Math3360:Mathematical ImagingLecture2:Image Transformationforlmage ProcessingTheChineseUniversityof HongKong
Math 3360: Mathematical Imaging The Chinese University of Hong Kong Lecture 2: Image Transformation for Image Processing
Recap: What is a digital image?Mathematicaldefinition:A2D (grayscale)digital imageisa2Dfunctiondefined ona2D domain(usuallyrectangulardomain):f:2→Rf(r,y)iscalledthebrightness/intensitylgreylevel(x,y) is the spatial coordinates of the image.Thus,a2Ddigitalimagelooks likethis:[f(1, 1)f(1,2)f(1, N)f(2, 1)f(2, 2)f(2, N)f(c,y) =...'...f(N,N)f(N,1)f(N,2):Eachelementinthematrixiscalled pixel (pictureelement);Usually, 0≤f(r,3) ≤ G-1 and (N = 2", G= 2m)IMAGEPROCESSINGISRELATEDTOLINEARALGEBRA!!
Recap: What is a digital image? ◼ Mathematical definition: ◼ A 2D (grayscale) digital image is a 2D function defined on a 2D domain (usually rectangular domain): ◼ is called the brightness/intensity/grey level; ◼ (x,y) is the spatial coordinates of the image. ◼ Thus, a 2D digital image looks like this: ◼ Each element in the matrix is called pixel (picture element); ◼ Usually, and IMAGE PROCESSING IS RELATED TO LINEAR ALGEBRA!!
Recap: What is a digital image?Mathematical definition of color image:A2D(color)digital imageisa2Dfunctiondefinedona2Ddomain(usuallyrectangulardomain):f :=(fR,fG,fB) : 2→R3fR,fG,fB aretheintensity/brightness/greylevel correspondingtoRGandBrespectively;CombinationofR,G,Bformsthefullspectrumofcolor!WEWILLFOCUSON:Grayscaleimage!
◼ Mathematical definition of color image: ◼ A 2D (color) digital image is a 2D function defined on a 2D domain (usually rectangular domain): ◼ are the intensity/brightness/grey level corresponding to R, G and B respectively ; ◼ Combination of R, G, B forms the full spectrum of color! WE WILL FOCUS ON: Grayscale image! Recap: What is a digital image?
Recap:"Image resolution"?Imageresolution:Recall:Adigitalimagelookslike:f(1, N)[f(1, 1)f(1, 2)f(2, N)f(2, 1)f(2,2)f(a,y)=:...f(N,1)f(N,2)f(N,N)where:0≤f(α,y)≤G-1 (N=2n,G=2m)(N,G)iscalledtheimageresolution.Sometimes,(n,m)isreferredtoasimageresolutionaswell
Recap: “Image resolution”? ◼ Image resolution: ◼ Recall: A digital image looks like: where: ◼ (N,G) is called the image resolution. ◼ Sometimes, (n,m) is referred to as image resolution as well
Recap:Read&WriteimageinMatlab?Keepinmind: imread&imwrite!Please attend TAsession whenyouwill learn MATLABcommandtodo mathematical imaging!
Recap: Read & Write image in Matlab? ◼ Keep in mind: imread & imwrite! ◼ Please attend TA session when you will learn MATLAB command to do mathematical imaging!