CS & CS Multimedia Processing Lecture 2. Intensity Transformation and Spatial Filtering Spring 2009

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

Spatial Domain Process 4/27/20153

Spatial Domain Process 4/27/20154

Spatial Domain Process 4/27/20155

Some Basic Intensity Transformation Functions 4/27/20156

Image Negatives 4/27/20157

Example: Image Negatives 4/27/20158 Small lesion

Log Transformations 4/27/20159

Example: Log Transformations 4/27/201510

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

Example: Gamma Transformations 4/27/201512

Example: Gamma Transformations 4/27/201513

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

4/27/201515

4/27/ 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

Bit-plane Slicing 4/27/201517

Example 4/27/201518

Example 4/27/201519

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

Histogram Processing 4/27/201521

4/27/201522

Histogram Equalization 4/27/201523

Histogram Equalization 4/27/201524

Histogram Equalization 4/27/201525

Histogram Equalization 4/27/201526

Example 4/27/201527

Example 4/27/201528

Histogram Equalization 4/27/201529

Example: Histogram Equalization 4/27/ 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.

Example: Histogram Equalization 4/27/201531

Example: Histogram Equalization 4/27/201532

4/27/201533

4/27/201534

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

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

Histogram Matching 4/27/201537

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

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

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

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

Example: Histogram Matching 4/27/ 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.

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

Example: Histogram Matching 4/27/201544

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

Example: Histogram Matching 4/27/201546

Example: Histogram Matching 4/27/201547

Example: Histogram Matching 4/27/201548

Example: Histogram Matching 4/27/201549

4/27/201550

Local Histogram Processing 4/27/ 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

Local Histogram Processing: Example 4/27/201552

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

Using Histogram Statistics for Image Enhancement 4/27/201554

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

Spatial Filtering 4/27/ 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

Spatial Filtering 4/27/201557

Spatial Correlation 4/27/201558

Spatial Convolution 4/27/201559

4/27/201560

Smoothing Spatial Filters 4/27/ 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.

Spatial Smoothing Linear Filters 4/27/201562

Two Smoothing Averaging Filter Masks 4/27/201563

4/27/201564

Example: Gross Representation of Objects 4/27/201565

Order-statistic (Nonlinear) Filters 4/27/ — 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

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

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

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

4/27/201570

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

Sharpening Spatial Filters: Laplace Operator 4/27/201572

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

4/27/201574

Unsharp Masking and Highboost Filtering 4/27/ ► 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

Unsharp Masking and Highboost Filtering 4/27/201576

Unsharp Masking: Demo 4/27/201577

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

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

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

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

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

Example 4/27/201583

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

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