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Questions and Answers
What does a vertically elongated aperture typically result in?
What does a vertically elongated aperture typically result in?
What is the effect of the gap duration on the phi phenomenon?
What is the effect of the gap duration on the phi phenomenon?
In the beta movement illusion, what do observers perceive?
In the beta movement illusion, what do observers perceive?
What consistently happens during the phi color phenomenon?
What consistently happens during the phi color phenomenon?
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How is the perception of movement in phi movement different from beta movement?
How is the perception of movement in phi movement different from beta movement?
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What is a characteristic of both the phi phenomenon and beta movement?
What is a characteristic of both the phi phenomenon and beta movement?
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Which statement accurately describes the relationship between the phi phenomenon and the duration of object illumination?
Which statement accurately describes the relationship between the phi phenomenon and the duration of object illumination?
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What does the linear interpolation formula calculate for a pixel value?
What does the linear interpolation formula calculate for a pixel value?
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Which of the following sensory challenges is most closely related to the illumination pattern in the phi phenomenon?
Which of the following sensory challenges is most closely related to the illumination pattern in the phi phenomenon?
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In image interpolation, what does sub-pixel precision refer to?
In image interpolation, what does sub-pixel precision refer to?
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What are the two main effects addressed in the context of sampling?
What are the two main effects addressed in the context of sampling?
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What method is employed to avoid issues related to spectral overlap during interpolation?
What method is employed to avoid issues related to spectral overlap during interpolation?
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What defines the reconstruction level in scalar quantization?
What defines the reconstruction level in scalar quantization?
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Which transformation is described by the notation (x,y) → (x',y')?
Which transformation is described by the notation (x,y) → (x',y')?
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What is a primary purpose of histogram modifications in image processing?
What is a primary purpose of histogram modifications in image processing?
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What is the result of using 1D first-order interpolation (linear)?
What is the result of using 1D first-order interpolation (linear)?
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What does the magnitude of the Fourier Transform indicate?
What does the magnitude of the Fourier Transform indicate?
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What is the role of the phase in the Fourier Transform?
What is the role of the phase in the Fourier Transform?
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In the discrete 2-D Fourier Transform, what variables govern the sums?
In the discrete 2-D Fourier Transform, what variables govern the sums?
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What do FT images generally display?
What do FT images generally display?
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In the formula for the 2D continuous Fourier Transform, the exponential term includes which of the following?
In the formula for the 2D continuous Fourier Transform, the exponential term includes which of the following?
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What is the summation limit for u and v in the discrete 2-D Fourier Transform?
What is the summation limit for u and v in the discrete 2-D Fourier Transform?
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What does the inverse Fourier Transform achieve?
What does the inverse Fourier Transform achieve?
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The formula for the discrete 2-D FT uses which factors in its exponential expression?
The formula for the discrete 2-D FT uses which factors in its exponential expression?
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What does a zero-crossing point typically indicate in image processing?
What does a zero-crossing point typically indicate in image processing?
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Which of the following best describes the purpose of the Laplacian operator?
Which of the following best describes the purpose of the Laplacian operator?
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In the context of gradient patterns, what does a value of –10 typically represent?
In the context of gradient patterns, what does a value of –10 typically represent?
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What is the significance of the coefficients in the Laplacian matrix?
What is the significance of the coefficients in the Laplacian matrix?
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What does the expression $∇^2f[(x,y)]$ represent in the context of the Laplacian operator?
What does the expression $∇^2f[(x,y)]$ represent in the context of the Laplacian operator?
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Why is the Laplacian operator described as having coefficients of +1 and -4?
Why is the Laplacian operator described as having coefficients of +1 and -4?
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What does the term 'grey levels' refer to in the given context?
What does the term 'grey levels' refer to in the given context?
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Which angle is associated with the orientation of edges in the provided gradient pattern?
Which angle is associated with the orientation of edges in the provided gradient pattern?
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What is the primary purpose of low-pass filtering in image processing?
What is the primary purpose of low-pass filtering in image processing?
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In the context of filtering via FFT, what does the variable 'H(u, v)' represent?
In the context of filtering via FFT, what does the variable 'H(u, v)' represent?
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What type of filter would be used to remove specific frequency ranges in an image?
What type of filter would be used to remove specific frequency ranges in an image?
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What mathematical operation is employed to perform direct filtering in the spatial domain?
What mathematical operation is employed to perform direct filtering in the spatial domain?
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Which of the following best describes the relationship between correlation and convolution?
Which of the following best describes the relationship between correlation and convolution?
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What does the term 'cutoff frequency' refer to in image filtering?
What does the term 'cutoff frequency' refer to in image filtering?
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When applying an averaging filter as a low-pass filter, what is the primary effect on the image?
When applying an averaging filter as a low-pass filter, what is the primary effect on the image?
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Which filter is designed to eliminate unwanted noise frequencies while preserving the main signal?
Which filter is designed to eliminate unwanted noise frequencies while preserving the main signal?
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What is the effect of high-frequency content in an image?
What is the effect of high-frequency content in an image?
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What spatial technique is used in the convolution of an image with a template?
What spatial technique is used in the convolution of an image with a template?
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What does the median filtering operation primarily achieve in image processing?
What does the median filtering operation primarily achieve in image processing?
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Which of the following statements regarding median filtering is true?
Which of the following statements regarding median filtering is true?
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What is the result of applying the median operation to the expression $a.I1 + b.I2$?
What is the result of applying the median operation to the expression $a.I1 + b.I2$?
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What is the primary function of edge detection in image processing?
What is the primary function of edge detection in image processing?
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Which of the following best describes the result when $
abla f(x, y) > Threshold$ at a point?
Which of the following best describes the result when $ abla f(x, y) > Threshold$ at a point?
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What type of filter is primarily used for edge enhancement in images?
What type of filter is primarily used for edge enhancement in images?
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Which of the following masks is associated with the Sobel operator?
Which of the following masks is associated with the Sobel operator?
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The gradient of an image is calculated using what type of equations?
The gradient of an image is calculated using what type of equations?
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Which component is crucial in defining the gradient at a point in an image?
Which component is crucial in defining the gradient at a point in an image?
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What phenomenon creates an illusion of movement through rapidly illuminated stationary objects placed side by side?
What phenomenon creates an illusion of movement through rapidly illuminated stationary objects placed side by side?
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In the phi phenomenon, what happens when the gap between flashes exceeds 500ms?
In the phi phenomenon, what happens when the gap between flashes exceeds 500ms?
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What type of illusion does beta movement produce?
What type of illusion does beta movement produce?
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During the phi color phenomenon, what do observers typically report about the dot's color?
During the phi color phenomenon, what do observers typically report about the dot's color?
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How is the motion perceived in phi movement different from that in beta movement?
How is the motion perceived in phi movement different from that in beta movement?
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What defines a vertically elongated aperture regarding motion perception?
What defines a vertically elongated aperture regarding motion perception?
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What is the maximum duration of the gap between flashes in the phi phenomenon for it to still be effective?
What is the maximum duration of the gap between flashes in the phi phenomenon for it to still be effective?
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What is an essential characteristic of beta movement?
What is an essential characteristic of beta movement?
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What is the primary function of image sampling?
What is the primary function of image sampling?
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Which type of images is characterized by a combination of text, graphics, and sound?
Which type of images is characterized by a combination of text, graphics, and sound?
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In image processing, what does low-pass filtering primarily achieve?
In image processing, what does low-pass filtering primarily achieve?
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What is required to perform grey-level quantization?
What is required to perform grey-level quantization?
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Which histogram operation improves image contrast?
Which histogram operation improves image contrast?
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What describes optical flow in image processing?
What describes optical flow in image processing?
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Which library is commonly used for image processing in Python?
Which library is commonly used for image processing in Python?
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What does the Fourier Transform primarily analyze in an image?
What does the Fourier Transform primarily analyze in an image?
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What is a primary benefit of median filtering in image processing?
What is a primary benefit of median filtering in image processing?
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Which mathematical expression indicates that median filtering is non-linear?
Which mathematical expression indicates that median filtering is non-linear?
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Which type of noise is median filtering specifically effective at removing?
Which type of noise is median filtering specifically effective at removing?
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What is the primary effect of low-pass filtering on an image?
What is the primary effect of low-pass filtering on an image?
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What criterion determines if a point is an edge point in gradient detection?
What criterion determines if a point is an edge point in gradient detection?
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In the filtering process via FFT, which step comes immediately after applying the frequency response?
In the filtering process via FFT, which step comes immediately after applying the frequency response?
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What does the cutoff frequency determine in an image filtering context?
What does the cutoff frequency determine in an image filtering context?
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In the context of edge detection, which operator is represented by the gradient patterns provided?
In the context of edge detection, which operator is represented by the gradient patterns provided?
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Which operation describes the effect of one signal on another in image processing?
Which operation describes the effect of one signal on another in image processing?
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Which mathematical operation is reflected in the notations $∇f(x, y)$?
Which mathematical operation is reflected in the notations $∇f(x, y)$?
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Which of the following describes the role of the Laplacian operator?
Which of the following describes the role of the Laplacian operator?
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What is a significant characteristic of circularly symmetric ideal filters?
What is a significant characteristic of circularly symmetric ideal filters?
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What does the term 'spatial masks' refer to in image processing?
What does the term 'spatial masks' refer to in image processing?
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What is the main purpose of using convolution in image processing?
What is the main purpose of using convolution in image processing?
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In the context of image processing, what does the gradient pattern $G_x$ primarily indicate?
In the context of image processing, what does the gradient pattern $G_x$ primarily indicate?
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When applying an averaging filter, what is the main effect observed on the image?
When applying an averaging filter, what is the main effect observed on the image?
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In the context of image filtering, what does the operation g(x, y) = f(x, y) ⊗ h(x, y) represent?
In the context of image filtering, what does the operation g(x, y) = f(x, y) ⊗ h(x, y) represent?
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Which of the following is considered a high-pass filtering technique?
Which of the following is considered a high-pass filtering technique?
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What is a key difference between correlation and convolution in image processing?
What is a key difference between correlation and convolution in image processing?
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Which type of filter is designed specifically to remove high-frequency noise while preserving essential image details?
Which type of filter is designed specifically to remove high-frequency noise while preserving essential image details?
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What does the Fourier Transform mathematically act like?
What does the Fourier Transform mathematically act like?
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What does the expression $F(u) = R(u) + jI(u)$ represent in the context of Fourier Transform?
What does the expression $F(u) = R(u) + jI(u)$ represent in the context of Fourier Transform?
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What is the purpose of the inverse Fourier Transform?
What is the purpose of the inverse Fourier Transform?
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In the Fourier Transform equation, what does the term $e^{-j2 ext{π}ux}$ represent?
In the Fourier Transform equation, what does the term $e^{-j2 ext{π}ux}$ represent?
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What is the significance of the formula $F(u) = rac{1}{ ext{π}u} ext{sin}( ext{π}uX)e^{-j ext{π}uX}$ in the context of Fourier Transform?
What is the significance of the formula $F(u) = rac{1}{ ext{π}u} ext{sin}( ext{π}uX)e^{-j ext{π}uX}$ in the context of Fourier Transform?
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What mathematical operation is commonly performed in the frequency domain to reconstruct signals?
What mathematical operation is commonly performed in the frequency domain to reconstruct signals?
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What type of output does the Fourier Transform provide regarding a function?
What type of output does the Fourier Transform provide regarding a function?
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Which component in the Fourier Transform indicates the magnitude of frequency?
Which component in the Fourier Transform indicates the magnitude of frequency?
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How does the Fourier Transform relate to frequency content?
How does the Fourier Transform relate to frequency content?
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What does the notation $F^{-1}(F(u))$ denote in Fourier analysis?
What does the notation $F^{-1}(F(u))$ denote in Fourier analysis?
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What is the main goal of histogram equalization in image processing?
What is the main goal of histogram equalization in image processing?
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In the histogram equalization algorithm, what value does 'k' represent?
In the histogram equalization algorithm, what value does 'k' represent?
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What does the cumulative histogram represent in the context of image processing?
What does the cumulative histogram represent in the context of image processing?
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What thresholding technique is described for quantization of an image into black and white?
What thresholding technique is described for quantization of an image into black and white?
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In histogram equalization, what does the equation $k ext{ }← ext{ } INT(CH(k) * ((K-1) / N))$ calculate?
In histogram equalization, what does the equation $k ext{ }← ext{ } INT(CH(k) * ((K-1) / N))$ calculate?
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Which mathematical transformation is used to analyze periodic functions as a sum of sines and cosines?
Which mathematical transformation is used to analyze periodic functions as a sum of sines and cosines?
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What is the significance of the coefficients in the result of a Fourier Transform?
What is the significance of the coefficients in the result of a Fourier Transform?
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What does the term 'gray levels' imply in the context of image processing?
What does the term 'gray levels' imply in the context of image processing?
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How does the inverse Fourier Transform relate to the original signal?
How does the inverse Fourier Transform relate to the original signal?
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Which method is primarily implemented to enhance image contrast through pixel intensity mapping?
Which method is primarily implemented to enhance image contrast through pixel intensity mapping?
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What does histogram thresholding achieve when an image is processed with a threshold of T = 128?
What does histogram thresholding achieve when an image is processed with a threshold of T = 128?
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In image processing, what does an enhanced histogram indicate post-equalization?
In image processing, what does an enhanced histogram indicate post-equalization?
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What does a cumulative histogram allow you to measure?
What does a cumulative histogram allow you to measure?
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What primary pixel operation is performed when using a threshold in histogram thresholding?
What primary pixel operation is performed when using a threshold in histogram thresholding?
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Study Notes
Digital Image Processing
- Course offered by Jean-luc.dugelay at Eurecom
- Course website: https://moodle.eurecom.fr/
- Includes lectures (50%) and labs (50%)
- Topics covered include filtering, histograms, edge detection, segmentation, motion estimation, Hough Transform, mathematical morphology, colors, and 3D image processing.
- Software/libraries used include Matlab/Image, Python, and OpenCV.
Digital Image Processing (DIP) Applications
-
Compression:
- Still images (JPEG)
- Moving images (MPEG)
- Telecom
- Medical Imaging
- Remote Sensing
- Multimedia
- Virtual Imaging
- Analysis and Interpretation
Areas of Study
- Computer Science
- Signal Processing
- Mathematics
- Information Theory
- Optic
- Electronics
- Human Vision
Human Vision vs. Machine
-
Kanizsa Triangle:
- Visual illusion illustrating edge completion
-
Tichener Circles:
- Visual illusion dealing with spatial organisation and perception of circles
- Comparing human perception with machine's interpretation in areas such as these illusions.
Phi Phenomenon
- Illusion of movement arising from rapidly changing stationary objects.
- Example: Light bulbs appearing to move when flashed in sequence.
- Perception disappears above 500 milliseconds between flashes.
- The gap duration affects the perception of motion.
Phi Color
- Subjects report dot color change after a certain time during sequential display.
Beta Movement
- Optical illusion, rapidly changing static images appear to smoothly flow.
- Similar to the Phi phenomenon, but not the same.
- Website: https://thebrain.mcgill.ca
Image Community
- Pictures/Applications: Television, video, medical, ultrasound, remote sensing, multispectrum
- Topics: Compression, segmentation, restoration
- Techniques: Wavelets, mathematical morphology, 3D
Different Types of Images
- Ultrasound Images: Medical images of patient (normal and with deposits in heart).
- Aerial Images: Pictures of city or geographical locations
- Multimedia Images: Pictures of people
Basic Processing Tools
- Filtering
- Histogram
- Edge detection and image segmentation
- Motion estimation (optical flow)
- Hough Transform
- Mathematical Morphology
- Colors
- 3D
Outline
- From 2-D signal to digital images
- Sampling and quantization
- Histograms (probability density)
- Filtering (noise reduction, edge detection)
- Linear/non-linear filtering (median filter)
- Frequency and spatial domain analysis (Fourier Transform)
Sampling & Quantization
- Image sampling: digitizing (x,y) coordinates
- Grey-level quantization: digitizing pixel amplitude.
- Converting continuous 2D signals into discrete matrix representations
Sampling (&Resampling)
- 1-D and 2-D processes for image representation
- Processes of image data conversion and adjustment
Moiré Effects (Aliasing)
- Visual artifact in images, often appearing as distorted patterns
- Due to sampling frequency inadequacies, aliasing distorts.
Image Interpolation and Resampling
- Methods for increasing image resolution (nearest-neighbor, linear)
Image Interpolation and Resampling
- Techniques for adapting images when geometry is affected
- Given pixel values at certain coordinates, methods interpolate for unknown values
Linear Interpolation Formula
- Formula illustrating computation of pixel values in between given picture elements.
- Formula for linear interpolation in terms of x.
2x1D
- Zero-order and first-order spatial domain interpolation
- Calculating output from adjacent input points.
Sub/Over Sampling, Bilinear Interpolation
- Calculation of values between sampled picture pixels
- Sub-pixel precision calculation of picture pixels.
Reconstruction of the Image from Its Samples
- Sampling frequency should reach Nyquist frequency to avoid aliasing.
- Low-pass filtering applied to remove spectral overlaps prior to sampling.
Scalar Quantization
- Method for mapping analog signal (input) levels into discrete output levels.
- Decision and reconstruction levels are discrete.
Histogram (Modifications):
- Equalization: Improves image contrast.
- Stretch: Increases or decreases image contrast.
- Thresholding: Segmenting an image into binary parts based on a threshold value.
- Related to contrast and data representation in images.
Histogram Equalization
- Algorithm: Method for converting image histograms to a more even or specified shape.
- Khoros routine: Specific procedures or steps used in a particular software package.
- Image with improved contrast and distribution of pixel values
Histogram Thresholding
- Technique (often numerical) for creating binary images (typically grayscale)
- Value (average grey-level) determines pixels becoming either black or white.
- Quantization into two levels (black/white).
Fourier Transform (FT)
- Foreword: An introduction to FT and its relation to image processing.
- Analogie: Discussing the similarities between FT and prisms.
- 1D continuous FT: Continuous mathematical formula for computing transform from continuous signal.
- Inverse 1D FT: Continuous mathematical formula for computing the reverse transform.
- Example (1-D FT): Illustrative case, computing from a box function (rectangular) for its representation at different frequencies.
- Example (1-D FT) Cont.: Extending the previous analysis on discrete representations of continuous 1D signals.
- 2D continuous Forward/Inverse FT: Continuous mathematical formulas for 2D data processing.
- Discrete 2D FT (NxN) : Discrete sampling counterparts, and their usage in image manipulations.
- Properties of the FT: Properties like DC value and separability.
- Separability shows the decomposition into 1D transform computations
Fourier Transform (FT) - Magnitude & Phase
- Magnitude: Represents the strength or frequency contribution in the image.
- Phase: Represents the phase shift or timing of the image frequencies.
- Display techniques: Showing magnitudes and phases (sometimes in log scale) of Fourier transforms help analyze the data’s frequency components.
2-D FT example
- Illustrating the concept of the Fourier Transform and its relation to images.
Filtering via FFT
- Lowpass, Highpass, Bandpass, Bandstop: Different filter types and their frequency effects on different input data.
- Cutoff Frequency: Value that distinguishes different frequency bands in the image data.
Low-pass Filtering via FFT
- Symmetric approach for FT transformation in 2D cases
- Use of symmetrical symmetry properties to simplify Fourier transforms between different portions/parts of the data.
Frequencies
- Low: Uniform areas and background.
- High: Edges and sharpness.
- Noise: Often in high frequencies, in cases like sharp edges.
Image Filtering via FFT
- Using Fast Fourier Transform for performing image filtering
- Frequency and Spatial domains used to filter images before inverse transformations.
Convolution Operation
- Concept of convolution and its application in image filtering
- Technique applied to modify picture image elements using weights and kernel.
Direct Low-pass Filtering by Averaging
- Averaging 2x2 and 3x3 filters used for low-pass filtering
- Edge blur effect is a side effect when used on images
Spatial Masks
- Convolution Operation: Operation between an input image and structuring element (filter mask).
- Correlation Operation: Similar to convolution without inverting the structuring element (filter mask).
- Describing filter weights and filter masks in the process of image filtering
Spatial Masks: Example (high-pass filtering (3x3)).
- Applying masks of a particular shape to an image to generate some output image.
Gradient Pattern, Laplacian Pattern
- Spatial gradient patterns for image edge detection
- Laplacian patterns for edge detection or sharpening.
References
- List of books for further studying digital image processing.
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Description
Test your knowledge on vision science with this quiz focused on phenomena like the phi phenomenon and beta movement. Explore the effects of aperture shape, gap duration, and sensory challenges related to illumination patterns. Perfect for students studying psychology and perception.
