27-03-2014, 02:34 PM
Spatial Filtering
Spatial Filtering.ppt (Size: 1.58 MB / Downloads: 18)
Background
Filter term in “Digital image processing” is referred to the subimage
There are others term to call subimage such as mask, kernel, template, or window
The value in a filter subimage are referred as coefficients, rather than pixels.
Basics of Spatial Filtering
The concept of filtering has its roots in the use of the Fourier transform for signal processing in the so-called frequency domain.
Spatial filtering term is the filtering operations that are performed directly on the pixels of an image
Mechanics of spatial filtering
The process consists simply of moving the filter mask from point to point in an image.
At each point (x,y) the response of the filter at that point is calculated using a predefined relationship
Note: Linear filtering
The coefficient w(0,0) coincides with image value f(x,y), indicating that the mask is centered at (x,y) when the computation of sum of products takes place.
For a mask of size mxn, we assume that m-2a+1 and n=2b+1, where a and b are nonnegative integer. Then m and n are odd.
Spatial correlation and convolution
Correlation is a function of displacement of the filter.
A function containing a single 1 with the rest being zeros is called a discrete unit impulse. Correlation of a function with a discrete unit impulse yields a rotated version of a function at the location of the impulse.
To perform a convolution, we need to pre-rotate the filter by 180 degrees and perform the same operation as in correlation.
Smoothing Spatial Filters
Smoothing filters are used for blurring and for noise reduction.
Blurring is used in preprocessing steps, such as removal of small details from an image prior to object extraction, and bridging of small gaps in lines or curves
Noise reduction can be accomplished by blurring