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What does the transformation T in pixel processing do?
What does the transformation T in pixel processing do?
In LTI systems, the output is affected by the input's location in the image.
In LTI systems, the output is affected by the input's location in the image.
False
What does LTI stand for in the context of image processing?
What does LTI stand for in the context of image processing?
Linear Time Invariant
In pixel processing, g(x,y) is the result of the transformation T applied to f(x,y). Thus, $g(x,y) = T(f(x,y))$. Here, $f(x,y)$ represents the ______.
In pixel processing, g(x,y) is the result of the transformation T applied to f(x,y). Thus, $g(x,y) = T(f(x,y))$. Here, $f(x,y)$ represents the ______.
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Match the following components with their descriptions in LTI systems:
Match the following components with their descriptions in LTI systems:
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Which of the following best describes a characteristic of LTI systems?
Which of the following best describes a characteristic of LTI systems?
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The response of LTI systems to a weighted sum of inputs is simply the sum of their individual outputs.
The response of LTI systems to a weighted sum of inputs is simply the sum of their individual outputs.
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What signal is typically used as the simplest input for an LTI system?
What signal is typically used as the simplest input for an LTI system?
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What is the output of a linear time invariant (LTI) system for an input sequence x[n] given its impulse response h[n]?
What is the output of a linear time invariant (LTI) system for an input sequence x[n] given its impulse response h[n]?
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The convolution sum allows us to express the output of an LTI system as a weighted sum of shifted unit impulses.
The convolution sum allows us to express the output of an LTI system as a weighted sum of shifted unit impulses.
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What is the procedure used to find the output of an LTI system when given an input sequence and its impulse response?
What is the procedure used to find the output of an LTI system when given an input sequence and its impulse response?
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In an LTI system, the output y[n] can be calculated using the formula y[n] = x[n] ∗ h[n], where ∗ represents __________.
In an LTI system, the output y[n] can be calculated using the formula y[n] = x[n] ∗ h[n], where ∗ represents __________.
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Match the function with its role in LTI systems:
Match the function with its role in LTI systems:
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What does the δ-function do in the context of a discrete-time system?
What does the δ-function do in the context of a discrete-time system?
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The system response for shifted/scaled unit impulses is independent of the nature of the input sequence.
The system response for shifted/scaled unit impulses is independent of the nature of the input sequence.
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What principle allows the output of an LTI system to be summed for each input contribution?
What principle allows the output of an LTI system to be summed for each input contribution?
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Study Notes
Chapter 3: Image Processing
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Contents:
- Pixel Processing
- LTI Systems (Linear Time Invariant) and Convolution
- Linear Image Filters
- Non-Linear Image Filters
3.1 Pixel Processing
- Transforming a pixel's brightness value depends only on its own value, not the values of other pixels.
- It's a mapping of one brightness/color value to another.
- g(x, y) = T(f(x, y)) where:
- F(x,y) is the original pixel value
- g(x,y) is the transformed pixel value
- T is the transformation function
- Examples of transformations:
- f-128
- f+128
- 255-f
- f/2
- f*2
- 0.3f R + 0.6f G + 0.1*f B
3.2 LTI Systems (Linear Time Invariant) and Convolution
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Linearity: The output is scaled by the same amount as the input. Its response to a weighted sum of inputs is equal to the weighted sum of responses to each individual input.
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Time Invariance: The output is delayed the same as the input. Delaying the input to the system delays the output by the same amount of time.
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Unit Impulse Response (h[n]):
- The system output (response) to a unit impulse input δ[n].
- Key for determining the system output for any input (x[n]) through superposition.
- Convolving the input signal (
x[n]) with the impulse response (h[n])
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Convolution:
- A method for determining the output of an LTI system.
- The result (
y[n]) of convolving the input (x[n]) with the impulse response (h[n]) is represented asy[n] = x[n] * h[n]. - Involves calculating scaled and shifted versions of
h[n]for each inputx[k], then adding these results for the output. -
δ[n]is the Kronecker delta function
-
Review of DT Sampling (Shifting) Property:
- The signal
x[n]is essentially a weighted sum of shifted unit impulses:x[n] = Σₖ x[k]δ[n - k].
- The signal
3.3 Linear Image Filters
- Convolution with Discrete Images:
-
h[i,j](impulse response) is the mask, kernel, or filter. - The output of the filter at location [i,j] is calculated through summing the product of corresponding pixels. (
g[i,j] = Σₘ=⁻ᵏⁿ=⁻ᵏ f(i +m, j +n)h(m,n)) - The filter kernel is overlaid on the image, shifted over different positions, multiplied, and the values summed.
- Boundary problems often require padding or reflection to handle border regions accurately.
- Specific examples of kernels are provided, such as a "Box Filter".
- Gaussian kernel is separable
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3.4 Non-Linear Image Filters
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Smoothing:
- Aims to reduce noise (salt and pepper noise).
- Applying a linear filter (Gaussian) can reduce noise but also blurs edges and details within an image.
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Median Filtering:
- A non-linear approach for noise reduction.
- The median of pixel values within a specified neighborhood (window size) is calculated as the new pixel value.
- It's effective at removing isolated noise points without as much blurring.
-
Bilateral Filtering:
- Another non-linear method for preserving edges while smoothing an image.
- Combines the spatial and intensity information related to pixel neighborhood data for calculating the new pixel value.
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Description
Test your understanding of key concepts in image processing, including pixel processing and linear time invariant (LTI) systems. This quiz covers important topics such as convolution and various image filters. Enhance your knowledge of how pixel transformations affect image quality and representation.
