Mathematics for MultimediaLaajuus (5 ECTS)

Objective

After completing the course the student will understand basic concepts in integration and image processing. Will know several ways to represent data and information. Will understand role of differentiation and integration in engineering applications. Will understand basic methods how to manipulate digital images.
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After completing the course the student will be able to solve simple integration problems analytically or numerically, also with the aid of a computer. Will be able to manipulate digital images by mask methods in spatial domain by a computer. Will be able to model simple and practical integration problems and solve them.

Content

Complex numbers: representations and rules. Bilinear interpolation. Gradient and directional derivative. Integral function and definite integral. Integration of elementary functions; esp. constant, linear and piecewise constant and piecewise linear functions: definite integral as a sum; integration of data. Idealised image as a mathematical model of an image and a digital image. Image processing with a computer: pixel group operations (masks, filtering, nearest neighbour methods); image enhancement: edges, smoothing, sharpening etc.; analysis of filters.
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Integration techniques: integration by parts and by substitution. Numerical methods of integration. Integrals in mathematical models: quantity elements. Filters as mapping functions. Least squares method in image processing. Nearest neighbour and bilinear interpolation in image processing. Processing a coloured image: Bayer filter pattern.

Qualifications

Engineering Mathematics