FinalReview_F10

FinalReview_F10 - Final Term Review Yao Wang Polytechnic...

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Final Term Review Yao Wang Polytechnic Institute of NYU, Brooklyn, NY 11201
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Topics Covered Before Midterm Image representation olor representation Color representation Quantization ontrast enhancement Contrast enhancement Spatial Filtering: noise removal, harpening edge detection sharpening, edge detection Frequency domain representations FT, DTFT, DFT Implementation of linear filtering using DTFT nd DFT Yao Wang, NYU-Poly EL5123: Final Review 2 and DFT
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Topics Covered After Midterm Non-linear filtering: median, morphological filtering Image sampling, interpolation and resizing Image compression Lossless coding: entropy bound, Huffman coding, runlength coding for bilevel images ransform coding: unitary transform quantization Transform coding: unitary transform, quantization, runlength coding of coefficients, JPEG Wavelet transform and JPEG2K, Scalability Geometric transformation Image Restoration Yao Wang, NYU-Poly EL5123: Final Review 3
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Non-Linear Filtering Convolution is a linear operation 1=f1*h g2=f2*h g1=f1 h, g2=f2 h (a1* f1+a2* f2)*h=a1* g1+a2*g2 Linear filtering can be analyzed in frequency domain easily Non-linear filtering Median Rank-order filtering Morphological filtering Yao Wang, NYU-Poly EL5123: Final Review 4
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Median Filter Problem with averaging or weighted averaging filter Blur edges and details in an image Not effective for impulse noise (Salt-and-pepper) edian filter: Median filter: Taking the median value instead of the average or weighted average of pixels in the window ort all the pixels in an increasing order, take the middle one Sort all the pixels in an increasing order, take the middle one The window shape does not need to be a square Special shapes can preserve line structures edian filter is a NON INEAR operation Median filter is a NON-LINEAR operation Generalization of median filtering Rank- rder filtering: taking the k- h largest value Yao Wang, NYU-Poly EL5123: Final Review 5 a ode te g ta gt e t a gest a ue
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Morphological Filtering Binary image ilation erosion closing opening dilation, erosion, closing, opening can be interpreted as set operation More sophisticated operations can extract image features (skeleton, edges, etc.) Gray scale image Dilation, erosion, closing, opening Proofs of properties of the morphological filters not required. Yao Wang, NYU-Poly EL5123: Final Review 6
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Binary Dilation Dilation of set F with a structuring element is represented by H is represented by H F } ) ˆ ( : { F H x H F x where Φ represent the empty set. is composed of all the points H F G that when Ĥ shifts its origin to these points, at least one point of Ĥ is included in F.
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FinalReview_F10 - Final Term Review Yao Wang Polytechnic...

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