1. DIGITAL SIGNAL PROCESSING IN ANALYSIS OF BIOMEDICAL IMAGES Prof. Aleš Procházka Institute of Chemical Technology in Prague Department of Computing and Control Engineering Digital Signal and Image Processing Research Group

2. MOTIVATION OF THE DSP RESEARCH GROUP INTEGRATION ROLE OF SIGNAL AND IMAGE PROCESSING IN THE FRAME OF INFORMATION ENGINEERING  Interdisciplinary area connecting mathematics and engineering: control, measuring engineering, vision, speech processing, biomedicine, environmental engineering …  Fundament for data acquisition, system identification and modelling, signal de-noising, feature extraction, segmentation, classification, compression, prediction, …  Similar mathematical background based on methods of time-frequency and time-scale analysis in different areas 1. INTRODUCTION

3. 2. APPLICATIONS Environmental Engineering Remote Data Processing Biomedical Image Analysis Signal Prediction INTERESTS OF DSP RESEARCH GROUP

4. DISCRETE FOURIER TRANSFORM IN RESOLUTION ENHANCEMENT 1-D DFT for k=0,1,…,N/2 – 1 and f(k)=k/N 2-D DFT for k=0,1,…,N/2 – 1, l= 0,1,…,M/2 – 1 and f 1 (k)=k/N, f 2 (l)=l/M 3. TIME-FREQUENCY ANALYSIS

5. WAVELET TRANSFORM IN SIGNAL PARTS DETECTION 4. TIME-SCALE ANALYSIS  Initial wavelet defined either in the analytical form or by a dilation equation  Dilation and translation coefficients: a=2^m, b=k 2^m  Initial wavelet is a pass-band filter  Wavelet dilation corresponds to its pass-band compression

6. Magnetic resonance image 5. DENOISING OF SIGNAL / IMAGE COMPONENTS ALGORITHM  Decomposition stage: – convolution of a given signal and the filter – downsampling by D  Coefficients - by rows and columns thresholding  Reconstruction stage: – row upsampling by factor U and row convolution – sum of the corresponding images – column upsampling by factor U and column convolution WAVELET TRANSFORM IN IMAGE DENOISING

7. MAGNETIC RESONANCE IMAGES OF A HUMAN BRAIN  Original resolution: 512 x 512 pixels 512 x 512 pixels  Resolution enhancement: 1024 x 1024 pixels 1024 x 1024 pixels WAVELET TRANSFORM IN IMAGE RESOLUTION ENHANCEMENT I. Image Resolution Enhancement using DFT II. Image Resolution Enhancement using DWT CONCLUSIONS  DFT: the structures and edges are very smooth edges are very smooth  DWT: sharper edges obtained obtained  DFT and DWT: various methods to various methods to enhance the resolution enhance the resolution can be applied can be applied 6. MR IMAGE RESOLUTION ENHANCEMENT

8. METHODS  Detection of features of missing regions and their replacement by the most similar ones 7. IMAGE RESTORATION  Multidirectional prediction of missing image parts  Multidemensional cubic and spline interpolation  Iterated wavelet interpolation METHODS OF IMAGE COMPONENTS RESTORATION

9. ALGORITHM  Image decomposition into a selected level  Wavelet coefficients thresholding  Image reconstruction  Replacement of values outside regions of interest by original values  The next iteration of image decomposition 8. ITERATED WAVELET TRANSFORM IN IMAGE RESTORATION WAVELET TRANSFORM IN ITERATED INTERPOLATION

10. 9. IMAGE SEGMENTATION WATERSHED TRANSFORM IN IMAGE SEGMENTATION ALGORITHM  Image thresholding and denoising  Distance and watershed transform use  Extraction of individual segments  Analysis of image components boundary signals and texture

11. 10. FEATURE EXTRACTION AND CLASSIFICATION RADON TRANSFORM IN ROTATION INVARIANT TEXTURE FEATURES ESTIMATION ALOGORITHM  Radon transform use for conversion of rotation to translation  Translation invariant wavelet transform use for feature estimation  Classification by neural networks

12. 11. FEATURE BASED SEGMENTATION FEATURE BASED BIOMEDICAL IMAGE SEGMENTATION PRINCIPLE  Each root pixel of the original image is associated with its feature derived from its neighbourhood  Pixels are individually classified into selected number of levels

13. 12. CONCLUSION  European Association for Signal and Image Processing  IEE London, IEEE  University of Cambridge, Brunel University, UK  University Las Palmas, Spain COLLABORATION SELECTED PAPERS  A. Procházka, I. Šindelářová, and J. Ptáček. Image De-noising and Restoration using Wavelet Transform. In European Control Conference ECC 2003 Conference Papers, Cambridge, UK, 2003.  A. Procházka and J. Ptácek. Wavelet Transform Application in Biomedical Image Recovery and Enhancement. In P. of 8th Multi-Conf. Systemics, Cybernetics and Informatic, Orlando, USA, 2004  A. Procházka, A. Gavlasova, M. Mudrova. Rotation Invariant Biomedical Object Recognition. In Proc. of the EUSIPCO Conf., EURASIP, Italy, 2006

14. http: // dsp.vscht.cz Institute of Chemical Technology in Prague Research Group of Digital Signal and Image Processing