The document discusses various techniques for digital image intensity transformations and histogram processing. It begins with an overview of intensity transformations versus geometric transformations. It then covers log transformations, power-law transformations, and piecewise linear transformations in detail. The document also discusses histogram equalization in depth, including its purpose, principles, and specific operations. Additionally, it compares histogram equalization to other enhancement methods like linear stretch and presents examples of when histogram equalization may fail. Finally, the document introduces fundamentals of spatial filtering, including linear spatial filtering operations using different sized box kernels.
This document provides an agenda and overview of topics related to intensity transformations and spatial filtering for image enhancement. It discusses piecewise-linear transformation functions including contrast stretching, intensity-level slicing, and bit-plane slicing. It also covers histogram processing techniques such as histogram equalization, histogram matching, and using histogram statistics. Finally, it outlines fundamentals of spatial filtering including the mechanics of spatial filtering, spatial correlation and convolution, and generating smoothing and sharpening spatial filters.
Here in the ppt a detailed description of Image Enhancement Techniques is given which includes topics like Basic Gray level Transformations,Histogram Processing.
Enhancement using Arithmetic/Logic Operations.
image averaging and image averaging methods.
Piecewise-Linear Transformation Functions
Spatial domain filtering and intensity transformations are techniques used in image processing. Spatial domain refers to the pixels that make up an image. Spatial domain techniques operate directly on pixels by applying operators to pixels and their neighbors. Common operators include averaging, median filtering, and contrast adjustments. Spatial filtering techniques include smoothing to reduce noise and sharpening to enhance edges through differentiation. Intensity transformations map input pixel values to output values using functions like logarithms, power laws, and piecewise linear approximations to modify image contrast and highlight certain intensity ranges.
Study on Contrast Enhancement with the help of Associate Regions Histogram Eq...IJSRD
Histogram equalization is an uncomplicated and extensively used image distinction enhancement technique. The crucial drawback of histogram equalization is it transforms the brightness of the image. To overcome this drawback, different histogram Equalization methods have been projected. These methods protect the brightness on the result image but, do not have a usual look. Therefore this paper is an attempt to bridge the gap and results after the processed Associate regions are collected into one image. The mock-up result explains that the algorithm can not only improve image information successfully but also remain the imaginative image luminance well enough to make it likely to be used in video arrangement directly.
This document discusses various techniques for image enhancement in the spatial domain, including histogram modification, averaging filters, and median filters. Histogram modification techniques like stretching, shrinking, and equalization can increase contrast and enhance an image. Averaging multiple noisy images together reduces noise by decreasing pixel variability. Median filters replace each pixel value with the median value in its neighborhood, which effectively removes salt-and-pepper noise while preserving edges. The document provides examples and equations to demonstrate these different spatial domain enhancement methods.
This document discusses various techniques for image enhancement in the spatial domain, including histogram modification, averaging filters, and median filters. Histogram modification techniques like stretching, shrinking, and equalization can increase contrast and enhance an image. Averaging multiple noisy images together reduces noise by decreasing pixel variability. Median filters replace each pixel value with the median value in its neighborhood, which effectively removes salt-and-pepper noise while preserving edges. The document provides examples and equations to demonstrate these different spatial domain enhancement methods.
1. Histogram modification techniques can be used to enhance color images by performing operations on individual color bands or by first converting to another color space like HSL and modifying the brightness band.
2. Modifying individual color bands can cause unwanted color shifts, so maintaining the original color ratios is important.
3. The most visually important color band, such as the one with highest contrast, is typically selected for histogram equalization or other modifications.
This document provides an agenda and overview of topics related to intensity transformations and spatial filtering for image enhancement. It discusses piecewise-linear transformation functions including contrast stretching, intensity-level slicing, and bit-plane slicing. It also covers histogram processing techniques such as histogram equalization, histogram matching, and using histogram statistics. Finally, it outlines fundamentals of spatial filtering including the mechanics of spatial filtering, spatial correlation and convolution, and generating smoothing and sharpening spatial filters.
Here in the ppt a detailed description of Image Enhancement Techniques is given which includes topics like Basic Gray level Transformations,Histogram Processing.
Enhancement using Arithmetic/Logic Operations.
image averaging and image averaging methods.
Piecewise-Linear Transformation Functions
Spatial domain filtering and intensity transformations are techniques used in image processing. Spatial domain refers to the pixels that make up an image. Spatial domain techniques operate directly on pixels by applying operators to pixels and their neighbors. Common operators include averaging, median filtering, and contrast adjustments. Spatial filtering techniques include smoothing to reduce noise and sharpening to enhance edges through differentiation. Intensity transformations map input pixel values to output values using functions like logarithms, power laws, and piecewise linear approximations to modify image contrast and highlight certain intensity ranges.
Study on Contrast Enhancement with the help of Associate Regions Histogram Eq...IJSRD
Histogram equalization is an uncomplicated and extensively used image distinction enhancement technique. The crucial drawback of histogram equalization is it transforms the brightness of the image. To overcome this drawback, different histogram Equalization methods have been projected. These methods protect the brightness on the result image but, do not have a usual look. Therefore this paper is an attempt to bridge the gap and results after the processed Associate regions are collected into one image. The mock-up result explains that the algorithm can not only improve image information successfully but also remain the imaginative image luminance well enough to make it likely to be used in video arrangement directly.
This document discusses various techniques for image enhancement in the spatial domain, including histogram modification, averaging filters, and median filters. Histogram modification techniques like stretching, shrinking, and equalization can increase contrast and enhance an image. Averaging multiple noisy images together reduces noise by decreasing pixel variability. Median filters replace each pixel value with the median value in its neighborhood, which effectively removes salt-and-pepper noise while preserving edges. The document provides examples and equations to demonstrate these different spatial domain enhancement methods.
This document discusses various techniques for image enhancement in the spatial domain, including histogram modification, averaging filters, and median filters. Histogram modification techniques like stretching, shrinking, and equalization can increase contrast and enhance an image. Averaging multiple noisy images together reduces noise by decreasing pixel variability. Median filters replace each pixel value with the median value in its neighborhood, which effectively removes salt-and-pepper noise while preserving edges. The document provides examples and equations to demonstrate these different spatial domain enhancement methods.
1. Histogram modification techniques can be used to enhance color images by performing operations on individual color bands or by first converting to another color space like HSL and modifying the brightness band.
2. Modifying individual color bands can cause unwanted color shifts, so maintaining the original color ratios is important.
3. The most visually important color band, such as the one with highest contrast, is typically selected for histogram equalization or other modifications.
PERFORMANCE EVALUATION OF DIFFERENT TECHNIQUES FOR TEXTURE CLASSIFICATION cscpconf
This document compares different techniques for texture classification, including wavelet transforms and co-occurrence matrices. It finds that the Haar wavelet technique is the most efficient in terms of time complexity and classification accuracy, except when images are rotated. The co-occurrence matrix method has higher time requirements but excellent classification results, except for rotated images where accuracy is greatly reduced due to its dependence on pixel values. Overall, the Haar wavelet proves to be the best method for texture classification based on the performance assessment parameters of time complexity and classification accuracy.
3 intensity transformations and spatial filtering slidesBHAGYAPRASADBUGGE
This document discusses basics of intensity transformations and spatial filtering of digital images. It covers the following key points:
- Intensity transformations map input pixel intensities to output intensities using an operator T. Common transformations include log, power-law, and piecewise-linear functions.
- Spatial filters operate on neighborhoods of pixels. Linear filters perform averaging or correlation while non-linear filters use ordering like median.
- Basic filters include smoothing to reduce noise, sharpening to enhance edges using Laplacian or unsharp masking, and gradient for edge detection.
- Fuzzy set theory can be applied to intensity transformations by defining membership functions for concepts like dark/bright. It can also be used for spatial filtering by defining
chapter 4 computervision.pdf IT IS ABOUT COMUTER VISIONshesnasuneer
This document discusses various methods of image pre-processing. It describes four categories of pre-processing based on pixel neighborhood size used: pixel brightness transformations, geometric transformations, local neighborhood methods, and global image restoration. It then focuses on pixel brightness transformations like brightness corrections and gray scale transformations. It also covers geometric transformations like rotation and scaling. Finally, it discusses interpolation methods like nearest neighbor, linear, and bicubic used during geometric transformations to assign brightness values.
Image pre-processing involves operations on images to improve image data by suppressing distortions or enhancing features. There are four categories of pre-processing methods based on pixel neighborhood size used: pixel brightness transformations, geometric transformations, local neighborhood methods, and global image restoration. Pre-processing aims to correct degradations by using prior knowledge about the degradation, image acquisition device, or objects in the image. Common pre-processing methods include brightness and geometric transformations as well as brightness interpolation when re-sampling images.
This document discusses image processing and histograms. It covers topics like image restoration, enhancement, and compression. It also discusses representing digital images with matrices and defines spatial and brightness resolution. Finally, it covers image histograms in depth, including defining histograms, properties, types, applications like thresholding and enhancement, and modifications like stretching, shrinking, and sliding histograms. As an example, it shows a histogram for a hypothetical 128x128 pixel image with 8 gray levels.
This document compares three image restoration techniques - Iterated Geometric Harmonics, Markov Random Fields, and Wavelet Decomposition - for removing noise from images. It describes each technique and the process used to test them. Noise was artificially added to images using different noise generation functions. Wavelet Decomposition and Markov Random Fields were then used to detect the noise locations. These noise locations were then used to create versions of the noisy images suitable for reconstruction via Iterated Geometric Harmonics. The reconstructed images were then compared to the original to evaluate the performance of each technique.
COM2304: Intensity Transformation and Spatial Filtering – I (Intensity Transf...Hemantha Kulathilake
At the end of this lesson, you should be able to;
describe spatial domain of the digital image.
recognize the image enhancement techniques.
describe and apply the concept of intensity transformation.
express histograms and histogram processing.
describe image noise.
characterize the types of Noise.
describe concept of image restoration.
This document provides an overview of machine vision techniques for region segmentation. It discusses region-based and boundary-based approaches to image segmentation. Key aspects covered include thresholding techniques, region representation using data structures like the region adjacency graph, and algorithms for region splitting and merging. Automatic threshold selection methods like the p-tile and mode methods are also summarized.
Intensity Transformation and Spatial filteringShajun Nisha
Dr. S. Shajun Nisha discusses intensity transformation and spatial filtering techniques in image processing. Intensity transformation functions modify pixel intensities based on a transformation function. Spatial filtering involves applying an operator over a neighborhood of pixels. Common intensity transformations include contrast stretching and logarithmic transforms. Histogram equalization is also described to improve contrast. Spatial filters include linear filters implemented using imfilter and non-linear filters like median filtering with ordfilt2 and medfilt2. Examples demonstrate applying these techniques to enhance images.
This document discusses intensity transformation and spatial filtering of digital images. It begins by distinguishing between processing images in the spatial domain versus the transform domain. In the spatial domain, pixel intensities are directly modified based on an operator applied to a neighborhood of pixels. Intensity transformations modify pixel values based on an intensity transformation function. Examples of basic intensity transformations discussed include image negatives, log transformations, power-law (gamma) transformations, and piecewise-linear transformations. Histogram processing techniques like histogram equalization, matching, and analysis are also covered.
Linear contrast stretching uniformly expands the intensity values in an image to utilize the full range of available intensities. Histogram equalization spreads out intensity values to improve contrast by effectively stretching the most frequent values. Piecewise linear stretching uses different linear functions to enhance different intensity ranges differently. Logarithmic stretching compresses higher intensity values while expanding lower ones, enhancing dark areas. Contrast stretching techniques aim to improve poor contrast by modifying intensity distributions, but can increase noise and lose original brightness levels.
Digital image processing - Image Enhancement (MATERIAL)Mathankumar S
This document discusses various image enhancement techniques including contrast stretching, compression of dynamic range, histogram equalization, and histogram specification. It provides definitions and explanations of these concepts with examples. Histogram equalization aims to produce a linear histogram to enhance an image, while histogram specification allows specifying a desired output histogram. Local enhancement can be achieved by applying these histogram processing methods over small non-overlapping regions instead of globally to reduce edge effects.
Histograms show the distribution of pixel intensities in an image by counting the number of pixels for each intensity value. Normalized histograms provide an estimate of the probability of each intensity occurring. Histogram equalization transforms the pixel intensity distribution of an image to a uniform distribution in order to increase contrast. It does this by using the cumulative distribution function to map intensities to new output values. Local histogram equalization performs this on neighborhoods within an image to enhance local details. Arithmetic and logical operations can also be used for image enhancement, such as AND, OR, and subtraction between images on a pixel-by-pixel basis.
Setting the lower order bit plane to zero would have the effect of reducing the number of distinct gray levels by half. This would cause the histogram to become more peaked, with more pixels concentrated in fewer bins.
This document discusses GPU-based implementations of bilateral filtering for images. Bilateral filtering smooths images while preserving edges by combining pixel values based on both geometric closeness and photometric similarity. It can be applied to color images in a way that is tuned to human color perception. A naïve bilateral filtering implementation iterates over all pixels, but it is well-suited for parallel GPU implementations due to its iterative and local nature. The document provides mathematical definitions of domain filtering, range filtering, and bilateral filtering, and notes that bilateral filtering combines the benefits of both by enforcing both geometric and photometric locality. It describes using Gaussian functions to implement the filters and discusses parameters for controlling the degree of blurring and edge preservation.
This document discusses techniques for digital image enhancement through histogram modification, including histogram stretching, shrinking, sliding, equalization, and specification. Histogram modification performs gray level mapping to modify image contrast by considering a histogram's shape and spread. Histogram stretching increases contrast by mapping values across the full range, while shrinking decreases contrast by compressing values. Sliding makes images lighter or darker by adding or subtracting from values. Equalization makes histograms as flat as possible to improve contrast, and specification allows interactively defining a target histogram to remap an image's values. These techniques are useful for improving low-contrast or unbalanced images.
How to Interpret Trends in the Kalyan Rajdhani Mix Chart.pdfChart Kalyan
A Mix Chart displays historical data of numbers in a graphical or tabular form. The Kalyan Rajdhani Mix Chart specifically shows the results of a sequence of numbers over different periods.
Fueling AI with Great Data with Airbyte WebinarZilliz
This talk will focus on how to collect data from a variety of sources, leveraging this data for RAG and other GenAI use cases, and finally charting your course to productionalization.
Contenu connexe
Similaire à 2024-master dityv5y65v56u4b6u64u46p 0318-25.pdf
PERFORMANCE EVALUATION OF DIFFERENT TECHNIQUES FOR TEXTURE CLASSIFICATION cscpconf
This document compares different techniques for texture classification, including wavelet transforms and co-occurrence matrices. It finds that the Haar wavelet technique is the most efficient in terms of time complexity and classification accuracy, except when images are rotated. The co-occurrence matrix method has higher time requirements but excellent classification results, except for rotated images where accuracy is greatly reduced due to its dependence on pixel values. Overall, the Haar wavelet proves to be the best method for texture classification based on the performance assessment parameters of time complexity and classification accuracy.
3 intensity transformations and spatial filtering slidesBHAGYAPRASADBUGGE
This document discusses basics of intensity transformations and spatial filtering of digital images. It covers the following key points:
- Intensity transformations map input pixel intensities to output intensities using an operator T. Common transformations include log, power-law, and piecewise-linear functions.
- Spatial filters operate on neighborhoods of pixels. Linear filters perform averaging or correlation while non-linear filters use ordering like median.
- Basic filters include smoothing to reduce noise, sharpening to enhance edges using Laplacian or unsharp masking, and gradient for edge detection.
- Fuzzy set theory can be applied to intensity transformations by defining membership functions for concepts like dark/bright. It can also be used for spatial filtering by defining
chapter 4 computervision.pdf IT IS ABOUT COMUTER VISIONshesnasuneer
This document discusses various methods of image pre-processing. It describes four categories of pre-processing based on pixel neighborhood size used: pixel brightness transformations, geometric transformations, local neighborhood methods, and global image restoration. It then focuses on pixel brightness transformations like brightness corrections and gray scale transformations. It also covers geometric transformations like rotation and scaling. Finally, it discusses interpolation methods like nearest neighbor, linear, and bicubic used during geometric transformations to assign brightness values.
Image pre-processing involves operations on images to improve image data by suppressing distortions or enhancing features. There are four categories of pre-processing methods based on pixel neighborhood size used: pixel brightness transformations, geometric transformations, local neighborhood methods, and global image restoration. Pre-processing aims to correct degradations by using prior knowledge about the degradation, image acquisition device, or objects in the image. Common pre-processing methods include brightness and geometric transformations as well as brightness interpolation when re-sampling images.
This document discusses image processing and histograms. It covers topics like image restoration, enhancement, and compression. It also discusses representing digital images with matrices and defines spatial and brightness resolution. Finally, it covers image histograms in depth, including defining histograms, properties, types, applications like thresholding and enhancement, and modifications like stretching, shrinking, and sliding histograms. As an example, it shows a histogram for a hypothetical 128x128 pixel image with 8 gray levels.
This document compares three image restoration techniques - Iterated Geometric Harmonics, Markov Random Fields, and Wavelet Decomposition - for removing noise from images. It describes each technique and the process used to test them. Noise was artificially added to images using different noise generation functions. Wavelet Decomposition and Markov Random Fields were then used to detect the noise locations. These noise locations were then used to create versions of the noisy images suitable for reconstruction via Iterated Geometric Harmonics. The reconstructed images were then compared to the original to evaluate the performance of each technique.
COM2304: Intensity Transformation and Spatial Filtering – I (Intensity Transf...Hemantha Kulathilake
At the end of this lesson, you should be able to;
describe spatial domain of the digital image.
recognize the image enhancement techniques.
describe and apply the concept of intensity transformation.
express histograms and histogram processing.
describe image noise.
characterize the types of Noise.
describe concept of image restoration.
This document provides an overview of machine vision techniques for region segmentation. It discusses region-based and boundary-based approaches to image segmentation. Key aspects covered include thresholding techniques, region representation using data structures like the region adjacency graph, and algorithms for region splitting and merging. Automatic threshold selection methods like the p-tile and mode methods are also summarized.
Intensity Transformation and Spatial filteringShajun Nisha
Dr. S. Shajun Nisha discusses intensity transformation and spatial filtering techniques in image processing. Intensity transformation functions modify pixel intensities based on a transformation function. Spatial filtering involves applying an operator over a neighborhood of pixels. Common intensity transformations include contrast stretching and logarithmic transforms. Histogram equalization is also described to improve contrast. Spatial filters include linear filters implemented using imfilter and non-linear filters like median filtering with ordfilt2 and medfilt2. Examples demonstrate applying these techniques to enhance images.
This document discusses intensity transformation and spatial filtering of digital images. It begins by distinguishing between processing images in the spatial domain versus the transform domain. In the spatial domain, pixel intensities are directly modified based on an operator applied to a neighborhood of pixels. Intensity transformations modify pixel values based on an intensity transformation function. Examples of basic intensity transformations discussed include image negatives, log transformations, power-law (gamma) transformations, and piecewise-linear transformations. Histogram processing techniques like histogram equalization, matching, and analysis are also covered.
Linear contrast stretching uniformly expands the intensity values in an image to utilize the full range of available intensities. Histogram equalization spreads out intensity values to improve contrast by effectively stretching the most frequent values. Piecewise linear stretching uses different linear functions to enhance different intensity ranges differently. Logarithmic stretching compresses higher intensity values while expanding lower ones, enhancing dark areas. Contrast stretching techniques aim to improve poor contrast by modifying intensity distributions, but can increase noise and lose original brightness levels.
Digital image processing - Image Enhancement (MATERIAL)Mathankumar S
This document discusses various image enhancement techniques including contrast stretching, compression of dynamic range, histogram equalization, and histogram specification. It provides definitions and explanations of these concepts with examples. Histogram equalization aims to produce a linear histogram to enhance an image, while histogram specification allows specifying a desired output histogram. Local enhancement can be achieved by applying these histogram processing methods over small non-overlapping regions instead of globally to reduce edge effects.
Histograms show the distribution of pixel intensities in an image by counting the number of pixels for each intensity value. Normalized histograms provide an estimate of the probability of each intensity occurring. Histogram equalization transforms the pixel intensity distribution of an image to a uniform distribution in order to increase contrast. It does this by using the cumulative distribution function to map intensities to new output values. Local histogram equalization performs this on neighborhoods within an image to enhance local details. Arithmetic and logical operations can also be used for image enhancement, such as AND, OR, and subtraction between images on a pixel-by-pixel basis.
Setting the lower order bit plane to zero would have the effect of reducing the number of distinct gray levels by half. This would cause the histogram to become more peaked, with more pixels concentrated in fewer bins.
This document discusses GPU-based implementations of bilateral filtering for images. Bilateral filtering smooths images while preserving edges by combining pixel values based on both geometric closeness and photometric similarity. It can be applied to color images in a way that is tuned to human color perception. A naïve bilateral filtering implementation iterates over all pixels, but it is well-suited for parallel GPU implementations due to its iterative and local nature. The document provides mathematical definitions of domain filtering, range filtering, and bilateral filtering, and notes that bilateral filtering combines the benefits of both by enforcing both geometric and photometric locality. It describes using Gaussian functions to implement the filters and discusses parameters for controlling the degree of blurring and edge preservation.
This document discusses techniques for digital image enhancement through histogram modification, including histogram stretching, shrinking, sliding, equalization, and specification. Histogram modification performs gray level mapping to modify image contrast by considering a histogram's shape and spread. Histogram stretching increases contrast by mapping values across the full range, while shrinking decreases contrast by compressing values. Sliding makes images lighter or darker by adding or subtracting from values. Equalization makes histograms as flat as possible to improve contrast, and specification allows interactively defining a target histogram to remap an image's values. These techniques are useful for improving low-contrast or unbalanced images.
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How to Interpret Trends in the Kalyan Rajdhani Mix Chart.pdfChart Kalyan
A Mix Chart displays historical data of numbers in a graphical or tabular form. The Kalyan Rajdhani Mix Chart specifically shows the results of a sequence of numbers over different periods.
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This talk will focus on how to collect data from a variety of sources, leveraging this data for RAG and other GenAI use cases, and finally charting your course to productionalization.
Have you ever been confused by the myriad of choices offered by AWS for hosting a website or an API?
Lambda, Elastic Beanstalk, Lightsail, Amplify, S3 (and more!) can each host websites + APIs. But which one should we choose?
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The original Czech 🇨🇿 version of the presentation can be found here: https://www.slideshare.net/slideshow/hlavni-novinky-souvisejici-s-ccs-tsi-2023-2023-1695/269688092 .
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5th Power Grid Model Meet-up
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Power Grid Model
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For the full video of this presentation, please visit: https://www.edge-ai-vision.com/2024/06/temporal-event-neural-networks-a-more-efficient-alternative-to-the-transformer-a-presentation-from-brainchip/
Chris Jones, Director of Product Management at BrainChip , presents the “Temporal Event Neural Networks: A More Efficient Alternative to the Transformer” tutorial at the May 2024 Embedded Vision Summit.
The expansion of AI services necessitates enhanced computational capabilities on edge devices. Temporal Event Neural Networks (TENNs), developed by BrainChip, represent a novel and highly efficient state-space network. TENNs demonstrate exceptional proficiency in handling multi-dimensional streaming data, facilitating advancements in object detection, action recognition, speech enhancement and language model/sequence generation. Through the utilization of polynomial-based continuous convolutions, TENNs streamline models, expedite training processes and significantly diminish memory requirements, achieving notable reductions of up to 50x in parameters and 5,000x in energy consumption compared to prevailing methodologies like transformers.
Integration with BrainChip’s Akida neuromorphic hardware IP further enhances TENNs’ capabilities, enabling the realization of highly capable, portable and passively cooled edge devices. This presentation delves into the technical innovations underlying TENNs, presents real-world benchmarks, and elucidates how this cutting-edge approach is positioned to revolutionize edge AI across diverse applications.
3. 3.1 Review
Geometric transformation vs Intensity transformation
Spatial domain
The value at the
corresponding position
of the image does not
change, but the pixel
position changes
The pixel position in
the image does not
change, but the value
changes
5. 3.2 The key points and difficulties of this class
Be familiar with the principal techniques used for intensity transformations
Learn basic log transformations and power-law transformations
Understand the realization process of the two transformations
15. Discussion
What are the advantages and disadvantages
of these transformations?
Trial and error
A certain basis
intensity distribution
peaks and valleys
Discuss the pros and cons of these methods:
Reasonable or not
Automatic degree
Robustness
16. 3.3 Intensity Transformation
Trial and error
A certain basis
intensity distribution
Discussion
You may ask, to achieve this result, I can directly use PS, what is the meaning of
learning these transformations?
We know how to use PS to achieve effects more
quickly and accurately without a lot of trying
We can perform different transformations in
different regions
We can perform different transformations on
different grayscale ranges
20. 3.2 Histogram Processing
Image gray histogram
No spatial information involved
The same histogram distribution may
correspond to different images
Information additivity
Related to the amount of information
21. Describe image with gray histogram
The grayscale of the image is concentrated
in the brighter area, and a considerable part
of them are concentrated in the part close to
1, resulting in overexposure of the image
The pixel distribution in the image
is “polarized”, resulting in the loss
of image details
The distribution of image histogram is related to the quality of image to some extent
3.4 Histogram equalization
22. A “clear” image
The histogram reflects the clarity of the image, when it is evenly distributed, the image is “clearer”
Histogram
equalization
each gray level should have a
certain number of gray values
Different objects should have
distinguishable grayscale variations
3.4 Histogram equalization
24. original image target image
For a random
distribution transform
to uniform distribution
original histogram
target histogram
L r s
S=T(r)
𝑝𝑝(𝑟𝑟𝑖𝑖) ≠ 𝑝𝑝(𝑟𝑟𝑗𝑗) 𝑝𝑝(𝑠𝑠𝑖𝑖) = 𝑝𝑝(𝑠𝑠𝑗𝑗)
𝑃𝑃 𝑇𝑇 𝑟𝑟𝑖𝑖 < 𝑠𝑠 < 𝑇𝑇 𝑟𝑟𝑗𝑗 =
∫𝑟𝑟𝒊𝒊
𝑟𝑟𝑗𝑗
𝑝𝑝 𝑟𝑟 𝑑𝑑𝑑𝑑 =
1
𝐿𝐿−1
× (𝑇𝑇 𝑟𝑟𝒋𝒋 − 𝑇𝑇 𝑟𝑟𝑖𝑖 )
𝑖𝑖𝑖𝑖 𝑟𝑟𝑗𝑗 > 𝑟𝑟𝑖𝑖, 𝑠𝑠𝑗𝑗> 𝑠𝑠𝑖𝑖
a b
𝑃𝑃(𝑎𝑎 ≤ 𝑠𝑠 ≤ 𝑏𝑏)
𝑠𝑠 = 𝑇𝑇 𝑟𝑟 = (𝐿𝐿 − 1) �
0
𝑟𝑟
𝑝𝑝(𝑟𝑟) 𝑑𝑑𝑑𝑑
3.4 Histogram equalization
25. k refers to the different gray values in the original image
P(k) corresponds to the frequency of the value in all pixels of the original image
Histogram
( normalized )
Unique Pixel of
𝒇𝒇(𝒙𝒙,𝒚𝒚)
𝒓𝒓𝟏𝟏 𝒓𝒓𝟐𝟐 … 𝒓𝒓𝒋𝒋 … 𝒓𝒓𝒌𝒌
frequency of
𝒇𝒇(𝒙𝒙,𝒚𝒚)
𝒑𝒑𝟏𝟏 𝒑𝒑𝟐𝟐 … 𝒑𝒑𝒋𝒋 … 𝒑𝒑𝒌𝒌
Pixel of
𝒈𝒈(𝒙𝒙, 𝒚𝒚)/(𝑳𝑳 − 𝟏𝟏)
𝒑𝒑𝟏𝟏 𝒑𝒑𝟏𝟏+𝒑𝒑𝟐𝟐 … +…+𝒑𝒑𝒋𝒋 … +…+𝒑𝒑𝒌𝒌
Discrete situation: Gray value quantification The quantization value closest to its
value is taken as the final gray value
𝑠𝑠 = 𝑇𝑇 𝑟𝑟 = (𝐿𝐿 − 1) �
0
𝑟𝑟
𝑝𝑝(𝑟𝑟) 𝑑𝑑𝑑𝑑
3.4 Histogram equalization
36. 1. After histogram equalization, how does the gray level of
the new imagechange?
2. What are the advantages and disadvantages of gray
histogram equalization? (Human intervention required;
reversible; Is it valid in all cases?)
Purpose of Histogram Equalization
Principle of Histogram Equalization
Specific operation of histogram equalization
3.4 Histogram equalization
Summary and Discussion
39. 3.5 Histogram Processing
Linear stretch Histogram equalization
Transformation
function
Comparisonof
image
enhancement
Simple transformation
Can be transformed
back to the original
image
Need to manually set
parameters
Poor generality
Less information loss
Automated, no
parameters required
Unable to restore
Poor generality
42. Some improvement methods
3.5 Histogram Processing
LOCAL HISTOGRAM PROCESSING
Some differences and consistency in the
local area need to be preserved, but they
are often destroyed because the global
calculated value is obviously different from
the local calculated value.
p.150-153
45. Histogram equalization where we take any histogram, any pixel distribution, and
we match it to something which is as uniform as possible.
3.5 Histogram Processing
𝒇𝒇(𝒙𝒙,𝒚𝒚)
Input
image
𝒈𝒈(𝒙𝒙, 𝒚𝒚)
Target
image
𝑠𝑠 = 𝑇𝑇 𝑟𝑟 = �
0
𝑟𝑟
𝑝𝑝𝑟𝑟(𝑢𝑢) 𝑑𝑑𝑑𝑑
𝑠𝑠 = 𝑇𝑇 z = �
0
𝑟𝑟
𝑝𝑝𝑧𝑧(𝑣𝑣) 𝑑𝑑𝑑𝑑
Histogram matching (specification)
46. 3.5 Histogram Processing
Histogram matching (specification)
Just by doing the histogram equalizations, we can match any two desired distributions
Step1: Compute the histogram of the input image r, and do histogram equalization to
get the histogram-equalized image s1.
Step2: Compute the histogram of the target image z, and do histogram equalization
to get the histogram-equalized image s2.
Step3: For every value of s1, use the stored values of s2 from Step 2 to find the
corresponding value closest to s1 . Store these mappings from s1 to z
Step4: For every value of the image r, let the {𝑟𝑟𝑘𝑘} to be {𝑧𝑧𝑘𝑘
′
} ,by using the mappings
found in Step 3 to get the histogram-specified image.
47. The expressions of spatial domain processing
neighborhoodis of size 1 × 1
The function T can be linear or non-linear,
new gray value can be obtained by transforming
the original pixel value, or it can be obtained by
transforming the neighborhoodpixels.
48. 3.6 Fundamentals of Spatial Filtering
If a pixel value in an
image is lost (or affected
by noise), can we use the
information in other
place to estimate its
value?
It can be approximately equal to the
average of all values of the entire image
It can be approximately given by the
average of several nearby pixel values
The value of each pixel changes by
globally
or
locally Related to its location
49. Spatial filtering modifies an image by
replacing the value of each pixel by a
function of the values of the pixel and its
neighbors.
linear spatial filter
nonlinear spatial filter
𝑌𝑌 = 𝑊𝑊𝑊𝑊 + 𝑏𝑏
3.6 Fundamentals of Spatial Filtering
50. The mechanics of linear spatial
filtering
A linear spatial filter performs a sum-of-
products operation between an image f
and a filter kernel w
kernel :
an array ;
size defines the neighborhood of operation;
coefficients determine the nature of the filter;
also can be called mask, template, window
一种特征提取器
3.6 Fundamentals of Spatial Filtering
51. The mechanics of linear spatial filtering
The size of the kernel is odd, because we
must ensure that the current point we are
dealing with is in the exact center
m=2a+1; n=2b+1
3.6 Fundamentals of Spatial Filtering
52. 3.6 Fundamentals of Spatial Filtering
The mechanics of linear spatial filtering
with box kernels
of sizes 3 × 3,
11 × 11,
and 21 × 21
the larger the neighborhood, the
more pixels we are averaging
53. 3.6 Fundamentals of Spatial Filtering
Spatial correlation and convolution
Correlationconsists of moving the
center of a kernel over an image, and
computing the sum of products at each
location.
VS
spatial convolution are the same,
except that the correlation kernel is
rotated by 180°
when the values of a kernel are symmetricaboutits center, correlationand convolutionyield sameresult
54. 3.6 Fundamentals of Spatial Filtering
We can define correlation and convolution
so that every element of w(instead of just
its center) visits every pixel in f. This
requires that the starting configuration be
such that the right, lower corner of the kernel
coincides with the origin of the image.
the size of the resulting full correlation or
convolution array will be of size(by padding)
Sv ×S h :
55. 3.6 Fundamentals of Spatial Filtering
Spatial correlation and convolution
“convolving a kernel with an image” often is used to denote the sliding, sum-of-products process
Sometimes an image is filtered (i.e., convolved) sequentially, multistage filtering can be done in a
single filtering operation,
These convolution kernels can be combined and of course can be separated
57. 3.7 Smoothing (Lowpass) Spatial Filters
Average kernel
Becauserandomnoisetypicallyconsistsof sharp transitionsin intensity, an obviousapplicationof
smoothingis noisereduction.
The differencebetween each pixeland its surroundingpixels will be smaller than theoriginalones,
so smoothingfiltercan be used to smooththe imageand remove somefalsecontours.
BOX FILTER KERNELS
Smoothing is used to reduce irrelevantdetailin an image
The kernel should be normalized
with box kernels
of sizes 3 × 3,
11 × 11,
and 21 × 21
59. 3.7 Smoothing (Lowpass) Spatial Filters
Average kernel
LOWPASS GAUSSIAN FILTER KERNELS
circularlysymmetric(also
called isotropic)kernel
Distances from
the center for
various sizes of
square kernels.
圆形对称(也称为各向同性)核
60. 3.7 Smoothing (Lowpass) Spatial Filters
Average kernel
LOWPASS GAUSSIAN FILTER KERNELS
K = 1
𝜎𝜎 = 1
如果所有内核都是高斯,我们可以
在表中使用结果来计算复合内核的
标准偏差(并定义它),而无需实
际执行所有内核的卷积。
If all kernels are Gaussian, we can use the
composite kernel (and define it), without actually
performing the convolution of all kernels.
61. 3.7 Smoothing (Lowpass) Spatial Filters
Average kernel
kernel of size 21 × 21,
standard deviations 3.5
kernel of size 43 × 43,
standard deviations 3.5
box kernels
of sizes 11 × 11,
21 × 21
Comparison
62. 3.7 Smoothing (Lowpass) Spatial Filters
Average kernel Comparison
with a box kernel of size 71 × 71
Gaussian kernel of size 151
× 151, with K = 1 and 𝜎𝜎= 25
• box filter producedlinearsmoothing, with the transitionfrom blackto whitehavingthe shapeof a ramp
• the Gaussianfilter yieldedsignificantlysmoother results aroundthe edge transitions
63. 3.7 Smoothing (Lowpass) Spatial Filters
Applications
Using lowpass filtering and thresholding for region extraction
2566 × 2758 Hubble Telescope
image
Result of lowpass filtering
with a Gaussian kernel
size 151 × 151, 𝜎𝜎 = 25
Result of thresholding the filtered
image
Average kernel
64. 3.7 Smoothing (Lowpass) Spatial Filters
Applications
Shading correction using lowpass filtering
Lowpass filtering is a rugged, simple
method for estimating shading patterns
512 × 512 Gaussian kernel (four
times the size of squares), K = 1, and
𝜎𝜎= 128 (equal to the size of squares)
Average kernel
65. 3.7 Smoothing (Lowpass) Spatial Filters
Order-statistic (nonlinear) filters
response is based on ordering (ranking) the pixels contained in the region
encompassed by the filter
Smoothing is achieved by replacing the value of the center pixel with the value
determined by the ranking result.
median filter: replaces the value of the center pixel by the median of the intensity
values in the neighborhood of that pixel
FORCE POINTS TO BE MORE LIKE THEIR NEIGHBORS
median filter
66. 3.7 Smoothing (Lowpass) Spatial Filters
Order-statistic (nonlinear) filters median filter
image corrupted by salt-
and-pepper noise
result using 19 × 19
Gaussian lowpass filter
kernel with 𝜎𝜎= 3
result using 7 × 7
median filter
67. 3.8 Sharpening (Highpass) Spatial Filters
Distribution of grayscale changes in the image
Scan line
The gray distribution of the image
in the direction of the scan line
First derivative
Second derivative
69. 3.8 Sharpening (Highpass) Spatial Filters
The gradientof an image f at coordinates(x, y) is defined as the two dimensional column vector
Image gradient
The magnitude (length) of vector f , denotedas M(x, y)
First derivative
70. 3.8 Sharpening (Highpass) Spatial Filters
Image gradient: derivative operation --> differential operation
For discrete images, differentiation can be approximated by difference
||𝛻𝛻𝑓𝑓|| = (𝑓𝑓 𝑥𝑥,𝑦𝑦 − 𝑓𝑓 𝑥𝑥 + 1, 𝑦𝑦 )2+(𝑓𝑓 𝑥𝑥, 𝑦𝑦 − 𝑓𝑓 𝑥𝑥, 𝑦𝑦 + 1 )2
computationally to approximate the squares and square root operations by absolute values
𝛻𝛻𝑓𝑓 ≈ 𝑓𝑓 𝑥𝑥, 𝑦𝑦 − 𝑓𝑓 𝑥𝑥 + 1,𝑦𝑦 + |𝑓𝑓 𝑥𝑥, 𝑦𝑦 − 𝑓𝑓 𝑥𝑥, 𝑦𝑦 + 1 |
The magnitude of the gradient is approximated as the (absolute) sum
of the adjacent pixel differencesalong the horizontal and vertical axes
71. 3.8 Sharpening (Highpass) Spatial Filters
① The pixel value of the new image is directly replaced by the gradient of the original image
② The output image is according to the gradient threshold
Image Sharpening 图像锐化
72. 3.8 Sharpening (Highpass) Spatial Filters
Image Sharpening using gradient
The edges of the image are enhanced, and some noise is also amplified
73. Robert Operator
3.8 Sharpening (Highpass) Spatial Filters
The differential sum of the two
directions after rotating ±45°
The area involved in the calculation is too
small, and the obtained edge is weak
Image Sharpening using gradient
74. 3.8 Sharpening (Highpass) Spatial Filters
Image Sharpening using gradient 3*3 kernel
image
x
y
Maintaining directional consistency in the calculation, 3*3 can be viewed as a
superposition of multiple 2*2 regions with respect to the current pixel position.
82. 3.8 Sharpening (Highpass) Spatial Filters
second-order derivative of f (x)
Flexible extensions of the Laplace operator
1 -2 1
-2 4 -2
1 -2 1
Background features can be “recovered” while still preserving the sharpening effect of the
Laplacian by adding the Laplacian image to the original.
Let c = −1
91. 3.8 Combining Spatial Enhancement Methods
a nuclear
whole body
bone scan
image
Objective: show more of the skeletal detail
method: enhance the edges
Laplacian of image Sharpened image
92. 3.8 Combining Spatial Enhancement Methods
Objective: show more of the skeletal detail
method: enhance the edges and suppress noise
Sobel gradient of image Sobel image smoothed with a 5 × 5 box filter
Mask image formed by
the product of (b) and (e).
93. 3.8 Combining Spatial Enhancement Methods
Objective: show more of the skeletal detail method: enhance the edges and suppress noise
Sharpened image obtained
by the adding images (a) and (f).
95. Homework Deadline: before 9 April
1. Consider that the maximum value of an image 𝑰𝑰𝟏𝟏is M and its minimum is m
(m≠M). An intensity transform that maps the image 𝑰𝑰𝟏𝟏 onto 𝑰𝑰𝟐𝟐 such that the
maximal value of 𝑰𝑰𝟐𝟐 is L and the minimal value is:
2. Why global discrete histogram equalization does not, in general, yield a flat
(uniform) histogram?
A Because images are in color.
B Becausethe histogramequalizationmathematicalderivationdoesn’texist for discretesignals.
C In global histogramequalization, all pixels with the same value are mapped to same value.
D Actually, global discretehistogramequalizationalways yields flat histograms by definition.
96. Homework
3. Discrete histogram equalization is an invertible operation, meaning we can
recover the original image from the equalized one by inverting the operation,
since?
A Actually, histogram equalization is in general non-invertible.
B There is a unique histogram equalization formula per image.
C Pixels with different values are mapped to pixels with different values.
D Images have unique histograms.
4. Given an image with only 3 pixels and 4 possible values for each one. Determine
the number of possible different images and the number of possible different
histograms. How many images and histograms?
97. Homework
5. This image is a 6*6 grayscale image I(x, y) , with 4 gray levels
(x = 0, 1, 2, ... 5; y = 0, 1, 2, ..., 5) , the value of each point in the
figure represents the gray value of the image pixels.
1) Calculate the histogram of the image
2) Using histogram equalization to process this image (write the
process details )
3) Write the new histogram after histogram equalization.
98. Homework
6. Which integer number minimizes
7. Which integer number minimizes
8. Applying a 3×3 averaging filter to an image a large (infinity) number of times is:
A Equivalent to replacing all the pixel values by 0..
B Equivalent to replacing all the pixel values by the average of the values in the
original image.
C The same as applying it a single time.
D The same as applying a median filter.
99. 9. In the original image used to generate the three blurred images shown, the vertical
bars are 5 pixels wide, 100 pixels high, and their separation is 20 pixels. The image was
blurred using square box kernels of sizes 23, 25, and 45 elements on the side,
respectively. The vertical bars on the left, lower part of (a) and (c) are blurred, but a
clear separation exists between them. However, the bars have merged in image (b),
despite the fact that the kernel used to generate this image is much smaller than the
kernel that produced image (c). Explain the reason for this.
Homework