# Method of Calculation of Averaged Digital Image Profiles by Envelopes as the Conic Sections

• Serhiy V. Balovsyak
• Oleksandr V. Derevyanchuk
• Igor M. Fodchuk
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 754)

## Abstract

The method of calculation of averaged digital image profiles has been developed. The image profile is dependence of the value of the pixel brightness on the image coordinate along the specified line segment. The corresponding software was developed in the MATLAB system.

Profile analysis is widely used in the processing of experimental and simulated digital images, especially if the images contain band-shaped objects. The presence of bands is characteristic of electron diffraction images, X-ray moire images, images of scanning probe microscopy, optical medical images, and others. Cross-section profiles contain important information about the explored object, since they describe the one-dimensional distribution of object brightness.

A single band profile may contain an appreciable noise component. Therefore, in order to increase the signal-to-noise ratio, a series of band profiles were obtained, on the basis of which the averaged profile was calculated. The calculation of the average profile is relatively easy to implement in cases when all the band profiles have the same scale, and line consisting of their starting points is parallel to line consisting of their ending points. However, the most of the experimental images undergo the geometric distortions, and the lines consisting of starting or ending points of the profiles correspond to conic-shaped curves. Therefore, in this paper we proposed firstly to approximate the curves consisting of starting/ending points by two envelopes, and then to calculate a series of profiles on the basis of these envelopes. Circles, ellipses, parabolas and hyperbolas were used as envelope functions.

The mathematical model, algorithm and software for calculating enveloping profiles in images are developed. The envelopes are calculated on the basis of the coordinates of the base points, which are determined by the user or calculated through the contours of the band. The high accuracy of the developed method for calculating averaged profiles has been confirmed in the processing of images of electron and X-ray diffraction, atomic force microscope, optical and medical images etc.

## Keywords

Digital image processing Signal-to-noise ratio Profile Envelope Ellipse Parabola Hyperbola

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© Springer International Publishing AG, part of Springer Nature 2019

## Authors and Affiliations

• Serhiy V. Balovsyak
• 1
• Oleksandr V. Derevyanchuk
• 1
• Igor M. Fodchuk
• 1
1. 1.Yuriy Fedkovych Chernivtsi National UniversityChernivtsiUkraine