1 Ideas from quantum mechanics, I 8 1.1 Broken scale invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2 Integrating out degrees of freedom . . . . . . . . . . . . . . . . . . . . . . . . 15 1.2.1 Attempt to consolidate understanding . . . . . . . . . . . . . . . . . 18 1.2.2 Wick rotation to real time. . . . . . . . . . . . . . . . . . . . . . . . . 20 1.3 Other ideas ...

Discrete morphological operations with line segments are notoriously hard to implement. In this paper we study different possible implementations of the line structuring element, compare them, and examine their rotation and translation invariance in the continuous-domain sense. That is, we are interested in obtaining a morphological operator that is invariant to rotations and translations of th...

We develop a theory of quasiparticle localization in superconductors in situations without spin rotation invariance. We discuss the existence and properties of superconducting phases with localized/delocalized quasiparticle excitations in such systems in various dimensionalities. Implications for a variety of experimental systems, and to the properties of random Ising models in two dimensions, ...

The steerable pyramid decomposition is an invertible representation similar to the two-dimensional discrete wavelet transform, but with interesting shiftand rotation-invariance properties. It is slightly overcomplete and amenable to a filter bank implementation via convolution and downand upsampling operations. This paper presents a simple method for designing the FIR filter kernels required to...

On the real unit interval, the notion of a Girard monoid coincides with the notion of a t-norm-based residuated lattice with strong induced negation. A geometrical approach toward these Girard monoids, based on the notion of rotation invariance, is turned in an adequate axiomatization for the Involutive Monoidal T-norm-based residuated Logic (IMTL).

We present an automatic crest lines extraction method from 3D triangulated meshes. We use a bivariate polynomial to approximate the surface locally and calculate the principal curvatures and directions on every vertex and a tracing algorithm to extract the crest lines. We show crest lines on various triangulated meshes and evaluate their invariance under rotation and stability under scaling.

In this paper, a new technique for object classi cation from silhouettes is presented. Hidden Markov Models are used as a classi cation mechanism. Through a set of experiments, we show the validity of our approach and show its invariance under severe rotation conditions. Also, a comparison with other techniques that use Hidden Markov Models for object classi cation from silhouettes is presented.

Local descriptors are increasingly used for the task of object recognition because of their perceived robustness with respect to occlusions and to global geometrical deformations. We propose a performance criterion for a local descriptor based on the tradeoff between selectivity and invariance. In this paper, we evaluate several local descriptors with respect to selectivity and invariance. The ...

Local Parameter Histograms (LPH) based on Gaussian Markov random fields (GMRFs) have been successfully used in effective texture discrimination. LPH features represent the normalized histograms of locally estimated GMRF parameters via local linear regression. However, these features are not rotation invariant. In this paper two techniques to design rotation invariant LPH texture descriptors are...

Rotation moment invariants have been of great interest in image processing and pattern recognition. This paper presents a novel kind of rotation moment invariants based on the Slepian functions, which were originally introduced in the method of separation of variables for Helmholtz equations. They were first proposed for time series by Slepian and his coworkers in the 1960s. Recent studies have...