HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 1 Detection of Cardboard Faults during the Production Process Nataša Babačev, Marko Barjaktarović University of Belgrade, Faculty of Electrical Engineering Desanka Radunović University of Belgrade, Faculty of Mathematics Belgrade, Serbia and Montenegro Bremen, Germany,

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 2 Introduction Production of cardboard in a long bolt Occurrence of faults and stains on the surface Detection and localization in real-time Existing algorithm using Kirsch operator Discrete Wavelet Transform using third level Haar wavelets Denoising and selection of vertical wavelet coefficients

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 3 Cardboard Production Cardboard exits the production machine Optoelectronic system photographs the surface 800*1024 pixels with 256 levels of gray Influence of the factory lights and optic lance Nonuniform distribution of gray Preprocessing of the image in order to get almost uniform distribution

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 4 Original image of cardboard

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 5 Almost uniform distribution

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 6 Image with fault and noise

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 7 Existing algorithm Wavelets represent the optimization of an existing algorithm by Marko Barjaktarović High level of noise due to short time of exposition and high speed of the cardboard Denoising is done by a filter of size 1x5 pixels Extracting of the edges of faults is done by using the modification of Sobel operator, i.e. Kirsch operator – 5x5 matrix

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 8 Result of the Kirsch operator

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 9 Converting to binary image The threshold is computed from the histogram

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 10 Denoising using erosion Clearing the image of dots that Kirsch operator detects as an edge because of local variations of gray The value of every pixel is replaced with the minimum value of neighboring pixels with the same -coordinate and or in order to preserve the line faults that occur Two consecutive erosions are needed

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 11 Erosion of the line fault

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 12 Line faults For a fault in a shape of thin line the result is more dots with the same -coordinate Distribution of area of all faults – objects on the image on -coordinate If the area is large for a narrow value of then it is considered a line fault

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 13 Distribution of area of a line fault

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 14 Optimization of the algorithm Denoising is done prior the edge detection Edge detection Both are done using third level Haar wavelets

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 15 Denoising with DWT level 3 Haar Soft thresholding Fixed form threshold t s – median absolute deviation of detail coefficients of scale 1

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 16 Denoised image with level 3 Haar

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 17 Extracting the edges DWT using third level Haar wavelets Faults occur in the direction of motion, i.e. vertical direction Only vertical detail coefficients are kept

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 18 IDWT with vertical coefficients

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 19 Binary values of pixels

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 20 Comparing the two methods Denoised image with DWT is clearer then in the existing algorithm Faster then detecting edges by Kirsch operator Less data stored in a sparse matrix After IDWT image is with less noise Erosion is still needed after IDWT

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 21 Image without faults after IDWT

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 22 Most common example of fault

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 23 Denoising with DWT level 3 Haar

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 24 Binary image of IDWT

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 25 Image after two erosions of IDWT

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 26 Further optimization The algorithm using wavelets for edge detection is still in development Possible optimization – leaving less vertical coefficients as non-zero The right threshold needs to be determined

HASSIP/DFG-SPP1114 Workshop “Recent Progress in Wavelet Analysis and Frame Theory” 27 Detection of Cardboard Faults during the Production Process Nataša Babačev, Marko Barjaktarović University of Belgrade, Faculty of Electrical Engineering Desanka Radunović University of Belgrade, Faculty of Mathematics Belgrade, Serbia and Montenegro Bremen, Germany,