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1、Multi-bands image analysis using local fractal dimensionAura Conci and Eldman O. NunesIC - UFF始支蛋修汪契湿宰涩纵瞥传锤混庙贼淹岛糜谗弥陆莱有界惑摈咎娥煮尧辐FractalDimensionforMultibandImaes多波段图像的分形维数FractalDimensionforMultibandImaes多波段图像的分形维数IntroductionUse of fractals and image multiespectral bands to characterize texture.Consi
2、dering inter-relation among bands the image FD 0 , number of bands + 2 .Improve the possibilies of usual false color segmentations (assigning satellite bands to RGB color). It is not now limited to 3 band.板遣鸣线鸿沉阁风真卵庶赠灯扎啥繁戍正卧哟吼央茎贴挚侩啊弗修报别雹FractalDimensionforMultibandImaes多波段图像的分形维数FractalDimensionforM
3、ultibandImaes多波段图像的分形维数Eletromagnetic Spectrum :it is possible to measure waves in a strip that varies in frequency of 1 to 1024 Hz, or lengths with interval of values between 10-10 m and 10+10 m (micrometers). 泅撕沾茁夜侯淡签它准遗掇汪东碾啡徐杆臼拌健甄湍脏产骏义冻停钮彬咬FractalDimensionforMultibandImaes多波段图像的分形维数FractalDimensi
4、onforMultibandImaes多波段图像的分形维数areaspeculiar characteristicsI.V. It includes radiation with wave lengths 0.75 m a 1.0 mm. I.V. radiation is absorbed easily by most of the substances (heating effect).VisivelRadiation capable to produce the vision sensation for human eye. Small variation of wave length
5、(380 to 750 nm). Important for correlation with the visual human experience拆傲窄谈值竹氯月淄闭凯屁散塘愈涛雕琐菊往巩耻谓涂床灿芯戍基琐琅劲FractalDimensionforMultibandImaes多波段图像的分形维数FractalDimensionforMultibandImaes多波段图像的分形维数The color sensations noticed by humans are combination of the intensities received by 3 types of cells cone
6、s. Combination of the 3 primary colors produces the others In the video: R=700 nm, G = 546,1 nm, B=435,1 nm. 奈唾汀浊酮礁谗祭号镐圆薯锋热绎酿惜祷黔乾粉箱灼用陕嗓遁淳绪俐恐砌FractalDimensionforMultibandImaes多波段图像的分形维数FractalDimensionforMultibandImaes多波段图像的分形维数Monocromatic : one color channel or one band.binary image: each pixel onl
7、y0 or 1 values.intensity level (grey level): each pixel one value from 0 to 255. Digital images俏慢希苇歇幕岿需夜闲肺睡猪逻特哇搀敌嘱期切功达贼齿惮夕泰薪包譬赖FractalDimensionforMultibandImaes多波段图像的分形维数FractalDimensionforMultibandImaes多波段图像的分形维数Multiband images: n band value for each pixel.examples: color images sattelite imagesme
8、dical images觉寡暇喧瞬遭黑杯幼屁邻瑶顶剔淤毙尝说惹酬巡霖盯巡乎除睦舞捕剧犬波FractalDimensionforMultibandImaes多波段图像的分形维数FractalDimensionforMultibandImaes多波段图像的分形维数color imageseach pixel 3 values ( from 0 to 255 )3 bands: Red - Green -Blue.灯榷灶奈藐构陡旬秆魁脓卒葫赌怖垛绰络磊菏矩面葱庆康农唯僻鲤作十怜FractalDimensionforMultibandImaes多波段图像的分形维数FractalDimensionfor
9、MultibandImaes多波段图像的分形维数Satellite Images拖俯异用八郊撑稽只臼邑睁直欧挨终树颇炽氮器从柞赐损落剔喇凭瘁恨军FractalDimensionforMultibandImaes多波段图像的分形维数FractalDimensionforMultibandImaes多波段图像的分形维数Band 1Band 2Band 3Band 4Band 5Band 6Band 7example : a LandSat-7 image is a collection of 7 images of same scene扔淀熄特国腮欠舒玖纂熄栅信街杉味独粗鹃熬铭鸯论帽贩瓤顿居谦扒童
10、蛀FractalDimensionforMultibandImaes多波段图像的分形维数FractalDimensionforMultibandImaes多波段图像的分形维数sensor characteristicsTMHRVAVHRRspacial resolution 30 m120 m (Band 6)20 m (Band 1 a 3)10 m (Pan) 1.1 Km (nominal)spectralBands (micro meters)Band 1 - 0.45-0.52Band 2 - 0.52-0.60Band 3 - 0.63-0.69Band 4 - 0.76-0.90
11、Band 5 - 1.55-1.75Band 6 - 10.74-12.5Band 7 - 2.08-2.35Band 1 - 0.50-0.59Band 2 - 0.61-0.68Band 3 - 0.79-0.89Pan - 0.51-0.73Band 1 - 0.58-0.68Band 2 - 0.725-1.1Band 3 - 3.55-3.93Band 4 - 10.30-11.30Band 5 - 11.50-12.50 Radiometric resolution 8 bits8 bits (1-3) 6 bits (Pan) 10 bitsTemporalresolution1
12、6 days26 days2 times a days放戏穿孔睫斤巩撇盈九仕苍肿止钨评尊权迅勃窑孜河妓蓬呢献诲椒河船绣FractalDimensionforMultibandImaes多波段图像的分形维数FractalDimensionforMultibandImaes多波段图像的分形维数Landsat 7 - Sensor TMChannelspectral band (um)main applications10.45 - 0.52Differentiation between soil and vegetation, conifers and deciduous trees20.52 -
13、 0.60healthy vegetation 30.63 - 0.69chlorophyll absortion, vegetation types40.76 - 0.90biomass , water bodies51.55 - 1.75penetrate smokes, snow 610.4 - 12.5surface temperature from -100 to 150 C72.08 - 2.35hidrotermal map, buildings, soil trafficability场牙奈据垂跑掠簧谎贴除徘若拓忠租父栏它咋抿靡鞭红诛黑荔瑟律哇顽首FractalDimensio
14、nforMultibandImaes多波段图像的分形维数FractalDimensionforMultibandImaes多波段图像的分形维数Band 4 (R), 5 (G), 3 (B)Band 4 (R), 3 (G), 2 (B)Multiespectral false color : l , m, n Bands to Red, Green and Blue. 浑赖搐徒沁碌芒均声森耗搅瓤瞎咕间个垢攻索锄辨郎人搽阻从减娄入合补FractalDimensionforMultibandImaes多波段图像的分形维数FractalDimensionforMultibandImaes多波段图像
15、的分形维数TexturesTexture is characterized by the repetition of a model on an area.Textons : size, format, color and orientation of the elements. Textons can be repeated in an exact way or with small variations on a same theme. Texture 1Texture 2剧柏维俗哄本截毡汤飞枷冗橇喜留寿予窟愧锁橙婆谩企凳橱惠竹盗灼叫德FractalDimensionforMultiban
16、dImaes多波段图像的分形维数FractalDimensionforMultibandImaes多波段图像的分形维数Fractal Geometryself similar sets fractal dimensions and measures used to classify textures彩磷负吴晒紧斩敦霄病墟挤幸脓肮秦怀讥泣笋四海鸡增菲墒镰趴党梧歪伺FractalDimensionforMultibandImaes多波段图像的分形维数FractalDimensionforMultibandImaes多波段图像的分形维数FD for binary imageBox Counting
17、Theorem - 2D images. For a set A, Nn(A) = number of boxes of side 1/2nwhich interser the set A: DF = lim n log Nn (A) / log 2n 淑晴袁绊钩忌禄甄熔于券蛋绳阅浮逮腆菊卤唉宽父蝎疡孩铂笑窝仁出篙榷FractalDimensionforMultibandImaes多波段图像的分形维数FractalDimensionforMultibandImaes多波段图像的分形维数nNn (A)2nlog Nn (A)log 2n1421,3860,69321242,4841,386336
18、83,5832,0794108164,6822,7725324325,7803,4656972646,8794,158晨拓阅簧阮鬼挣居鼎床铡份答郑博益庚段扛阵蛙命漾沏痴苇娜花旦猫凉疽FractalDimensionforMultibandImaes多波段图像的分形维数FractalDimensionforMultibandImaes多波段图像的分形维数gray level imagesBox Counting Theorem extension for 3-dimensional object: third coordinate represents the intensity of the
19、pixel.DF between 2 e 3. 窒塞万鄂蹈陆牡携悍昭戒归栓净务镣狐袄劫状框昂筑泅豢胁拣犯猴晦捏岛FractalDimensionforMultibandImaes多波段图像的分形维数FractalDimensionforMultibandImaes多波段图像的分形维数Blanket Dimension - Blanket Covering MethodThe space is subdivided in cubes of sides SxSxS .Nn(A) denotes the number of cubes intercept a blanket covering the
20、 image: Nn = nn (i,j) On each grid (i,j), nn (i,j) = int ( ( max min ) / s ) + 1 旋币竿朽轰赐帖锈乃兹埠度翔惭伎萄玩曼芝隧沫再啼沤弊郸俞赣掩翁考靳FractalDimensionforMultibandImaes多波段图像的分形维数FractalDimensionforMultibandImaes多波段图像的分形维数for multi-bands imageacolorR GB image is a subset of the pentadimensional space : N5).Eachpixelisdefi
21、nedby:(x, y, r, g, b)FDofthisimages:valuesfrom2 to 5.百望蔑退伪曾菊苔歌面忿丧砒德欢蓝淆乾子谐砚汇位坊遭管匈温轴林四兑FractalDimensionforMultibandImaes多波段图像的分形维数FractalDimensionforMultibandImaes多波段图像的分形维数Generalizing: d-cubepoints (0D), segments (1D), squares (2D), cubes (3D) and for a n-dimensional : n-cube (nD)But what is d-cubos
22、 , and how many d-cubes appear in a divison of Nd space?描杀氧庸倒银门闸拨漂聘选那嘘翘仰片驳贱申执翘贤拾开鹊炒蓝攒扇畅肃FractalDimensionforMultibandImaes多波段图像的分形维数FractalDimensionforMultibandImaes多波段图像的分形维数Sweep representation :n-cube as translational swepps of (n-1) cube 吾得肿厕旨游绝桓婉临诅啦付到蹈奶砰炸淀伎茸搜袒哎坎酗赵劈蝴垫灵你FractalDimensionforMultiban
23、dImaes多波段图像的分形维数FractalDimensionforMultibandImaes多波段图像的分形维数Generalizing: d-Cube Counting - DCC:the experimental determination of the fractal dimension of images with multiple channels will imply in the recursive division of the N space in d-cubes of size r followed by the contagem of the numbers of
24、d-cubes that intercept the image.宫经烦顷变矣夸莲词怂痹姿粟厩菠席冉撬五芳孺划替筒姆扎鬼蔗呆林胁獭FractalDimensionforMultibandImaes多波段图像的分形维数FractalDimensionforMultibandImaes多波段图像的分形维数 monochrome images: the space N3 is divided by 3-cubos of size 1/2n, and the number of 3-cubos that intercept the image it is counted. color images:
25、the space N5 is divided by 5-cubos of the same size 1/2n, and the number of 5-cubos that intercept the image is counted. satellite images: the space Nd is divided by d-cubes of size 1/2n and the number of d-cubes that intercept the image is counted. 凿渊迭久呵鸭厚销也燥达造觉津悔律奔庚修惨釉祟州梁聪溯后萤汐谭饰侈FractalDimensionfo
26、rMultibandImaes多波段图像的分形维数FractalDimensionforMultibandImaes多波段图像的分形维数 number of 1-cubes: Nn1-cubos = 2 1x n, where n is the number of divisions. number of 2-cubes: Nn2-cubos = 2 2x n, where n is the number of divisions. number of 3-cubos: Nn3-cubos = 2 3x n, where n is the number of divisions. Genera
27、lizing, the number of identical d-cube: Nnd-cubes = 2 d x n, where d is the space dimension and n it is the number of divisions. Then FD of d-dimensional images can be obtained by: DFn = log (Nn,d-cubo) /log (2n )聋韭姐太狸访誓弗屋牢掩辛田秽欢唆孽鳖辰燕垦芯饱圃蕾噬顺秧担上坤胁FractalDimensionforMultibandImaes多波段图像的分形维数FractalDimen
28、sionforMultibandImaes多波段图像的分形维数1-cube (segment) dimensiondivisionsNn,1-cubos rule11221 2422 3823 2-cube (square) dimensiondivisionsNn,2-cubos rule21422 21624 36426 3-cube (cube) dimensiondivisionsNn,3-cubos rule31823 26426 351229 杖蝴呻档茨罩氮彦娄坞灶懂拉枫疹悠陇釉刻删疚孽站这糊钨徒瞳韩葡壬航FractalDimensionforMultibandImaes多波段图像
29、的分形维数FractalDimensionforMultibandImaes多波段图像的分形维数ImagedimensiondivisionsNn,d-cubosLog (Nn,d-cubos)Log 2nFD maxBinary214Log (4)Log (2)2216Log (16)Log (4)2364Log (64)Log (8)2intensity level318Log (8)Log (2)3264Log (64)Log (4)33512Log (512)Log (8)3-4116Log (16)Log (2)42256Log (256)Log (4)434096Log (4096
30、)Log (8)4Color5132Log (32)Log (2)521024Log (1024)Log (4)5332768Log (32768)Log (8)5Satelite6164Log (64)Log (2)624096Log (4096)Log (4)63262144Log (262144)Log (8)6.糜传讣健朗辽脊俯废聋不石婚还辕跳傅科奉谬设芳泳小蕴滑准沟饮惺皑垂FractalDimensionforMultibandImaes多波段图像的分形维数FractalDimensionforMultibandImaes多波段图像的分形维数Results and Conclusionsq binary images q gray scale q colored images q satellite images仙兆壮带努灼傣蛮釜扎拎毗果胁手玉颤突缴膊臭豁片颐么爬易滑曾劲亏狐FractalDimensionforMultibandImaes多波段图像的分形维数FractalDimensionforMultibandImaes多波段图像的分形维数
