency improvement methods towards the Earth Movers Distance were frequently investigated on feature histograms, not much work is known to study this similarity model on feature signatures denoting object-specific feature representations. Given a very large multimedia database of features signatures, how can k-nearest-neighbor queries be processed efficiently by using the Earth Movers Distance? In this paper, we propose an efficient filter approximation technique to lower bound the Earth Movers Distance on feature signatures by restricting the number of earth flows locally. Extensive experiments on real world data indicate the high efficiency of the proposal, attaining order-of-magnitude query processing time cost reduction for high dimensional feature signatures.