Point Information Gain and Multidimensional Data Analysis

Abstract

Abstract:We generalize the point information gain (PIG) and derived quantities, i.e., point information gain entropy (PIE) and point information gain entropy density (PIED), for the case of the Rényi entropy and simulate the behavior of PIG for typical distributions. We also use these methods for the analysis of multidimensional datasets. We demonstrate the main properties of PIE/PIED spectra for the real data with the examples of several images and discuss further possible utilizations in other fields of data processing.

Spectroscopic Approach to Correction and Visualisation of Bright-Field Light Transmission Microscopy Biological Data

“…The sets of images for ND <0.1-0.8 were processed by Image Info Extractor Professional software (ICS FFPW) (chosen Rényi parameter α = 2) [28]. The point information gain entropy (PIE) gives a total change of the image information after iterative removing of one pixel from an individual image.…”

Optimization of Computational Burden of the Point Information Gain

“…An important question is how much information is included in a data point and how the points can be distinguished from each other. This question was solved by a derivation of the variable Point Information Gain (PIG, Γ) [12][13][14][15][16][17][18][19][20][21][22] which evaluates an information content of a single pixel in local and global context. This variable says how much is one individual pixel important for understanding of an image or image's part.…”

“…In addition, the method of the PIG preserves the details, highlights the edges, and decreases random noise in one calculation. Examples of usage of the PIG in image (pre)processing were published previously [12][13][14][15][16][17][18][19][20][21][22] The computation tool for image preprocessing using the PIG method is called the Image Info Extractor Professional software (IIEP; Institute of Complex Systems, Nové Hrady). The theoretical concept and practical utilization of this kind of software was introduced previously and this paper is supplemental to [17].…”

“…Examples of usage of the PIG in image (pre)processing were published previously [12][13][14][15][16][17][18][19][20][21][22] The computation tool for image preprocessing using the PIG method is called the Image Info Extractor Professional software (IIEP; Institute of Complex Systems, Nové Hrady). The theoretical concept and practical utilization of this kind of software was introduced previously and this paper is supplemental to [17]. The task of this paper is, using the examples of the Shannonian PIG with whole image approach and for cross neighbourhood for each pixel, to present a kind of computational optimization and the implementation of this computation on GPUs in order to achieve a higher computation performance of the IIEP software.…”

Observation of Dynamics Inside an Unlabeled Live Cell Using a Bright-Field Photon Microscopy: Evaluation of Organelles’ Trajectories

“…In order to highlight the intracellular structures' borders in digital images, we proposed a novel information-entropic variable derived from the Rényi information entropy -a point information gain. In the image processing, beside the others benefits [2,3,4], this variable enables to work with intensity histograms and to calculate one resulted value of the point information gain for similar intensity values.…”