Math 3360: Mathematical ImagingLecture12:Linearfiltering
Math 3360: Mathematical Imaging Lecture 12: Linear filtering
Linearfilter = ConvolutionLinearfilteringofa(2M+1)x(2N+1)imageI(definedon[-M,M]x[-N,N])= CONVOLUTION OF I and HH is called thefilter.Differentfiitercanbeused:MeanfilterGaussianfilterLaplcianfilterVariationofthesefilters(Non-linear)MedianfilterEdgepreservingmeanfilter
Linear filter = Convolution ◼ Linear filtering of a (2M+1)x(2N+1) image I (defined on [-M,M]x[-N,N]) = CONVOLUTION OF I and H ◼ H is called the filter. ◼ Different filter can be used: ◼ Mean filter ◼ Gaussian filter ◼ Laplcian filter ◼ Variation of these filters (Non-linear) ◼ Median filter ◼ Edge preserving mean filter
Linearfilter(o,0)=Hot SpotLinear Filters: convolutionH=tu
Linear filter
Type of filter(b)(a)
Type of filter
In Photoshop=2i=21ZZ1I'(u, v) ←Offset +I(u+i,v+i)Hi,i)Scalej=-2=-2XCustomOKResetLoad.Save口100%-?EreviewQffset:DScale15
In Photoshop