Lecture 4 - Filters Flashcards

Question

What is Salt and Peper Noise?

Answer 1

Salt and pepper noise: contains random occurrences of black and white pixels

Answer 2

Variations in intensity drawn from a Gaussian normal distribution

Answer 3

- Filtering: Use filters to remove noise - Filters (masks) operate on a neighborhood of pixels. - The sub-image is called a filter (or mask, kernel, template, window). - The values in a filter sub-image are referred to as coefficients, rather than pixels.

Answer 4

- Min: Set the pixel value to the minimum in the neighborhood - Max: Set the pixel value to the maximum in the neighborhood - Average: Set the pixel value to the average of the neighborhoods - Median: The median value of a set of numbers is the midpoint value in that set (e.g. from the set [1, 7, 15, 18, 24] 15 is the median). Sometimes the median works better than the average

Answer 5

- Remove noise - Sharpen contrast - Highlight contours - Detect edges Image filters - linear or nonlinear. - Linear filters are also know as convolution filters - Nonlinear operations such as median filter

Answer 6

- Linearity: filter(f1 + f2) = filter(f1) + filter(f2) - Shift invariance: same behavior regardless of pixel location. - The value of the output depends on the pattern in the image neighborhood, not the position of the neighborhood - filter(shift(f)) = shift(filter(f)) - Any linear, shift-invariant operator can be represented as a convolution - Commutative: a * b = b * a - Associative: a * (b * c) = (a * b) * c - Often apply several filters one after another: (((a * b1) * b2) * b3) - This is equivalent to applying one filter: a * (b1 * b2 * b3) - Distributes over addition: a * (b + c) = (a * b) + (a * c) - Scalars factor out: ka * b = a * kb = k (a * b) - Identity: unit impulse e = [0, 0, 1, 0, 0], a * e = a - Differentiation

Answer 7

One of the simplest spatial filtering operations we can perform is a smoothing operation (remove sharp features) - Simply average all of the pixels in a neighborhood around a central value - Especially useful in removing noise from images - Also useful for highlighting gross detail REFER TO SLIDES FOR EXAMPLE

Answer 8

More effective smoothing filters can be generated by assigning different pixels in the neighborhood different weights in the averaging function - Pixels closer to the central pixel are more important - Reduce smoothing effect - Often referred to as a weighted averaging REFER TO SLIDES FOR EXAMPLES

Answer 9

REFER TO SLIDES WITH FORMULA

Answer 10

- A Median Filter operates over a window by selecting the median intensity in the window. - No new pixel values introduced - Removes spikes: good for impulse, salt & pepper noise - It is not as efficient at averaging away regular Gaussian noise REFER TO SLIDES FOR EXAMPLES

Answer 11

REFER TO SLIDES FOR EXAMPLES

Answer 12

Linear filters Remove “high-frequency” components from the image (low-pass filter) – Images become more smooth Convolution of a Gaussian with a Gaussian is another Gaussian – So can smooth with small-width kernel, repeat, and get same result as larger-width kernel would have – Convolving two times with Gaussian kernel of width 𝜎 is same as convolving once with kernel of width 𝜎sqrt(2) Separable kernels – Factors into product of two 1D Gaussians

Answer 13

REFER TO SLIDES (SHOWS 1D AND 2D)

Answer 14

REFER TO SLIDES Low-pass filtering -> convolve the image with a box / Gaussian filter High-pass filtering -> result equals 0, given a box filter/average filter

Answer 15

Here we take the original image and boost the high frequency components. Can think of HighPass = Original – LowPass. Thus HighBoost = b*Original – LowPass = (b-1)*Original + Original – LowPass = (b-1)*Original + HighPass b is the boosting factor. When b=1, HighBoost = HighPass

Answer 16

– to build an image pyramid, or – simply to reduce the resolution for efficient storage, transmission, processing

Answer 17

1.Sample more often 2.Get rid of all frequencies that are greater than half the new sampling frequency (Nyquist frequency) Disadvantage: Will lose information, But it’s better than aliasing

Answer 18

Apply a smoothing filter

Answer 19

* Key component of many high level computer vision tasks * How to create an image pyramid? * Represent each image as a layer 1. Convolve layer 𝑖 with a Gaussian filter 2. Subsample layer 𝑖 by a factor of two (remove all even-numbered rows and columns) to get layer 𝑖 + 1 * Repeat steps 1 and 2 until a stopping criteria is satisfied

Answer 20

- Finding object of known shape and appearance in an image To identify the object, we have to compare the template image against the source image by sliding it. - At each location, we find the matching score between the image and the template * Sum of Squared Difference (SSD) in pixel values * (Normalized) Correlation coefficient * (Normalized) Cross-correlation

Lecture 4 - Filters Flashcards

(44 cards)