Linear Filters Flashcards
What is spatial transformation?
Like intensity transformations, but instead selects a general window around the target pixel, and manipulates that instead.
What are some reasons for the use of spatial transformations over intensity transformations?
Images are spatially organised data structures, many important attributes vary slowly across the image, such as :
Object identity, viewed surface orientation, colour, etc…
Processes restricted to a small area have access to more information, but are still likely to consider a single object, surface, illumination pattern etc…
What is image noise?
Noise is small errors in image values
Imperfect sensors can sometimes produce noise
Image compression methods can be lossy - repeated coding and decoding adds more noise
How is noise often modelled?
Recorded value = true value + random noise value
What is Gaussian noise?
Sensors often give a measurement a little off the true value (near the right value, rather than far from it)
This is modelled using a Gaussian, with a mean of 0.
Variance indicates how much noise there is
The level of noise is related to the variance. The higher the variance, the more noise there is present
How can you reduce noise?
If you have multiple images, taking the mean value of each pixel will reduce noise - if you average a large set of estimates of the same pixel, the random noise values will cancel out/be ignored.
What is spatial filtering - convolution?
A filter window is applied to the picture window, to generate a new image. How this is done, is it takes the value at the pixel in the filter window, and multiplies it with the value found at the same location in the picture window. This then produces the new image
What is Gaussian Filtering?
This is convolution with a mask whose weights are determined by a 2D Gaussian function
Higher weight is given to pixels near the source pixel, as these are more likely to lie on the same object as the source pixel
What is a Discrete Gaussian filter?
Restricts us to a square window, and samples the Gaussian function. The result is then normalised so that the filter entries add to 1.
This process approximates the Gaussian with a discrete filter.
What determines how big a filter window should be?
A higher filter will get more pixels per space filtered. Therefore, a higher variance gives more than 98% of the values that we want
What are separable filters?
A separable filter is one which can be ‘pulled apart’ into different segments. For example, a 2D Gaussian filter can be separated into two 1D Gaussian filters, a horizontal and a vertical one.
What makes a separated filter ‘better’?
The separated filter is much more efficient. Example:
Given an NxN image and an n x n filter, we need to do O(N^2 * n^2) operations using a 2D filter
However, applying two n x 1 filters to an N x N image, this takes O(2N^2 x n)
