[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

In this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations. Our scale and affine invariant detectors are based on the following recent results: (1) Interest points extracted with the Harris detector can be adapted to affine transformations and give repeatable results (geometrically stable). (2) The characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives (the Laplacian). (3) The affine shape of a point neighborhood is estimated based on the second moment matrix.

Our scale invariant detector computes a multi-scale representation for the Harris interest point detector and then selects points at which a local measure (the Laplacian) is maximal over scales. This provides a set of distinctive points which are invariant to scale, rotation and translation as well as robust to illumination changes and limited changes of viewpoint. The characteristic scale determines a scale invariant region for each point. We extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood. An iterative algorithm modifies location, scale and neighborhood of each point and converges to affine invariant points. This method can deal with significant affine transformations including large scale changes. The characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point.

We present a comparative evaluation of different detectors and show that our approach provides better results than existing methods. The performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale/affine invariant descriptors computed on the regions associated with our points.

/pdf/scale-affine-invariant-interest-point-detectors-189ragelfl.pdf

Scale & Affine Invariant Interest Point Detectors

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

From the Publisher: 
The accessible presentation of this book gives both a general view of the entire computer vision enterprise and also offers sufficient detail to be able to build useful applications. Users learn techniques that have proven to be useful by first-hand experience and a wide range of mathematical methods. A CD-ROM with every copy of the text contains source code for programming practice, color images, and illustrative movies. Comprehensive and up-to-date, this book includes essential topics that either reflect practical significance or are of theoretical importance. Topics are discussed in substantial and increasing depth. Application surveys describe numerous important application areas such as image based rendering and digital libraries. Many important algorithms broken down and illustrated in pseudo code. Appropriate for use by engineers as a comprehensive reference to the computer vision enterprise.

Computer vision : a modern approach = 计算机视觉 : 一种现代的方法

In this paper gaze shifts are considered as a realization of a stochastic process with non-local transition probabilities in a saliency field that represents a landscape upon which a constrained random walk is performed. The search is driven by a Langevin equation whose random term is generated by a Levy distribution, and by a Metropolis algorithm. Results of the simulations are compared with experimental data, and a notion of complexity is introduced to quantify the behavior of the system in different conditions.

/pdf/modelling-gaze-shift-as-a-constrained-random-walk-3j89piggdo.pdf

Modelling gaze shift as a constrained random walk

The Pareto probability distribution is widely applied in dierent fields such us finance, physics, hydrology, geology and astronomy. This note deals with an application of the Pareto distribution to astrophysics and more precisely to the statistical analysis of masses of stars and of diameters of asteroids. In particular a comparison between the usual Pareto distribution and its truncated version is presented. Finally, a possible physical mechanism that produces Pareto tails for the distribution of the masses of stars is presented.

http://personalpages.to.infn.it/~zaninett/projects/paretozan.pdf

On the truncated Pareto distribution with applications

This paper deals with a novel way for representing and computing image features encapsulated within different regions of scale-space. Employing a thermodynamical model for scale-space generation, the method derives features as those corresponding to "entropy rich" image regions where, within a given range of spatial scales, the entropy gradient remains constant. Different types of image features, defining regions of different information content, are accordingly encoded by such regions within different bands of spatial scale.

On the representation of image structures via scale space entropy conditions

We explore the relationships between two classical means of mathematically representing visual patterns that are invariant under geometric transformations. One, based on integral transforms, in particular, Fourier transforms, produces transform magnitudes invariant to pairwise combinations of translations, rotations, and size changes. The second, based on the degree to which the pattern remains invariant to differential operators (which are the infinitesimal generators of the geometric transformations), results in algebraic relations between pattern structures and group theoretical properties of the transforms. Formal relationships are established between these representations, relating the kernel properties of the integral transforms to the associated Lie transformation groups.

Relationship between integral transform invariances and Lie group theory

https://boccignone.di.unimi.it/IUM2_files/VisionReserch09Pre.pdf

Mario Ferraro

Papers

Modelling gaze shift as a constrained random walk

On the truncated Pareto distribution with applications

On the representation of image structures via scale space entropy conditions

Relationship between integral transform invariances and Lie group theory

Visuomotor Characterization of Eye Movements in a Drawing Task