Chain Codes. Shape Representation and Description. Signatures. Polygonal Approximations

Transcription

1 Shae Reresentaton and Descrton Reresentaton Matchng or comarng reresentatons for shae recognton Invarance wth resect to nusance arameters Image codng Descrton Classf shaes based on a descrtor Invarance wth resect to nusance arameters 4-drectonal 4 5 Chan Codes drectonal Polgonal Aromatons Sgnatures Defne a olar coordnate sstem wth ts orgn at the centrod of the shae. Parameterze the shae n olar coordnates. 4

2 Seletons Reduce the shae to a seleton. Convert the seleton to an undrected grah. Pel wth one neghbor s an end ont Pel wth two neghbors s a normal ont Pel wth more than two neghbors s a node ont One reresentaton for a grah s an adacenc matr. Use grah matchng algorthms to recognze shaes. Two grahs that have the same structure are sad to be somorhc. Let A and B be the adacenc matrces of two grahs wth the same number of vertces. If there ests a ermutaton matr, P, such that PAP - = B, then A and B are somorhc. Seletons 5 6 Length Number of els n boundar Boundar Descrtors More accurate: multl dagonals b square root of Dameter largest dstance between an two boundar els Chord a lne connectng two boundar onts Maor as the longest chord Mnor as the longest chord that s erendcular to the maor as Boundar Descrtors Basc rectangle bo algned wth the maor as that comletel encloses the shae Mnmum enclosng rectangle smallest bo that comletel encloses the shae Eccentrct the length of the maor as dvded b the length of the mnor as 7 8

3 Shae Numbers The shae number s the normalzed frst dfference chan code. The order, n, of the chan code s the number of dgts n the code. Shae number ma deend uon the orentaton of the grd. Rotate the shae to algn the grd wth the basc rectangle. Fourer Descrtors,,,,,,, a u P s e s e u u P s e u 9 Fourer Descrtors Fourer Descrtors Rotaton: s s e a u e Translaton: s u Scalng: Startng ont: s s e u

4 Fourer Descrtors Fourer Descrtors functon fourer_desc = -4:5; q = 5 * ones (sze ()); = [- -q q]; = [q - -q ]; s = + * ; = length (s) a = fft (s); fgure; sublot (,, ); stem (real (a)); ttle (Real art of Fourer descrtors); sublot (,, ); stem (mag (a)); ttle (Imagnar art of Fourer descrtors); fgure; stem (log ( + abs (a))); ttle (Log magntude of Fourer descrtors); = / + ; fgure; sublot (,, ); lot (fft (a)); ttle (All Fourer descrtors); a((-4):(+4)) = ; sublot (,, ); lot (fft (a)); ttle (Omttng 9 of Fourer descrtors); a((-6):(+6)) = ; sublot (,, ); lot (fft (a)); ttle (Omttng of Fourer descrtors); a((-56):(+56)) = ; sublot (,, 4); lot (fft (a)); ttle (Omttng of Fourer descrtors); Translaton nvarant: gnore a() Scalng nvarant: Normalze usng largest Fourer coeffcent Normalze usng sgnal ower Rotaton and startng ont nvarant: Consder onl the magntude of the Fourer coeffcent Adust rotaton and startng ont to mae two Fourer coeffcents real Perform matchng wth rotaton and startng ont as varables d mn, s s e 4 Comactness: Euler number: Regonal Descrtors ermeter comactness area E C H Teture Statstcal Aroaches (z ) hstogram of el gra levels n regon Mean: n th central moment: Relatve smoothness: Average entro: m R e n L z z L L z z z z n m log z z 5 6

5 " Teture Co-occurrence Matrces Teture Co-occurrence Matrces P oston oerator A co-occurrence matr a number of tmes el wth gra level z occurs n oston P relatve to el wth gra level z A s a square matr wth dmensons equal to the number of gra levels. Accounts for sacal relatonshs between el values Le an enhanced autocorrelaton functon P below and to the rght z z z A Teture Co-occurrence Matrces d Moments Let n be the total number of el ars satsfng P Defne: C n A Element dfference moment of order : ma, c The th moment: Dscretzed: m q f, d d Inverse element dfference moment of order : Unformt: Entro: c c Bnar mage: m m m, S q q f, number of els n S c log c 9

6 # " " # " % d Moments d Moments Centrod: m m m S # m m m S Invarant moments: Central moments:, S Normalzed central moments: # q m & number of els n S 4 d Moments d Moments functon [c,c,h,h] = nvarant_moments (A) A = (A > ); m = sum (sum (A)); = (:sze(a,)) * ones(,sze(a,)); = ones(sze(a,),) * (:sze(a,)); n = fnd (A == ); (n) = ; (n) = ; m = sum (sum ()); m = sum (sum ()); c = m / m; c = m / m; n = fnd (A ~= ); (n) = (n) - c; (n) = (n) - c; mu = sum (sum (.* )); mu = sum (sum (.* )); mu = sum (sum (.* )); eta = mu / m^; eta = mu / m^; eta = mu / m^; h = eta + eta; h = (eta - eta)^ + 4*eta^; 4