Chapter2

DigitalImageFundamentalsChapter2

DigitalImageFundamentals2.1ElementsofVisualPerception2.2Light&EMSpectrum2.3ImageSensing&Acquisition2.3.4AsimpleImageFormationModelf(x,y)=i(x,y)r(x,y)i(x,y):illuminationcomponents,0<i(x,y)<∞r(nóng)(x,y):reflectancecomponents,0<r(x,y)<12.4.1BasicConceptinSampling&Quantization2.4.1BasicConceptinSampling&Quantization2.4.1BasicConceptinSampling&Quantization2.4.2RepresentingDigitalImageMatrixor2-DArray2.4.3Spatial&IntensityResolutionSpatialResolutionLinepairsperunitdistanceDots(pixels)perunitdistanceDpi:dotperinchSpatialresolutionisameasureoftheaccuracyordetailofagraphicdisplay,expressedasdotsperinch,pixelsperinch,linesperinch,etc.SpatialResolution

Exercise10inch,1024X768SpatialResolution=?ExerciseDiagonallength=10inch2.4.3Spatial&IntensityResolutionIntensityResolutionIntensityLevelUsuallyisanintegerpoweroftwo8bitsHDMI

1.3

support10bits,12bits,16bitsforeachcolorcomponent(channel)IntensityResolutionIntensityResolutionHowtogetn-bitsimage?7bit6bit5bit4bit3bit2bit1bit0bit007bit6bit5bit4bit3bit2bit7bit6bit5bit4bit3bit2bit00>><<IntensityResolution[Programming]Exercise:byte[,]get_n_bits_image(byte[,]f,intn);2.5SameBasicRelationshipbetweenpixels2.5.1Neighborsofapixel2.5.1Neighborsofapixelp:(x,y)4-Neighborsofp:N4(p)={(x+1,y),(x-1,y),(x,y+1),(x,y-1)}2.5.1Neighborsofapixelp:(x,y)D-Neighbors(Diagonal-Neighbors)ofp:ND(p)={(x+1,y+1),(x-1,y+1),(x+1,y-1),(x-1,y-1)}2.5.1Neighborsofapixelp:(x,y)8-Neighborsofp:N8(p)=N4(p)UND(p)2.5.2Adjacency,Connectivity,RegionandBoundariesAdjacencyBinaryimage:Intensity{0,1}Usually0meansbackgroundand1meansforeground

0000000000000000000110000011110000111100001111000000000000000000AdjacencyBothpandqareintheforeground(V:{1})4-adjacency:qinN4(p)8-adacency:qinN8(p)m-adjacency(mixedadjacency)qinN4(p)orqinN8(p)andthesetN4(p)∩N4(q)hasnopixelswhosevaluearefromV(V:{1})Adjacencym-adjacency(mixedadjacency)qinN4(p)orqinN8(p)andthesetN4(p)∩N4(q)hasnopixelswhosevaluearefromV(V:{1})00000011010001m-Adjacencyp:(yellow),q:(green)BluebackgroundpixelmeanssetN4(p)∩N4(q)m-adjacency(mixedadjacency)qinN4(p)orqinN8(p)andthesetN4(p)∩N4(q)hasnopixelswhosevaluearefromV(V:{1})00000000000000000000000000000m-Adjacencyp:(yellow),q:(blue)BluebackgroundpixelmeanssetN4(p)∩N4(q)m-adjacency(mixedadjacency)qinN4(p)orqinN8(p)andthesetN4(p)∩N4(q)hasnopixelswhosevaluearefromV(V:{1})00000[Programing]boolIs_4adjacent(intpx,intpy,intqx,intqy);boolIs_8adjacent(intpx,intpy,intqx,intqy);BoolIs_m_adjacent(byte[,]f,intpx,intpy,intqx,intqy);DigitalPathDigitalPathfrompixelptopixelqisasequenceofdistinctpixelswithcoordinates(x0,y0),(x1,y1),…,(xn,yn)where(xi-1,yi-1)and(xi,yi)areadjacent,i:[1..n]DigitalPathp6p7p8p9=qp5p4p3p2p1p0=pDigitalPath(Closed)p6p7p8p9p5p10p4p11p3p12p2P13=qp1p0=pConnectedSet(Region)ConnectedSet(Region)qqpPS2S1AdjacentRegionsIfRiURjisaconnectedset,RiandRjaraadjacentregions.RjRiDisjointRegionsNotAdjacentForeground/BackgroundBFForeground/BackgroundKdisjointregions,Rk,k=1,2,..,KRu=R1UR2U…URK(Ru)c,cmeanscomplementForeground:RuBackground:(Ru)cForeground/BackgroundB:(Ru)cF：RuBoundary(Border/Contour)ofRegionInnerBorderofRegionB(in)={(x,y)|(x,y)∈R,(x,y)adjacentto(R)c}p4p5P6p7p8P3p9P2p12p11p10P1p13p0p15p14Exercise:

byte[,]getInnerBorder(byte[,]f)Intput:fisabinaryimage,0meansbackgroundand255meansforeground(regions)Output:binaryimage.255meansinnerbordersoftheregionsininputimageBoundary(Border/Contour)ofRegionInnerBorderofRegionExercise:

byte[,]getOuterBorder(byte[,]f)OuterBorderofRegionB(out)={(x,y)|(x,y)∈(R)c,(x,y)adjacenttoR}Exercise:

byte[,]getOuterBorder(byte[,]f)Intput:fisabinaryimage,0meansbackgroundand255meansforeground(regions)Output:binaryimage.255meansouterbordersoftheregionsininputimage2.5.3DistanceMeasureDistanceFunctionp(x,y),q(s,t),z(u,v)D(p,q)≥0,D(p,q)=0iffp=qD(p,q)=D(q,p)D(p,z)≤D(p,q)+D(q,z)2.5.3DistanceMeasureEuclideandistance[Eu’cl[ai]dean] 2.5.3DistanceMeasureCity-blockdistanceD4(p,q)=│x-s│+│y-t│;p:(x,y),q(s,t)2.5.3DistanceMeasureChessboarddistanceD8(p,q)=max(│x-s│,│y-t│) chessman:king2.5.3DistanceMeasureChessboarddistanceqPExerciseMax(De,D4,D8)=?Min(De,D4,D8)=?D4(p,q)=│x-s│+│y-t│D8(p,q)=max(│x-s│,│y-t│)Exerc