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CS489-02 & CS589-02 Multimedia Processing Lecture 2. Intensity Transformation and Spatial Filtering Spring 2009

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Spatial Domain vs. Transform Domain Spatial domain Image plane itself, directly process the intensity values of the image plane Transform domain Process the transform coefficients, not directly process the intensity values of the image plane 4/27/20152

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Spatial Domain Process 4/27/20153

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Spatial Domain Process 4/27/20154

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Spatial Domain Process 4/27/20155

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Some Basic Intensity Transformation Functions 4/27/20156

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Image Negatives 4/27/20157

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Example: Image Negatives 4/27/20158 Small lesion

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Log Transformations 4/27/20159

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Example: Log Transformations 4/27/201510

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Power-Law (Gamma) Transformations 4/27/201511

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Example: Gamma Transformations 4/27/201512

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Example: Gamma Transformations 4/27/201513

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Piecewise-Linear Transformations Contrast Stretching — Expands the range of intensity levels in an image ― spans the full intensity range of the recording medium Intensity-level Slicing — Highlights a specific range of intensities in an image 4/27/201514

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4/27/201516 Highlight the major blood vessels and study the shape of the flow of the contrast medium (to detect blockages, etc.) Measuring the actual flow of the contrast medium as a function of time in a series of images

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Bit-plane Slicing 4/27/201517

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Example 4/27/201518

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Example 4/27/201519

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Histogram Processing Histogram Equalization Histogram Matching Local Histogram Processing Using Histogram Statistics for Image Enhancement 4/27/201520

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Histogram Processing 4/27/201521

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Histogram Equalization 4/27/201523

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Histogram Equalization 4/27/201524

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Histogram Equalization 4/27/201525

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Histogram Equalization 4/27/201526

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Example 4/27/201527

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Example 4/27/201528

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Histogram Equalization 4/27/201529

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Example: Histogram Equalization 4/27/201530 Suppose that a 3-bit image (L=8) of size 64 × 64 pixels (MN = 4096) has the intensity distribution shown in following table. Get the histogram equalization transformation function and give the p s (s k ) for each s k.

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Example: Histogram Equalization 4/27/201531

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Example: Histogram Equalization 4/27/201532

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Question Is histogram equalization always good? No 4/27/201535

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Histogram Matching Histogram matching (histogram specification) —A processed image has a specified histogram 4/27/201536

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Histogram Matching 4/27/201537

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Histogram Matching: Procedure Obtain p r (r) from the input image and then obtain the values of s Use the specified PDF and obtain the transformation function G(z) Mapping from s to z 4/27/201538

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Histogram Matching: Example Assuming continuous intensity values, suppose that an image has the intensity PDF Find the transformation function that will produce an image whose intensity PDF is 4/27/201539

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Histogram Matching: Example Find the histogram equalization transformation for the input image Find the histogram equalization transformation for the specified histogram The transformation function 4/27/201540

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Histogram Matching: Discrete Cases Obtain p r (r j ) from the input image and then obtain the values of s k, round the value to the integer range [0, L- 1]. Use the specified PDF and obtain the transformation function G(z q ), round the value to the integer range [0, L-1]. Mapping from s k to z q 4/27/201541

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Example: Histogram Matching 4/27/201542 Suppose that a 3-bit image (L=8) of size 64 × 64 pixels (MN = 4096) has the intensity distribution shown in the following table (on the left). Get the histogram transformation function and make the output image with the specified histogram, listed in the table on the right.

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Example: Histogram Matching 4/27/201543 Obtain the scaled histogram-equalized values, Compute all the values of the transformation function G,

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Example: Histogram Matching 4/27/201544

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Example: Histogram Matching 4/27/201545 Obtain the scaled histogram-equalized values, Compute all the values of the transformation function G, s0s0 s2s2 s3s3 s5s5 s6s6 s7s7 s1s1 s4s4

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Example: Histogram Matching 4/27/201546

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Example: Histogram Matching 4/27/201547

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Example: Histogram Matching 4/27/201548

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Example: Histogram Matching 4/27/201549

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Local Histogram Processing 4/27/201551 Define a neighborhood and move its center from pixel to pixel At each location, the histogram of the points in the neighborhood is computed. Either histogram equalization or histogram specification transformation function is obtained Map the intensity of the pixel centered in the neighborhood Move to the next location and repeat the procedure

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Local Histogram Processing: Example 4/27/201552

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Using Histogram Statistics for Image Enhancement 4/27/201553 Average Intensity Variance

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Using Histogram Statistics for Image Enhancement 4/27/201554

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Using Histogram Statistics for Image Enhancement: Example 4/27/201555

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Spatial Filtering 4/27/201556 A spatial filter consists of (a) a neighborhood, and (b) a predefined operation Linear spatial filtering of an image of size MxN with a filter of size mxn is given by the expression

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Spatial Filtering 4/27/201557

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Spatial Correlation 4/27/201558

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Spatial Convolution 4/27/201559

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Smoothing Spatial Filters 4/27/201561 Smoothing filters are used for blurring and for noise reduction Blurring is used in removal of small details and bridging of small gaps in lines or curves Smoothing spatial filters include linear filters and nonlinear filters.

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Spatial Smoothing Linear Filters 4/27/201562

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Two Smoothing Averaging Filter Masks 4/27/201563

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Example: Gross Representation of Objects 4/27/201565

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Order-statistic (Nonlinear) Filters 4/27/201566 — Nonlinear — Based on ordering (ranking) the pixels contained in the filter mask — Replacing the value of the center pixel with the value determined by the ranking result E.g., median filter, max filter, min filter

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Example: Use of Median Filtering for Noise Reduction 4/27/201567

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Sharpening Spatial Filters 4/27/201568 ► Foundation ► Laplacian Operator ► Unsharp Masking and Highboost Filtering ► Using First-Order Derivatives for Nonlinear Image Sharpening

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Sharpening Spatial Filters: Foundation 4/27/201569 ► The first-order derivative of a one-dimensional function f(x) is the difference ► The second-order derivative of f(x) as the difference

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Sharpening Spatial Filters: Laplace Operator 4/27/201571 The second-order isotropic derivative operator is the Laplacian for a function (image) f(x,y)

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Sharpening Spatial Filters: Laplace Operator 4/27/201572

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Sharpening Spatial Filters: Laplace Operator 4/27/201573 Image sharpening in the way of using the Laplacian:

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Unsharp Masking and Highboost Filtering 4/27/201575 ► Unsharp masking Sharpen images consists of subtracting an unsharp (smoothed) version of an image from the original image e.g., printing and publishing industry ► Steps 1. Blur the original image 2. Subtract the blurred image from the original 3. Add the mask to the original

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Unsharp Masking and Highboost Filtering 4/27/201576

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Unsharp Masking: Demo 4/27/201577

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Unsharp Masking and Highboost Filtering: Example 4/27/201578

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Image Sharpening based on First-Order Derivatives 4/27/201579 Gradient Image

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Image Sharpening based on First-Order Derivatives z1z1z1z1 z2z2z2z2 z3z3z3z3 z4z4z4z4 z5z5z5z5 z6z6z6z6 z7z7z7z7 z8z8z8z8 z9z9z9z9 4/27/201580

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Image Sharpening based on First-Order Derivatives z1z1z1z1 z2z2z2z2 z3z3z3z3 z4z4z4z4 z5z5z5z5 z6z6z6z6 z7z7z7z7 z8z8z8z8 z9z9z9z9 4/27/201581

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Image Sharpening based on First-Order Derivatives 4/27/201582

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Example 4/27/201583

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4/27/201584 Example: Combining Spatial Enhancement Methods Goal: Enhance the image by sharpening it and by bringing out more of the skeletal detail

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4/27/201585 Example: Combining Spatial Enhancement Methods Goal: Enhance the image by sharpening it and by bringing out more of the skeletal detail

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