The Helpful Mathematics
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Articles

Articles demonstrate ideas used in production. Every article contains download sample to give a touch to the real world of mathematical ideas used in the modern software.

Corrupted and restored images

Article 1. Median filter

Category. Digital signal and image processing (DSP and DIP) software development.

Median filter is a filter of nonlinear class. This article is a practical guide for understanding and implementation of the filter — it contains theory, C++ source code, programming instructions and sample application. The application demonstrates the capability of the median filter to restore images corrupted by destructive noise. This is not the only kind of corruption the filter can filter out. Download the sample and try this “miracle” of image processing science. Generator of destructive noise and sample image are also supplied.

Original and rotated images

Article 2. Image rotation

Category. Pixel graphics rendering software development.

That is not so easy to rotate the image in the screen because the screen picture is discrete. So what is the way? One should use special algorithms to calculate antialiased image. This sample demonstrates antialiased image rotation. You can process any 24-bit BMP file.

Demo screenshot

Article 3. Deformation visualisation

Category. Scientific graphics rendering software development.

Did you ever interested in question what form had a ball while rebounding from the ground? Do you want to see that? Live mechanics, physics and a bit more. Real-time interactive OpenGL graphics.

Pendulum

Article 4. Pendulum in viscous media

Category. Microcontroller firmware development.

Note. The sample is a part of a production project.

This sample demonstrates solving of the problem of optimal control theory. It is pure MatLab calculation sample.

Original and smoothed images

Article 5. Mean filter, or average filter

Category. Digital signal and image processing (DSP and DIP) software development.

Mean filter, or average filter maybe is the simplest filter of linear class. Nevertheless, it is used widely in signal and image processing, usually as a part of processing pipeline for signal (image) averaging and preparing it for further processing. The article is a practical introduction to this useful tool — it contains theory, C++ source code, programming instructions and sample application for demonstrating filter features.