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Directional Image Representations
Zátyik, Ján ; Rajmic, Pavel (referee) ; Průša, Zdeněk (advisor)
Various methods describes an image by specific shapes, which are called basis or frames. With these basis can be transformed the image into a representation by transformation coefficients. The aim is that the image can be described by a small number of coefficients to obtain so-called sparse representation. This feature can be used for example for image compression. But basis are not able to describe all the shapes that may appear in the image. This lack increases the number of transformation coefficients describing the image. The aim of this thesis is to study the general principle of calculating the transformation coefficients and to compare classical methods of image analysis with some of the new methods of image analysis. Compares effectiveness of method for image reconstruction from a limited number of coefficients and a noisy image. Also, compares image interpolation method using characteristics of two different transformations with bicubic transformation. Theoretical part describes the transformation methods. Describes some methods from aspects of multi/resolution, localization in time and frequency domains, redundancy and directionality. Furthermore, gives examples of transformations on a particular image. The practical part of the thesis compares efficiency of the Fourier, Wavelet, Contourlet, Ridgelet, Radon, Wavelet Packet and WaveAtom transform in image recontruction from a limited number of the most significant transformation coefficients. Besides, ability of image denoising using these methods with thresholding techniques applied to transformation coefficients. The last section deals with the interpolation of image interpolation by combining of two methods and compares the results with the classical bicubic interpolation.
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Using wavelet packet transformation for image compression
Kučera, Michal ; Rajmic, Pavel (referee) ; Kyselý, František (advisor)
The need for storing and transferring digital image data is still growing nowadays. The Compression is necessary to achieve effective usage of transfer and storage capacity. This Bachelor’s Thesis is concerned with compression method based on wavelet packet transform, which is derived from wavelet transform. It is focused especially on best basis search algorithms from whole wavelet packet tree. There is a comparison between 6 best basis and near-best basis search criterions by R. R. Coifman, M. V. Wickerhauser and C. Taswell in this thesis, which is achieved by using Matlab environment based program. The program was created for testing and demonstrative purpose only and that’s why it contains certain limitation such as only black and white image processing and its limited resolution. There is applied constant threshold on testing image after the several best basis criterions application. The Mean Squared Error is used for comparing outcome quality of compressed and original image. The function that acquires minimal Mean Squared Error is considered the best best-basis search criterion in term of visual quality. The results show that some of the Taswell’s functions significantly improve the visual quality of the image at the price of worse compression ratio against common Shannon entropy.
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Using wavelet packet transformation for image compression
Kučera, Michal ; Rajmic, Pavel (referee) ; Kyselý, František (advisor)
The need for storing and transferring digital image data is still growing nowadays. The Compression is necessary to achieve effective usage of transfer and storage capacity. This Bachelor’s Thesis is concerned with compression method based on wavelet packet transform, which is derived from wavelet transform. It is focused especially on best basis search algorithms from whole wavelet packet tree. There is a comparison between 6 best basis and near-best basis search criterions by R. R. Coifman, M. V. Wickerhauser and C. Taswell in this thesis, which is achieved by using Matlab environment based program. The program was created for testing and demonstrative purpose only and that’s why it contains certain limitation such as only black and white image processing and its limited resolution. There is applied constant threshold on testing image after the several best basis criterions application. The Mean Squared Error is used for comparing outcome quality of compressed and original image. The function that acquires minimal Mean Squared Error is considered the best best-basis search criterion in term of visual quality. The results show that some of the Taswell’s functions significantly improve the visual quality of the image at the price of worse compression ratio against common Shannon entropy.
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Directional Image Representations
Zátyik, Ján ; Rajmic, Pavel (referee) ; Průša, Zdeněk (advisor)
Various methods describes an image by specific shapes, which are called basis or frames. With these basis can be transformed the image into a representation by transformation coefficients. The aim is that the image can be described by a small number of coefficients to obtain so-called sparse representation. This feature can be used for example for image compression. But basis are not able to describe all the shapes that may appear in the image. This lack increases the number of transformation coefficients describing the image. The aim of this thesis is to study the general principle of calculating the transformation coefficients and to compare classical methods of image analysis with some of the new methods of image analysis. Compares effectiveness of method for image reconstruction from a limited number of coefficients and a noisy image. Also, compares image interpolation method using characteristics of two different transformations with bicubic transformation. Theoretical part describes the transformation methods. Describes some methods from aspects of multi/resolution, localization in time and frequency domains, redundancy and directionality. Furthermore, gives examples of transformations on a particular image. The practical part of the thesis compares efficiency of the Fourier, Wavelet, Contourlet, Ridgelet, Radon, Wavelet Packet and WaveAtom transform in image recontruction from a limited number of the most significant transformation coefficients. Besides, ability of image denoising using these methods with thresholding techniques applied to transformation coefficients. The last section deals with the interpolation of image interpolation by combining of two methods and compares the results with the classical bicubic interpolation.
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