Normalized Cuts
Imaging Fundamentals
NOT ON EXAM
Stuvia.com - The Marketplace to Buy and Sell your Study Material Log Transformations: maps a narrow range of low grayscale values in the input image into a wider range of output values
Module 1 – Introduction Examples of poor technical image quality: Aliasing (moiré or glitch) is seen in approximately flat. Adaptive histogram equalization breaks your image into small x-direction y
Digital Images: The values of digital images are all discrete and integers. The values If Ncut(A,B) < Threshold, sampled systems. When the input frequency is greater than half the sample blocks, and then does histogram equalization in these small blocks.
can be considered as a large (numpy) array of discrete dots. Each dot has a a cut will be made. frequency (or: when the signal is sampled at less than twice the highest frequency), Prewitt
brightness associated with it. These dots are called picture elements (= pixels). the samples points do not adequately represent the input signal. Inputs at these
higher frequencies are observed at a lower, aliased frequency.
Neighborhood: A neighborhood can be characterized by its shape (e.g., 3X5 Image Quality Affects Deep Neural Networks: - Blurring – Noise - Low contrast - (=Normalisation) see more at
Sobel
neighborhood). Usually, the neighborhood is an odd number. If the -In medical imaging only the ultrasound picture is not coming from an JPEG distortion. If they’re higher, worse the neural networks perform. So, before in-class quiz questions!
e)Contrast Stretching: can be used to distribute the intensity range. Note that, in
neighborhood is an even number, interpolation is involved. electromagnetic spectrum. you run your classifiers, you can apply image enhancement to improve your
DNN misclassify images due contrast to gamma transformations, for contrast stretching (rescale intensity), the
Images are presented
Saturation and Noise: Saturation is the highest level of intensity that you can reach. downstream deep neural networks training. to poor technical image quality values do not have to be floating. A mask can’t be overlayed on border of image
The pixels surrounding a given
If there is a lot of saturation, you cannot see much detail because it is too bright. Image Noise: Noise is any degradation in the image signal, caused by external as part of the mask would not cover any pixels (padded mask).
as matrics (arrays). pixel is its neighborhood. 2-Spatial Filtering: Masks: You overlay a mask (in this case a 3x5 mask) over your Center element of
Images can be written You can use contrast enhancement to improve your image. You can also have disturbance. Note that image noise can occur when the image is compressed as well,
pixel to apply an operation. If you have an averaging mask, and e is your pixel, the kernel is placed
as a function f(x,y):
images that have noise. Noise exists when there is not enough light. not only when the image is acquired. over the source
- origin: top left pixels surrounding e (a, b, c, …, i) are used for the operation. Spatial filtering is an pixel.
Intensity resolution: is the smallest change of intensity in your image and it is Salt & Pepper Noise: The intensity of some of the pixels has been randomly
- x: vertical down example of a convolution operation. You also apply convolutions in neural The source pixel is
- y: horizontal right referred to by the number of bits. The most common is 8-bit (255 grayscale levels). changed to white and black (rather than the original intensity). networks. How do convolutions work? Convolutions require 3 steps: 1. Position then replaced with a
- (x,y): pixel Gaussian Noise: Also called white noise. The intensity of some of the pixels has weighted sum of
2^8=256 the mask over the current pixel; 2. Form all products or filter elements with the itself and nearby
fluctuated. white noise with a mean of zero and standard deviation of ‘sigma’
(0-255) corresponding elements of the neighbourhood; 3. Add up all the products. These 3 pixels.
Types of Images: The higher the brightness, the higher the number. Speckle Noise: Typically occurs when the image is acquired by radar, such as
steps are usually repeated for every pixel in the image. This is called linear filtering:
-Binary: Each pixel is either black (0) or white (1). You only need one bit to military operations. Each pixel is multiplied by some random value.
process is applied one by one in the image and summed up. (Convolution vs. last row becomes top row
represent the pixel. Image Blur: Out-of-focus and Motion blur.
Correlation: only difference is conv. Rotated the kernel(mask) by 180 degrees. last column -> first column
-Grayscale: Each pixel is a shade of gray. Normally the values range from 0 (black) Aliasing: You acquire the signal at an interval that is slightly less than the original
Spatial resolution is the density of pixels in the image. The greater the spatial 2a) Smoothing Filters: Linear: In simple average every pixel has same weight like Linear:
to 255 (white). Each pixel can be represented by eight bits, or exactly one byte. signal. Aliasing in Images: The image is resized by taking every
resolution, the more pixels are used to display the image, and the image tends be 1/9. However in weighted average centre or pixels near centre has more weight. 1/9 x 1 1 1
-Color: Multi-channel images are a stack of multiple matrices; representing the other pixel (1:2 resize). If a repetitive pattern of high frequency is sampled
Gaussian filter: Based on standard deviation smoothened the image. Non-linear 111
multiple channel values for each pixel. E.g., RGB color is described by the amount clearer. at a low resolution, more patterns results.spatial frequencies are measured in cycles/meter (c/m) 111
Interpolation: You can use interpolation to reduce or increase the image size. filter: you put a mask of over an image,and take the median value. Used to correct Weighted:
of red, green and blue in it. Red(255,0,0) - Green(0,255,0) - Blue(0,0,255) Image Enhancement: 1. Spatial Domain (Image Domain): based on direct
- Halve the size of your image: take out every other row and every other column salt and pepper noise because of the nonlinear character of this smoothing filter. 1/16 x 1 2 1
Black(0,0,0) - Gray(128,128,128) - White(255,255,255) manipulation of pixels in an image (Point Operations and Spatial Filtering 242
Each parameter (red, green, blue) defines the intensity of the color - Double the size of the image: all pixels are repeated to produce an image with the same /Convolutions. 2. Frequency Domain: filtering based on modifying the Fourier 2b) Sharpening filters: You can sharpen an image by taking the derivative. Laplacian
Color Models: 121
with a value between 0 and 255.
size as the original, but with half the resolution in each direction. filter: second-order derivative filter that is used to enhance edges in an image.
-Red-Green-Blue (RGB) (primary colors) transform of an image. frequency is measured in Hertz (Hz) = cycles/s
Unlike first-order methods like the Sobel or Prewitt filters which detect edges by bigger mask size
-Cyan-Magenta-Yellow-Black (CMYK):- Additive colors can be mixed to produce the Color Look Up Tables and Colormaps: Operations that change the display without Image Enhancement in the Spatial Domain: 1-Point operations:
changing the image are: LUT (colormap) and contrast stretching. Operations that a)Intensity Thresholding: Intensity thresholding converts a grayscale image to binary finding the intensity gradients in an image, the Laplacian filter detects regions of (gaussian conv.)
=smoother image
colors: Cyan, Yellow, and White.- Subtractive colors can be mixed to produce the
change the image can be reversible and non-reversible (majority). rapid intensity change more directly, which are typically indicative of edges. It is
colors: Red, Green, Blue and Black. image (pixel by pixel): 1. Choosing a gray level T in the original image;2. A pixel
C = Cyan: green + blue = white – red Unsigned vs signed integer uint8 and int8 are very similar, but there are important becomes white if its gray level is > T; 3. A pixel becomes black if its gray level is <= extremely sensitive to noise. 2c) Edge Detection Filters: Prewitt and Sobel:
differences. int8 has range of –127 to 127. uint8 has a range of 0 to 255 (u = 2d) Image Pyramids: Gaussian Pyramid: Reduces the image size and blurs it,
(secondary colors) M = Magenta: red + blue = white – green T.
unsigned). a=250: a+100=94 (95 but incl. 0), a=120: a-150=226 (120-150=-30, -30+256) which is used for image downscaling and multi-resolution analysis.
Y = Yellow: red + green = white – blue Q: mask 5x5, center restricted
Arithmetic Operations:These operations applying a simple function y=f(x) to each Laplacian Pyramid: Is a bandpass version of the image pyramid, used for to be distance >= 2 pixels
K = Black
gray value in the image (e.g., add, subtract, etc.). Simple functions include:- adding reconstructing an image from its lower resolution. In-class Quiz Questions- from border of image, what
happens to resultant image?
the whiter the color, or subtract a constant value to each pixel - adding or subtract an image from Gaussian noise is: white noise with a mean of zero and a standard deviation of A: The resultant image will
the lower the saturation:
another image of the same size (width and height and channels) - multiplying each sigma.-Aliasing occurs when a signal is sampled: at slightly less than the time be a little smaller size than
objects appear darker
pixel by a constant: y = C·x - complement: for a grayscale image, you reserve
reverse the b)Otsu’s method: - Assumes that the image contains two class of pixels: backgroundinterval of the original signal. -Which of these are true :a. Contrast stretchingthe original image.
(white becomes black)
bright and dark values To be able to apply arithmetic operations, images have to be (Group A) and foreground (Group B). The foreground is typically what you are stretches the range of intensity values it contains to make full use of possible values
The hue value for red is 0
as it is positioned at 0 degrees a well-lit color has a
the same size. This is because of linear algebra: columns and rows need to have the interested in (e.g., the rice grains in the image of the practical lecture); - Minimizes b. Contrast stretching is sensitive to outliers (e.g., a small number of pixels with high
on the hue color circle. high intensity value:
same size. the spread (intra-class variance); the distributions (mean, variance, SD) of the and low intensities due to salt and pepper noise)c. Histogram equalization is not
objects appear whiter
-HSV (Hue, Saturation,Value) - Hue: the “true color” attribute (red, green, blue, Grayscale conversions in PIL and scikit-image : intensities of the two groups; intra=within; inter=between sensitive to outliers. In a bright image, the components of histogram are
orange, yellow, and so on).- Saturation: the amount by which the color has been
violet - In scikit image, the value of each grayscale pixel is calculated as the weighted sum - Maximizes inter-class variance (the difference between the mean of concentrated on which side of the grey scale? Answer: High You should normalize
diluted with white. The whiter the color, the lower the saturation.- Value: the degree of the corresponding red, green and blue pixels as: Group A and the mean of Group B). your image (scale between 0 and 1) for the following intensity transformations: Log
of brightness – a well-lit color has high intensity; a dark color has low intensity. Y = 0.2125 R + 0.7154 G + 0.0721 B c)Adaptive Thresholding: “Local” thresholds calculated with fixed block_size and Gamma transformations. Exam Which of the following
Q: Histogram equalisationfilters are used
(HE) causes for of the intensity distribution to
the spread
be more even in an image (a bit of a distorted image). Gamma transformation of 0.5
-HSL (Hue, Saturation,Luminosity): In the HSV model, (mixed with black) These weights are used by CRT phosphors as they better represent human surrounding each pixel (i.e., local neighborhoods). Adaptive thresholding produces smoothing? Averaging and Gaussian makes theFilter.
imageWhich of the
brigther (esp. following
dark filter(s)not
regions). However, areasused
bright as HE, it looks
the value is the degree of brightness. A well-lit color has a high intensity (value); a perception of red, green and blue than equal weights (i.e., 0.3; 0.3; 0.3) better results when there is a large variation in background intensity. Adaptive for sharpening? Laplacian Filter. more like a (ligther) filter was applied to the image.
dark color has a low intensity (value). The original hue value has a luminosity of - In PIL, a color image is converted to grayscale (mode “L”), using the ITUR 601-2 thresholding is similar to adaptive histogram, in the sense that you break your image Module 3
5 Image Enhancement in the Frequency Domain
128. When decreasing luminosity (minimum is 0), the color becomes darker (shade). luma transform: into small sections and apply localized thresholding. Fourier Transforms Convolution in an image domain is equivalent to a simple
When increasing luminosity (maximum is 255), the color becomes brighter (tint). L = 0.299 R + 0.587 G + 0.114 B multiplication in the frequency domain. Multiplication in the frequency domain is
Why do we convert images to greyscale? Traditional image analysis algorithms faster especially when the kernel and/or the image is large. Allows a signal to be
especially image enhancements algorithms, tend to work on only one channel such decomposed into a sum of sine waves of different frequencies, phases and
Intensity transformations: amplitudes. Fourier transform make images sine and cosine waves instead of pixels.
that you can convert to greyscale, or you can apply the three (R, G, B) channels improve the appearance
separately. of images, which improves
Second picture is harmonics. An image is a weighted sum of cos (even) and sin (odd) images.
Fundamental Steps in IA the performance of image ◦ Frequencies: amount by which grey values change with distance.
Image Acquisiton-Preprocessing-Morphological Operations-Image The intensity value of each pixel is transformed using segmentation algorithms ◦ High frequency components - large changes in grey values over small distances;
and feature recognition.
Segmentation-Object Recognition-Quantification-Visualization
a transfer function to form a constrst-adjusted image. (edges and noise)
d)Gamma Transformations: When γ=1, the transformation is linear, and the output
Statistical Analysis
image is the same as the input image. If γ<1, the transformation is sub-linear, and ◦ Low frequency components - by little change in the gray values. (backgrounds,
luminosity=lightness of img (e.g. due to weather) In-class quiz questions : the output image will appear lighter, which can enhance details in dark regions. skin textures) Magnitude (amplitude): How much each sinusoid contributes to form the whole signal f(n).
1. The maximum intensity level in an 8bit image is 255. Conversely, if γ>1, the transformation is super-linear, and the output image will
Phase: How each sinusoid lines up relative to one another to form the whole signal f(n).
2. The red color in a hue image will correspond to 0. appear darker, which can enhance details in bright regions.(Note that you should never
NOT ON EXAM 3. Each element (point) of an image matrix (numpy array) is called a pixel. apply gamma transformations to unsigned integer images, because your image intensity should be
4. Black color in a uint8 (unsigned 8bit) image is usually represented by the value 0. between 0 (completely dark) and 1 (completely bright). That is why you should convert your image
5. The maximum intensity level in a 4bit image is 15. to float, and normalize the values between 0 and 1, before applying gamma transformation.)
Previous Exam Question 1: Which channel is the Hue Channel? Justify your y=4
y=5
All the bands
Fundamental steps(e.g., X-ray,
in Digital Imageradio, visual), are part of the electromagnetic spectrum.
Processing
Outputs of these steps are generally images:
Each band has a certain wave length. The main source of energy is radiation from
- Image Acquisition
electromagnetic waves. They are
- Preprocessing: The preprocssing step corrects massless particles
for defects movingtheatcontrast
and enhances the speed of light,
to improve and
features e)Intensity Histograms: The histogram of a digital image indicates how the intensity
Fourier transform is
invertible (inverse)!
ofthey contain
interest energy.
in the image Gamma rays
for subsequent have
analysis a very
(contrast short wave-length,
stretching, and are typically
denoising, sharpening).
- Morphological Operations: Morphological processing deals with tools for extracting image components that
of pixels distributes among the whole pixels (how many pixels are at a certain
used in PET machines and PET deposits for positron emission tomography intensity range). An intensity histogram shows the darkness, brightness and contrast
are useful in the representation and description of shape (skeletonization, binary closing). answer.
machines.
Outputs Radio
of these steps waves haveimage
are generally veryattributes:
long wave lengths. Images coming from radio of an image. RGB: 3 intensity histograms (per channel) - can be combined.
- waves
Fig. (b) Image 1 is the hue channel. The red has a value of 0 [2 pts], the value for
belong
Morphological to astronomy. Between UV and infra-red is the visible spectrum. It is
Operations:
◦ High pass filters passes over the high frequency components and reduces or
- Image Segmentation: Segmentation is the process of partitioning the image into multiple segments (sets of yellow is higher than red but lower than green. The green channel is darker than the
a band with wavelengths around 450 nanometers to 750 nanometers. This is the eliminates low frequency components. High-pass: Accentuates the details
pixels or objects), which are more meaningful and easier to analyze (intensity thresholding). blue channel and the magenta channel is the brightest [2 pts]. These intensity values
- band
Object that we areThe most familiar with.
stepThis band consists
such asof
cellmany
nuclei colors from redon
f)Histogram Equalization: The global histogram may not be a good representation ◦ Low pass filters passes over the low frequency components and reduces or
Recognition: object recognition assigns a label, to an object based
correspond to the hue scale. As for the other channels: Fig. (c) Image 2 is the
(with
its a longer
descriptors wavelength)
(single to blue
object: classification (with a lower
+ localization, wavelength).
multiple: This
object detection, bandsegmentation).
instance is easiest to
- Quantification: To derive quantitative information from features, we can use tools in Python to measure saturation channel, because the intensities for all the colors are nearly the same. Fig. for local statistics in two parts of the image. We can apply histogram equalization in eliminates high frequency components. Low-pass: reduces the noise
distinguish because
and otherof the many identifiable colors.
region properties quantities. (d) Image 3 is the blue channel, because the intensities where the pixel contain blue such a way that the number of pixels per intensity range is equal. It transforms the ◦ Band pass filters passes frequencies within a certain range and rejects (attenuates)
Image Formation: A digital image plane acquired by recording are brighter. White and cyan and magenta contain blue. intensities of your pixel in such a way that the histogram of your output image is frequencies outside that range. Band-pass: Keeps frequencies in a narrow band Wlow < W < Whigh
a digital value proportional to the intensity of the light on each pixel of a detector. Module 2 - Image Enhancement in the Spatial Domain Low Pass (Smoothing) Filters Band-stop: Keeps frequencies outside a narrow band (W < Wlow and Whigh < W)
Colormaps: Pixel values may be displayed in different ways (determined by a LUT). Image Enhancement:
Downloaded by: yvanavervoortPoint
Tekst - Do
Operators are limited:
|
not know each pixel is in the image. Want to earn $1.236
Only for grayscale (& binary) images! To process an image so that the result is more suitable - Do not know anything about their neighbors
Tekst Distribution of this document is illegal extra per year?
than the original image for a specific application. - Most image features such as edges and textures involve a pixel’s neighborhood.
Spatial filters allow us to manipulate these features!
Imaging Fundamentals
NOT ON EXAM
Stuvia.com - The Marketplace to Buy and Sell your Study Material Log Transformations: maps a narrow range of low grayscale values in the input image into a wider range of output values
Module 1 – Introduction Examples of poor technical image quality: Aliasing (moiré or glitch) is seen in approximately flat. Adaptive histogram equalization breaks your image into small x-direction y
Digital Images: The values of digital images are all discrete and integers. The values If Ncut(A,B) < Threshold, sampled systems. When the input frequency is greater than half the sample blocks, and then does histogram equalization in these small blocks.
can be considered as a large (numpy) array of discrete dots. Each dot has a a cut will be made. frequency (or: when the signal is sampled at less than twice the highest frequency), Prewitt
brightness associated with it. These dots are called picture elements (= pixels). the samples points do not adequately represent the input signal. Inputs at these
higher frequencies are observed at a lower, aliased frequency.
Neighborhood: A neighborhood can be characterized by its shape (e.g., 3X5 Image Quality Affects Deep Neural Networks: - Blurring – Noise - Low contrast - (=Normalisation) see more at
Sobel
neighborhood). Usually, the neighborhood is an odd number. If the -In medical imaging only the ultrasound picture is not coming from an JPEG distortion. If they’re higher, worse the neural networks perform. So, before in-class quiz questions!
e)Contrast Stretching: can be used to distribute the intensity range. Note that, in
neighborhood is an even number, interpolation is involved. electromagnetic spectrum. you run your classifiers, you can apply image enhancement to improve your
DNN misclassify images due contrast to gamma transformations, for contrast stretching (rescale intensity), the
Images are presented
Saturation and Noise: Saturation is the highest level of intensity that you can reach. downstream deep neural networks training. to poor technical image quality values do not have to be floating. A mask can’t be overlayed on border of image
The pixels surrounding a given
If there is a lot of saturation, you cannot see much detail because it is too bright. Image Noise: Noise is any degradation in the image signal, caused by external as part of the mask would not cover any pixels (padded mask).
as matrics (arrays). pixel is its neighborhood. 2-Spatial Filtering: Masks: You overlay a mask (in this case a 3x5 mask) over your Center element of
Images can be written You can use contrast enhancement to improve your image. You can also have disturbance. Note that image noise can occur when the image is compressed as well,
pixel to apply an operation. If you have an averaging mask, and e is your pixel, the kernel is placed
as a function f(x,y):
images that have noise. Noise exists when there is not enough light. not only when the image is acquired. over the source
- origin: top left pixels surrounding e (a, b, c, …, i) are used for the operation. Spatial filtering is an pixel.
Intensity resolution: is the smallest change of intensity in your image and it is Salt & Pepper Noise: The intensity of some of the pixels has been randomly
- x: vertical down example of a convolution operation. You also apply convolutions in neural The source pixel is
- y: horizontal right referred to by the number of bits. The most common is 8-bit (255 grayscale levels). changed to white and black (rather than the original intensity). networks. How do convolutions work? Convolutions require 3 steps: 1. Position then replaced with a
- (x,y): pixel Gaussian Noise: Also called white noise. The intensity of some of the pixels has weighted sum of
2^8=256 the mask over the current pixel; 2. Form all products or filter elements with the itself and nearby
fluctuated. white noise with a mean of zero and standard deviation of ‘sigma’
(0-255) corresponding elements of the neighbourhood; 3. Add up all the products. These 3 pixels.
Types of Images: The higher the brightness, the higher the number. Speckle Noise: Typically occurs when the image is acquired by radar, such as
steps are usually repeated for every pixel in the image. This is called linear filtering:
-Binary: Each pixel is either black (0) or white (1). You only need one bit to military operations. Each pixel is multiplied by some random value.
process is applied one by one in the image and summed up. (Convolution vs. last row becomes top row
represent the pixel. Image Blur: Out-of-focus and Motion blur.
Correlation: only difference is conv. Rotated the kernel(mask) by 180 degrees. last column -> first column
-Grayscale: Each pixel is a shade of gray. Normally the values range from 0 (black) Aliasing: You acquire the signal at an interval that is slightly less than the original
Spatial resolution is the density of pixels in the image. The greater the spatial 2a) Smoothing Filters: Linear: In simple average every pixel has same weight like Linear:
to 255 (white). Each pixel can be represented by eight bits, or exactly one byte. signal. Aliasing in Images: The image is resized by taking every
resolution, the more pixels are used to display the image, and the image tends be 1/9. However in weighted average centre or pixels near centre has more weight. 1/9 x 1 1 1
-Color: Multi-channel images are a stack of multiple matrices; representing the other pixel (1:2 resize). If a repetitive pattern of high frequency is sampled
Gaussian filter: Based on standard deviation smoothened the image. Non-linear 111
multiple channel values for each pixel. E.g., RGB color is described by the amount clearer. at a low resolution, more patterns results.spatial frequencies are measured in cycles/meter (c/m) 111
Interpolation: You can use interpolation to reduce or increase the image size. filter: you put a mask of over an image,and take the median value. Used to correct Weighted:
of red, green and blue in it. Red(255,0,0) - Green(0,255,0) - Blue(0,0,255) Image Enhancement: 1. Spatial Domain (Image Domain): based on direct
- Halve the size of your image: take out every other row and every other column salt and pepper noise because of the nonlinear character of this smoothing filter. 1/16 x 1 2 1
Black(0,0,0) - Gray(128,128,128) - White(255,255,255) manipulation of pixels in an image (Point Operations and Spatial Filtering 242
Each parameter (red, green, blue) defines the intensity of the color - Double the size of the image: all pixels are repeated to produce an image with the same /Convolutions. 2. Frequency Domain: filtering based on modifying the Fourier 2b) Sharpening filters: You can sharpen an image by taking the derivative. Laplacian
Color Models: 121
with a value between 0 and 255.
size as the original, but with half the resolution in each direction. filter: second-order derivative filter that is used to enhance edges in an image.
-Red-Green-Blue (RGB) (primary colors) transform of an image. frequency is measured in Hertz (Hz) = cycles/s
Unlike first-order methods like the Sobel or Prewitt filters which detect edges by bigger mask size
-Cyan-Magenta-Yellow-Black (CMYK):- Additive colors can be mixed to produce the Color Look Up Tables and Colormaps: Operations that change the display without Image Enhancement in the Spatial Domain: 1-Point operations:
changing the image are: LUT (colormap) and contrast stretching. Operations that a)Intensity Thresholding: Intensity thresholding converts a grayscale image to binary finding the intensity gradients in an image, the Laplacian filter detects regions of (gaussian conv.)
=smoother image
colors: Cyan, Yellow, and White.- Subtractive colors can be mixed to produce the
change the image can be reversible and non-reversible (majority). rapid intensity change more directly, which are typically indicative of edges. It is
colors: Red, Green, Blue and Black. image (pixel by pixel): 1. Choosing a gray level T in the original image;2. A pixel
C = Cyan: green + blue = white – red Unsigned vs signed integer uint8 and int8 are very similar, but there are important becomes white if its gray level is > T; 3. A pixel becomes black if its gray level is <= extremely sensitive to noise. 2c) Edge Detection Filters: Prewitt and Sobel:
differences. int8 has range of –127 to 127. uint8 has a range of 0 to 255 (u = 2d) Image Pyramids: Gaussian Pyramid: Reduces the image size and blurs it,
(secondary colors) M = Magenta: red + blue = white – green T.
unsigned). a=250: a+100=94 (95 but incl. 0), a=120: a-150=226 (120-150=-30, -30+256) which is used for image downscaling and multi-resolution analysis.
Y = Yellow: red + green = white – blue Q: mask 5x5, center restricted
Arithmetic Operations:These operations applying a simple function y=f(x) to each Laplacian Pyramid: Is a bandpass version of the image pyramid, used for to be distance >= 2 pixels
K = Black
gray value in the image (e.g., add, subtract, etc.). Simple functions include:- adding reconstructing an image from its lower resolution. In-class Quiz Questions- from border of image, what
happens to resultant image?
the whiter the color, or subtract a constant value to each pixel - adding or subtract an image from Gaussian noise is: white noise with a mean of zero and a standard deviation of A: The resultant image will
the lower the saturation:
another image of the same size (width and height and channels) - multiplying each sigma.-Aliasing occurs when a signal is sampled: at slightly less than the time be a little smaller size than
objects appear darker
pixel by a constant: y = C·x - complement: for a grayscale image, you reserve
reverse the b)Otsu’s method: - Assumes that the image contains two class of pixels: backgroundinterval of the original signal. -Which of these are true :a. Contrast stretchingthe original image.
(white becomes black)
bright and dark values To be able to apply arithmetic operations, images have to be (Group A) and foreground (Group B). The foreground is typically what you are stretches the range of intensity values it contains to make full use of possible values
The hue value for red is 0
as it is positioned at 0 degrees a well-lit color has a
the same size. This is because of linear algebra: columns and rows need to have the interested in (e.g., the rice grains in the image of the practical lecture); - Minimizes b. Contrast stretching is sensitive to outliers (e.g., a small number of pixels with high
on the hue color circle. high intensity value:
same size. the spread (intra-class variance); the distributions (mean, variance, SD) of the and low intensities due to salt and pepper noise)c. Histogram equalization is not
objects appear whiter
-HSV (Hue, Saturation,Value) - Hue: the “true color” attribute (red, green, blue, Grayscale conversions in PIL and scikit-image : intensities of the two groups; intra=within; inter=between sensitive to outliers. In a bright image, the components of histogram are
orange, yellow, and so on).- Saturation: the amount by which the color has been
violet - In scikit image, the value of each grayscale pixel is calculated as the weighted sum - Maximizes inter-class variance (the difference between the mean of concentrated on which side of the grey scale? Answer: High You should normalize
diluted with white. The whiter the color, the lower the saturation.- Value: the degree of the corresponding red, green and blue pixels as: Group A and the mean of Group B). your image (scale between 0 and 1) for the following intensity transformations: Log
of brightness – a well-lit color has high intensity; a dark color has low intensity. Y = 0.2125 R + 0.7154 G + 0.0721 B c)Adaptive Thresholding: “Local” thresholds calculated with fixed block_size and Gamma transformations. Exam Which of the following
Q: Histogram equalisationfilters are used
(HE) causes for of the intensity distribution to
the spread
be more even in an image (a bit of a distorted image). Gamma transformation of 0.5
-HSL (Hue, Saturation,Luminosity): In the HSV model, (mixed with black) These weights are used by CRT phosphors as they better represent human surrounding each pixel (i.e., local neighborhoods). Adaptive thresholding produces smoothing? Averaging and Gaussian makes theFilter.
imageWhich of the
brigther (esp. following
dark filter(s)not
regions). However, areasused
bright as HE, it looks
the value is the degree of brightness. A well-lit color has a high intensity (value); a perception of red, green and blue than equal weights (i.e., 0.3; 0.3; 0.3) better results when there is a large variation in background intensity. Adaptive for sharpening? Laplacian Filter. more like a (ligther) filter was applied to the image.
dark color has a low intensity (value). The original hue value has a luminosity of - In PIL, a color image is converted to grayscale (mode “L”), using the ITUR 601-2 thresholding is similar to adaptive histogram, in the sense that you break your image Module 3
5 Image Enhancement in the Frequency Domain
128. When decreasing luminosity (minimum is 0), the color becomes darker (shade). luma transform: into small sections and apply localized thresholding. Fourier Transforms Convolution in an image domain is equivalent to a simple
When increasing luminosity (maximum is 255), the color becomes brighter (tint). L = 0.299 R + 0.587 G + 0.114 B multiplication in the frequency domain. Multiplication in the frequency domain is
Why do we convert images to greyscale? Traditional image analysis algorithms faster especially when the kernel and/or the image is large. Allows a signal to be
especially image enhancements algorithms, tend to work on only one channel such decomposed into a sum of sine waves of different frequencies, phases and
Intensity transformations: amplitudes. Fourier transform make images sine and cosine waves instead of pixels.
that you can convert to greyscale, or you can apply the three (R, G, B) channels improve the appearance
separately. of images, which improves
Second picture is harmonics. An image is a weighted sum of cos (even) and sin (odd) images.
Fundamental Steps in IA the performance of image ◦ Frequencies: amount by which grey values change with distance.
Image Acquisiton-Preprocessing-Morphological Operations-Image The intensity value of each pixel is transformed using segmentation algorithms ◦ High frequency components - large changes in grey values over small distances;
and feature recognition.
Segmentation-Object Recognition-Quantification-Visualization
a transfer function to form a constrst-adjusted image. (edges and noise)
d)Gamma Transformations: When γ=1, the transformation is linear, and the output
Statistical Analysis
image is the same as the input image. If γ<1, the transformation is sub-linear, and ◦ Low frequency components - by little change in the gray values. (backgrounds,
luminosity=lightness of img (e.g. due to weather) In-class quiz questions : the output image will appear lighter, which can enhance details in dark regions. skin textures) Magnitude (amplitude): How much each sinusoid contributes to form the whole signal f(n).
1. The maximum intensity level in an 8bit image is 255. Conversely, if γ>1, the transformation is super-linear, and the output image will
Phase: How each sinusoid lines up relative to one another to form the whole signal f(n).
2. The red color in a hue image will correspond to 0. appear darker, which can enhance details in bright regions.(Note that you should never
NOT ON EXAM 3. Each element (point) of an image matrix (numpy array) is called a pixel. apply gamma transformations to unsigned integer images, because your image intensity should be
4. Black color in a uint8 (unsigned 8bit) image is usually represented by the value 0. between 0 (completely dark) and 1 (completely bright). That is why you should convert your image
5. The maximum intensity level in a 4bit image is 15. to float, and normalize the values between 0 and 1, before applying gamma transformation.)
Previous Exam Question 1: Which channel is the Hue Channel? Justify your y=4
y=5
All the bands
Fundamental steps(e.g., X-ray,
in Digital Imageradio, visual), are part of the electromagnetic spectrum.
Processing
Outputs of these steps are generally images:
Each band has a certain wave length. The main source of energy is radiation from
- Image Acquisition
electromagnetic waves. They are
- Preprocessing: The preprocssing step corrects massless particles
for defects movingtheatcontrast
and enhances the speed of light,
to improve and
features e)Intensity Histograms: The histogram of a digital image indicates how the intensity
Fourier transform is
invertible (inverse)!
ofthey contain
interest energy.
in the image Gamma rays
for subsequent have
analysis a very
(contrast short wave-length,
stretching, and are typically
denoising, sharpening).
- Morphological Operations: Morphological processing deals with tools for extracting image components that
of pixels distributes among the whole pixels (how many pixels are at a certain
used in PET machines and PET deposits for positron emission tomography intensity range). An intensity histogram shows the darkness, brightness and contrast
are useful in the representation and description of shape (skeletonization, binary closing). answer.
machines.
Outputs Radio
of these steps waves haveimage
are generally veryattributes:
long wave lengths. Images coming from radio of an image. RGB: 3 intensity histograms (per channel) - can be combined.
- waves
Fig. (b) Image 1 is the hue channel. The red has a value of 0 [2 pts], the value for
belong
Morphological to astronomy. Between UV and infra-red is the visible spectrum. It is
Operations:
◦ High pass filters passes over the high frequency components and reduces or
- Image Segmentation: Segmentation is the process of partitioning the image into multiple segments (sets of yellow is higher than red but lower than green. The green channel is darker than the
a band with wavelengths around 450 nanometers to 750 nanometers. This is the eliminates low frequency components. High-pass: Accentuates the details
pixels or objects), which are more meaningful and easier to analyze (intensity thresholding). blue channel and the magenta channel is the brightest [2 pts]. These intensity values
- band
Object that we areThe most familiar with.
stepThis band consists
such asof
cellmany
nuclei colors from redon
f)Histogram Equalization: The global histogram may not be a good representation ◦ Low pass filters passes over the low frequency components and reduces or
Recognition: object recognition assigns a label, to an object based
correspond to the hue scale. As for the other channels: Fig. (c) Image 2 is the
(with
its a longer
descriptors wavelength)
(single to blue
object: classification (with a lower
+ localization, wavelength).
multiple: This
object detection, bandsegmentation).
instance is easiest to
- Quantification: To derive quantitative information from features, we can use tools in Python to measure saturation channel, because the intensities for all the colors are nearly the same. Fig. for local statistics in two parts of the image. We can apply histogram equalization in eliminates high frequency components. Low-pass: reduces the noise
distinguish because
and otherof the many identifiable colors.
region properties quantities. (d) Image 3 is the blue channel, because the intensities where the pixel contain blue such a way that the number of pixels per intensity range is equal. It transforms the ◦ Band pass filters passes frequencies within a certain range and rejects (attenuates)
Image Formation: A digital image plane acquired by recording are brighter. White and cyan and magenta contain blue. intensities of your pixel in such a way that the histogram of your output image is frequencies outside that range. Band-pass: Keeps frequencies in a narrow band Wlow < W < Whigh
a digital value proportional to the intensity of the light on each pixel of a detector. Module 2 - Image Enhancement in the Spatial Domain Low Pass (Smoothing) Filters Band-stop: Keeps frequencies outside a narrow band (W < Wlow and Whigh < W)
Colormaps: Pixel values may be displayed in different ways (determined by a LUT). Image Enhancement:
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Tekst - Do
Operators are limited:
|
not know each pixel is in the image. Want to earn $1.236
Only for grayscale (& binary) images! To process an image so that the result is more suitable - Do not know anything about their neighbors
Tekst Distribution of this document is illegal extra per year?
than the original image for a specific application. - Most image features such as edges and textures involve a pixel’s neighborhood.
Spatial filters allow us to manipulate these features!
