Similarity measure

In statistics and related fields, a similarity measure or similarity function or similarity metric is a real-valued function that quantifies the similarity between two objects. Although no single definition of a similarity exists, usually such measures are in some sense the inverse of distance metrics: they take on large values for similar objects and either zero or a negative value for very dissimilar objects. Though, in more broad terms, a similarity function may also satisfy metric axioms. Cosine similarity is a commonly used similarity measure for real-valued vectors, used in (among other fields) information retrieval to score the similarity of documents in the vector space model. In machine learning, common kernel functions such as the RBF kernel can be viewed as similarity functions. Use of different similarity measure formulas Different types of similarity measures exist for various types of objects, depending on the objects being compared. For each type of object th

3D Shape Similarity

Fan Zhang

Microsoft Kinect, Google's Project Tango and Lytro's light field camera are all examples of 3D depth sensing reaching the consumer market. As this technology becomes more widestream, new signal processing techniques are needed to exploit this data. Recent techniques in 3D shape similarity assesment present exciting opportunities to develop new algorithms in this area. The aim of this project is to create a tutorial to these techniques using an iPython notebook. Particular emphasis will be placed on an excellent review paper [1] and book [2]. Seneca, the Roman philosopher, said “While we teach, we learn,” and creating a tutorial on these topics is an excellent exercise to understand a complex subject that is at the heart of many modern computer vision techniques. [1] S. Biasotti et al "Recent Trends, Applications, and Perspectives in 3D Shape Similarity Assessment", 2015. [2] A. Bronstein, M. Bronstein, R. Kimmel "Numerical Geometry of Non-Rigid Shapes", 2008. LCAV1556050917

2016

Shachi Shailesh Deshpande, Bernard Moret

Many important questions in molecular biology, evolution, and biomedicine can be addressed by comparative genomic approaches. One of the basic tasks when comparing genomes is the definition of measures of similarity (or dissimilarity) between two genomes, for example, to elucidate the phylogenetic relationships between species. The power of different genome comparison methods varies with the underlying formal model of a genome. The simplest models impose the strong restriction that each genome under study must contain the same genes, each in exactly one copy. More realistic models allow several copies of a gene in a genome. One speaks of gene families, and comparative genomic methods that allow this kind of input are called gene family-based. The most powerfulbut also most complexmodels avoid this preprocessing of the input data and instead integrate the family assignment within the comparative analysis. Such methods are called gene family-free. In this article, we study an intermediate approach between family-based and family-free genomic similarity measures. Introducing this simpler model, called gene connections, we focus on the combinatorial aspects of gene family-free genome comparison. While in most cases, the computational costs to the general family-free case are the same, we also find an instance where the gene connections model has lower complexity. Within the gene connections model, we define three variants of genomic similarity measures that have different expression powers. We give polynomial-time algorithms for two of them, while we show NP-hardness for the third, most powerful one. We also generalize the measures and algorithms to make them more robust against recent local disruptions in gene order. Our theoretical findings are supported by experimental results, proving the applicability and performance of our newly defined similarity measures.

Mary Ann Liebert2017

Alignment of uncalibrated images for multi-view classification

Ömer Sercan Arik, Pascal Frossard, Elif Vural

Efficient solutions for the classification of multi-view images can be built on graph-based algorithms when little information is known about the scene or cameras. Such methods typically require a pairwise similarity measure between images, where a common choice is the Euclidean distance. However, the accuracy of the Euclidean distance as a similarity measure is restricted to cases where images are captured from nearby viewpoints. In settings with large transformations and viewpoint changes, alignment of images is necessary prior to distance computation. We propose a method for the registration of uncalibrated images that capture the same 3D scene or object. We model the depth map of the scene as an algebraic surface, which yields a warp model in the form of a rational function between image pairs. The warp model is computed by minimizing the registration error, where the registered image is a weighted combination of two images generated with two different warp functions estimated from feature matches and image intensity functions in order to provide robust registration. We demonstrate the flexibility of our alignment method by experimentation on several wide-baseline image pairs with arbitrary scene geometries and texture levels. Moreover, the results on multi-view image classification suggest that the proposed alignment method can be effectively used in graph-based classification algorithms for the computation of pairwise distances where it achieves significant improvements over distance computation without prior alignment.

2011

Shachi Shailesh Deshpande, Bernard Moret

Mary Ann Liebert2017

3D Shape Similarity

New Genome Similarity Measures based on Conserved Gene Adjacencies

Alignment of uncalibrated images for multi-view classification

Alignment of uncalibrated images for multi-view classification

New Genome Similarity Measures based on Conserved Gene Adjacencies

3D Shape Similarity