Shape matching and classification using height functions

Bag of contour fragments for robust shape classification

We show that it is possible to improve the average time of the Boyer-Moore string matching algorithm using more space. This is accomplished by applying a transformation that virtually increases the size of the alphabet in use. The improvement is such that for long patterns it is possible to obtain an algorithm more than 50 per cent faster than the original one. We include experimental results on random and English text. Some improvements for searching on English text are also discussed.

Improved string searching

The Kantorovich inequality for error analysis of the Kalman filter with unknown noise distributions

A fringe analysis method based on a new way of describing the composition of a fringe in terms of tree collections is presented. It is shown that the derived matrix recurrence relation converges to the solution of a linear system involving the transition matrix, even when the transition matrix has eigenvalues with multiplicity greater than one. As a consequence, bounds and some exact results on the expected number of splits per insertion and on the expected depth of the deepest safe node in 23 trees and B-trees, on the expected height of 23 trees are obtained, and improvements of the bounds on the expected number of nodes in 23 trees are derived also. Bounds and some exact results for 23 trees and B-trees using an overflow technique are obtained.

The Theory of Fringe Analysis and Its Application to 2-3 Trees and B-Trees

(1982). Kantorovich-Type Inequalities. The American Mathematical Monthly: Vol. 89, No. 5, pp. 314-330.

Kantorovich-Type Inequalities

We give a short review of the history of the inequality $\sum _{i = 1}^nn{x_i}/({x_{i + 1}} + {x_{i + 2}}) \geq n/2,$ conjectured by H.S. Shapiro in 1954, whose exact domain of validity was determined in 1989 by B.A. Troesch, concluding an eventful, sometimes seemingly hopeless search.

A review of Shapiro’s cyclic inequality

For x > 0, t ∈ ℝ put 

$$ {\text{g}}_{\text{t}} \left( {\text{x}} \right): = \left\{ {\begin{array}{*{20}c} { - {\text{x}}^{\text{t}} ,} & {{\text{if}}\,{\text{t}} \in \left( {0,\,1} \right),} \\ {{\text{x}}^{\text{t}} } & {{\text{otherwise}}.} \\ \end{array} } \right. $$

A Problem Concerning Majorization

Perceptually motivated shape evolution with shape-preserving property

Despite of intensive research on shape decomposition algorithms, their performance evaluation remains qualitative today The intention of this work is to close this gap by proposing a general framework for quantitative performance evaluation of shape decomposition algorithms The proposed framework is of supervised nature and based on a benchmark database from a large-scale psychological study with manually specified ground truth We discuss various variants of dissimilarity functions for comparing two decompositions A preliminary comparison study using five shape decomposition methods and an ensemble technique demonstrates the usefulness of our approach In particular, the quantitative results well coincide with visual comparison of decompositions

Achim Clausing

Papers

Kantorovich-Type Inequalities

A review of Shapiro’s cyclic inequality

A Problem Concerning Majorization

Perceptually motivated shape evolution with shape-preserving property

Framework for quantitative performance evaluation of shape decomposition algorithms