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Digital Image Processing Lecture 8: Image Enhancement in Frequency Domain II Naveed Ejaz
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6/25/20162 Fourier Transform Review Notice how we get closer and closer to the original function as we add more and more frequencies
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6/25/20163 Fourier Transform Review Frequency domain signal processing example in Excel
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6/25/20164 Properties of Fourier Transform
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6/25/20165 2-D DFT
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6/25/20166 Translation Property of 2-D DFT
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6/25/20167 Shifting the Origin to the Center
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6/25/20168 Shifting the Origin to the Center
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6/25/20169 Properties of Fourier Transform
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6/25/201610 Properties of Fourier Transform
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6/25/201611 Reciprocality of Lengths due to Scaling Property
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6/25/201612 Properties of Fourier Transform
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6/25/201613 Rotation Examples
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6/25/201614 Properties of Fourier Transform
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6/25/201615 Properties of Fourier Transform
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6/25/201616 Properties of Fourier Transform As we move away from the origin in F(u,v) the lower frequencies corresponding to slow gray level changes Higher frequencies correspond to the fast changes in gray levels (smaller details such edges of objects and noise) The direction of amplitude change in spatial domain and the amplitude change in the frequency domain are orthogonal (see the examples)
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6/25/201617 DFT Examples
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6/25/201618 DFT Examples
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6/25/201619 DFT Examples
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6/25/201620 Masking, Correlation and Convolution
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6/25/201621 Properties of Fourier Transform
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6/25/201622 Filtering using Fourier Transforms
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6/25/201623 Example of Gaussian LPF and HPF
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6/25/201624 Example of Modified HPF
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6/25/201625 Relationship b/w Spatial domain filters and Fourier domain filters
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6/25/201626 Relationship b/w Spatial domain filters and Fourier domain filters
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6/25/201627 Filters to be Discussed
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6/25/201628 Ideal Low Pass Filter
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6/25/201629 Ideal Low Pass Filter
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6/25/201630 Ideal Low Pass Filter (example)
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6/25/201631 Why Ringing Effect
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6/25/201632 Ringing Effect (example)
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6/25/201633 Butterworth Low Pass Filter
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6/25/201634 Butterworth Low Pass Filter
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6/25/201635 Butterworth Low Pass Filter (example)
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6/25/201636 Butterworth Low Pass Filter
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6/25/201637 Gaussian Low Pass Filters
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6/25/201638 Gaussian Low Pass and High Pass Filters
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6/25/201639 Gaussian Low Pass Filters
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6/25/201640 Gaussian Low Pass Filters (example)
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6/25/201641 Gaussian Low Pass Filters (example)
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6/25/201642 Sharpening Fourier Domain Filters
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6/25/201643 Sharpening Spatial Domain Representations
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6/25/201644 Sharpening Fourier Domain Filters (Examples)
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6/25/201645 Sharpening Fourier Domain Filters (Examples)
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6/25/201646 Sharpening Fourier Domain Filters (Examples)
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6/25/201647 Laplacian in Frequency Domain
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6/25/201648 Laplacian in Frequency Domain
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6/25/201649 Unsharp Masking, High Boost Filtering
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6/25/201650 High Frequency Emphasis
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6/25/201651 Example of Modified High Pass Filtering
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6/25/201652 Homomorphic Filtering
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6/25/201653 Homomorphic Filtering
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6/25/201654 Homomorphic Filtering
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6/25/201655 Homomorphic Filtering
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6/25/201656 Homomorphic Filtering (Example)
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6/25/201657 Basic Filters And scaling rest of values.
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6/25/201658 Example (Notch Function)
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6/25/201659 Properties of Fourier Transform
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6/25/201660 Implementation/Optimization of Fourier Transform First multiply the factor (-1) (x+y) to the original function f(x,y) to shift the origin in DFT to center of the image. Find Fourier transform by decomposing into 2-D function into 1-D transformations. Inverse DFT can be computed using the forward DFT algorithm with slight modification. Optimization of Fourier transform – Brute Force method (decomposition into 1-D Fourier transform) – Fast Fourier Transform (FFT)
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6/25/201661 Implementation/Optimization of Fourier Transform
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6/25/201662 Comparison of Number of Operations for DFT Techniques
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6/25/201663 Need of Padding Due to Symmetrical Properties of DFT
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6/25/201664 Need of Padding Due to Symmetrical Properties of DFT To overcome this problem sue periodicity of DFT Extended/padded functions are used, given by (in 1-D)
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6/25/201665 Need of Padding Due to Symmetrical Properties of DFT
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6/25/201666 Need of Padding Due to Symmetrical Properties of DFT
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6/25/201667 Need of Padding Due to Symmetrical Properties of DFT
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6/25/201668 Padding During Filtering in Frequency Domain
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