Lecture 2 Intensity Transformation and Spatial Filtering Spatial
- Slides: 97
Lecture 2. Intensity Transformation and Spatial Filtering
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 10/28/2020 2
Spatial Domain Process 10/28/2020 3
Spatial Domain Process 10/28/2020 4
Spatial Domain Process 10/28/2020 5
Some Basic Intensity Transformation Functions 10/28/2020 6
Image Negatives 10/28/2020 7
Example: Image Negatives Small lesion 10/28/2020 8
Log Transformations 10/28/2020 9
Example: Log Transformations 10/28/2020 10
Power-Law (Gamma) Transformations 10/28/2020 11
Example: Gamma Transformations 10/28/2020 12
Example: Gamma Transformations Cathode ray tube (CRT) devices have an intensity-to-voltage response that is a power function, with exponents varying from approximately 1. 8 to 2. 5 10/28/2020 13
Example: Gamma Transformations 10/28/2020 14
Example: Gamma Transformations 10/28/2020 15
Piecewise-Linear Transformations ► Contrast Stretching — Expands the range of intensity levels in an image so that it spans the full intensity range of the recording medium or display device. ► Intensity-level Slicing — Highlighting a specific range of intensities in an image often is of interest. 10/28/2020 16
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Highlight the major blood vessels and study the shape of the flow of the contrast medium (to detect blockages, etc. ) 10/28/2020 Measuring the actual flow of the contrast medium as a function of time in a series of images 18
Bit-plane Slicing 10/28/2020 19
Bit-plane Slicing 10/28/2020 20
Bit-plane Slicing 10/28/2020 21
Histogram Processing ► Histogram Equalization ► Histogram Matching ► Local Histogram Processing ► Using Histogram Statistics for Image Enhancement 10/28/2020 22
Histogram Processing 10/28/2020 23
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Histogram Equalization 10/28/2020 25
Histogram Equalization 10/28/2020 26
Histogram Equalization 10/28/2020 27
Histogram Equalization 10/28/2020 28
Example 10/28/2020 29
Example 10/28/2020 30
Histogram Equalization 10/28/2020 31
Example: Histogram Equalization 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 ps(sk) for each sk. 10/28/2020 32
Example: Histogram Equalization 10/28/2020 33
Example: Histogram Equalization 10/28/2020 34
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Figure 3. 22 (a) Image from Phoenix Lander. (b) Result of histogram equalization. (c) Histogram of image (a). (d) Histogram of image (b). (Original image courtesy of NASA. )
Question Is histogram equalization always good? No 10/28/2020 38
Histogram Matching Histogram matching (histogram specification) — generate a processed image that has a specified histogram 10/28/2020 39
Histogram Matching 10/28/2020 40
Histogram Matching: Procedure ► Obtain pr(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 10/28/2020 41
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 10/28/2020 42
Histogram Matching: Example Find the histogram equalization transformation for the input image Find the histogram equalization transformation for the specified histogram The transformation function 10/28/2020 43
Histogram Matching: Discrete Cases ► Obtain pr(rj) from the input image and then obtain the values of sk, round the value to the integer range [0, L-1]. ► Use the specified PDF and obtain the transformation function G(zq), round the value to the integer range [0, L-1]. ► Mapping from sk to zq 10/28/2020 44
Example: Histogram Matching 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. 10/28/2020 45
Example: Histogram Matching Obtain the scaled histogram-equalized values, Compute all the values of the transformation function G, 10/28/2020 46
Example: Histogram Matching 10/28/2020 47
Example: Histogram Matching Obtain the scaled histogram-equalized values, Compute all the values of the transformation function G, s 0 s 2 s 1 s 3 s 4 s 5 s 6 s 7 10/28/2020 48
Example: Histogram Matching 10/28/2020 49
Example: Histogram Matching 10/28/2020 50
Example: Histogram Matching 10/28/2020 51
Example: Histogram Matching 10/28/2020 52
Example: Histogram Matching 10/28/2020 53
Example: Histogram Matching 10/28/2020 54
Figure 3. 24 (a) An image, and (b) its histogram.
Figure 3. 25 (a) Histogram equalization transformation obtained using the histogram in Fig. 3. 24(b). (b) Histogram equalized image. (c) Histogram of equalized image.
Figure 3. 26 Histogram specification. (a) Specified histogram. (b) Transformation labeled (1), labeled (2). (c) Result of histogram specification. (d) and Histogram of image (c).
Local Histogram Processing 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 10/28/2020 58
Local Histogram Processing: Example 10/28/2020 59
Figure 3. 33 (a) Original image. (b) Result of local enhancement based on local histogram statistics. Compare (b) with Fig. 3. 32(c).
Using Histogram Statistics for Image Enhancement Average Intensity Variance 10/28/2020 61
Using Histogram Statistics for Image Enhancement 10/28/2020 62
Using Histogram Statistics for Image Enhancement: Example 10/28/2020 63
Spatial Filtering A spatial filter consists of (a) a neighborhood, and (b) a predefined operation Linear spatial filtering of an image of size Mx. N with a filter of size mxn is given by the expression 10/28/2020 64
Spatial Filtering 10/28/2020 65
Spatial Correlation 10/28/2020 66
Spatial Convolution 10/28/2020 67
Figure 3. 35 Illustration of 1 -D correlation and convolution of a kernel, w, with a function f consisting of a discrete unit impulse. Note that correlation and convolution are functions of the variable x, which acts to displace one function with respect to the other. For the extended correlation and convolution results, the starting configuration places the rightmost element of the kernel to be coincident with the origin of f. Additional padding must be used.
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Figure 3. 58 Transfer functions of ideal 1 -D filters in the frequency domain (u denotes frequency). (a) Lowpass filter. (b) Highpass filter. (c) Bandreject filter. (d) Bandpass filter. (As before, we show only positive frequencies for simplicity. )
Table 3. 7 Summary of the four principal spatial filter types expressed in terms of lowpass filters. The centers of the unit impulse and the filter kernels coincide.
Smoothing Spatial Filters 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. 10/28/2020 72
Spatial Smoothing Linear Filters 10/28/2020 73
Two Smoothing Averaging Filter Masks 10/28/2020 74
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Example: Gross Representation of Objects 10/28/2020 76
Order-statistic (Nonlinear) Filters — 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 10/28/2020 77
Example: Use of Median Filtering for Noise Reduction 10/28/2020 78
Sharpening Spatial Filters ► Foundation ► Laplacian Operator ► Unsharp Masking and Highboost Filtering ► 10/28/2020 Using First-Order Derivatives for Nonlinear Image Sharpening — The Gradient 79
Sharpening Spatial Filters: Foundation ► The first-order derivative of a one-dimensional function f(x) is the difference ► The second-order derivative of f(x) as the difference 10/28/2020 80
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Sharpening Spatial Filters: Laplace Operator The second-order isotropic derivative operator is the Laplacian for a function (image) f(x, y) 10/28/2020 82
Sharpening Spatial Filters: Laplace Operator 10/28/2020 83
Sharpening Spatial Filters: Laplace Operator Image sharpening in the way of using the Laplacian: 10/28/2020 84
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Unsharp Masking and Highboost Filtering ► 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 10/28/2020 86
Unsharp Masking and Highboost Filtering 10/28/2020 87
Unsharp Masking: Demo 10/28/2020 88
Figure 3. 55 (a) Unretouched “soft-tone” digital image of size (b) Image blurred using a Gaussian lowpass filter with σ = 5. (c) Mask. (d) Result of unsharp masking using Eq. (3 -65) with k = 1. (e) and (f) Results of highboost filtering with k = 2 and k = 3, respectively.
Unsharp Masking and Highboost Filtering: Example 10/28/2020 90
Image Sharpening based on First-Order Derivatives Gradient Image 10/28/2020 91
Image Sharpening based on First-Order Derivatives z 1 z 2 z 3 z 4 z 5 z 6 z 7 z 8 z 9 10/28/2020 92
Image Sharpening based on First-Order Derivatives z 1 z 2 z 3 z 4 z 5 z 6 z 7 z 8 z 9 10/28/2020 93
Image Sharpening based on First-Order Derivatives 10/28/2020 94
Example 10/28/2020 95
Example: Combining Spatial Enhancement Methods Goal: Enhance the image by sharpening it and by bringing out more of the skeletal detail 10/28/2020 96
Example: Combining Spatial Enhancement Methods Goal: Enhance the image by sharpening it and by bringing out more of the skeletal detail 10/28/2020 97
- Intensity transformations and spatial filtering
- Some basic intensity transformation functions
- Intensity transformation and spatial filtering
- Intensity transformations and spatial filtering
- Intensity transformations and spatial filtering
- Intensity transformations and spatial filtering
- Ingress filtering vs egress filtering
- Abbe imaging and spatial filtering experiment
- Spatial filtering in digital image processing
- Contra harmonic mean filter
- Spatial filtering
- Image processing matlab
- Spatial filtering
- Combining spatial enhancement methods
- Restoration in the presence of noise only-spatial filtering
- Spatial filtering matlab
- Intensity transformation in digital image processing
- Hsi color wheel
- Intensity transformation in digital image processing
- 01:640:244 lecture notes - lecture 15: plat, idah, farad
- Spatial data vs non spatial data
- Spatial data transformation
- Collaborative filtering pros and cons
- Packet filter firewall definition
- Risk ranking and filtering
- 2^x=256
- Microsoft windows filtering platform hyper-v
- Collaborative filtering medium
- Knapp's model of relational development
- Stateless packet filtering
- Application proxy filtering
- Linear filtering
- Linear convolution using dft
- Fwpm_filter0
- Constrained least squares filtering
- Competitive filtering
- Matched filtering gravitational waves
- Linear filtering citra
- Theory of filtration
- Filtering mode
- Perceptron-based prefetch filtering
- Band pass filtering in biomedical instrumentation
- Content filtering trusts
- Recursive bilateral filtering
- Grating couplers wikipedia
- Linear filtering
- Association rules vs collaborative filtering
- Post filtering in computer graphics
- Ofsted web filtering
- Safe internet service
- Caobin
- Contoh packet filtering firewall
- Image filtering
- Homomorphic filtering block diagram
- Yehuda koren
- Hrnn recommendation
- Particle filtering
- Filtering self-rescue respirator
- Frequency filtering
- Socks protocol
- Frequency filtering
- Activated carbon filter
- Frequency filtering
- Filtering organizational behavior
- Neighborhood processing
- Collaborative filtering with temporal dynamics
- Post filtering in computer graphics
- Bwhitmiss
- Adverd of place
- Sound intensity and resonance
- Maxwell's equations
- Pressure intensity formula
- Poynting vector and intensity
- Poynting vector and intensity
- Factors affecting width and intensity of spectral lines
- Fitness components
- Hue value intensity
- Hsi color wheel
- Equation for electric field intensity
- An almond or lens-shaped cloud which appears stationary
- Supports intensity scale rating key
- Limitations of lambert beer law
- Radiation intensity of antenna
- Earthquake intensity depends primarily on the height of
- Rir scale
- A literary work in which special intensity
- A literary work in which special intensity is
- Low intensity vibration device
- How to calculate wavelength of light
- Gray level slicing in image processing
- Grading of murmurs
- Extensive culture
- Electric field intensity formula
- Ec 6602
- Digital image processing gonzalez
- Color intensity scale
- Color intensity scale
- Distribution intensity meaning