X International conference�“Information Technology and Implementation” (IT&I-2023)�Kyiv, Ukraine

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Experimental Curves Segmentation Using Variable Resolution

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Anton Sharypanov, Vladimir Kalmykov, Vitaly Vishnevskey

Institute of Mathematical Machines and Systems NASU�

Dedicated to the tenth anniversary of the Faculty of Information Technology

Realization of a function that can’t be represented by spline adequately

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

y = f(x), (a ≤ x ≤ b)

t0

t1

tN

Approximation of function y = f(x) realization with splines:

It is necessary to determine the set of boundary points T={t0,t1,…,tN}

and their quantity N in order to segment the curve.

0

ti

Decreasing of neuron’s receptive field excitation zone during visual act characterizes variable resolution(*)

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

a

Stimuli of different sizes

Δt_i

i= 1 2 3 4 5 6 …

PSH N^o

6

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5

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4

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3

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2

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1

n axes represents the number of spikes in corresponding time slice Δt_i. Maximum number of spikes corresponds to interval where the size of stimulus meets the excitatory zone size.

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а – decreasing of receptive field excitatory zone area during visual act

(*) N.F. Podvigin, 1979; Ruksenas O., 2007

Visual neuron’s receptive field as discrete realization of mathematical point neighborhood

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

Mathematical model of visual neuron’s receptive field functioning is the procedure of continuity checking for brightness function in point using variable point neighborhood

x₁

x₂

x₃

x₄

An example of computational resources saving using coarse-to-fine (*)

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

a – found moving objects in frame;

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b,c,d – sequential application of classifiers that allow to exclude inappropriate regions (white fields) from further processing.

(*) M. Pedersoli, A. Vedaldi, J. Gonz`alez. A Coarse-to-fine approach for fast deformable object detection. In CVPR, june 2011

Image segmentation with Canny method using different values of σ

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

σ = 1 σ = 1.7 σ = 4

An example of objects for segmentation

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

Measurement №

Measurement №

Brightness values

Function graphs segmentation using variable resolution

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

Graph is distorted by noise

No noise

Measurement №

Measurement №

Brightness values

Resolution №

Cardiac signal segmentation experiments

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

Time measurement №

Voltage, μV

Voltage, μV

Practical task: construction of rhythmograms and amplitudeograms for heart rate variability analysis

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

A_j

RR_i

RR_i

i

A_j

j

a)

b)

c)

Segmentation results for cardiograms that were obtained during hypoxic probes

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

High percentage of found R-peaks, but rather low percentage of identically segmented cardiograms – why?

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

Conclusion

• The segmentation of the experimental curve can be carried out as a search for the points of discontinuity of the piecewise smooth function that generates it. It is possible to construct new methods for segmenting experimental curves using the concept of variable resolution based on the classical theory of continuity of functions and actual advances in the field of neurophysiology of vision. In the algorithm under consideration processing results for all used resolutions are taken into account when making decision on segmentation. The efficiency of the algorithm is confirmed by the results of processing for signals and graphs distorted by interference. In this case no a priori information about the noise level was used.
• The experiment on cardiogram segmentation with algorithm being discussed using variable resolution provided satisfactory results compared to reference algorithms. Amplitudeograms and rhythmograms that were built from R-peak markup could be used as initial data in further research work involving heart rate variability.
• These solutions will be used in the development of new methods for processing halftone images as well.

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

Thank you!

Information Technology and Implementation, November 20, 2023, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine