Figure 1. LBP in the field of texture analysis operators.

Transcription

1 L MEHODOLOGY he loal inary pattern (L) texture analysis operator is defined as a gray-sale invariant texture measure, derived from a general definition of texture in a loal neighorhood. he urrent form of the L operator is quite different from its asi version: the original definition is extended to aritrary irular neighourhoods, and a numer of extensions have een developed. he asi idea is however the same: a inary ode that desries the loal texture pattern is uilt y thresholding a neighourhood y the gray value of its enter. he operator is related to many well-known texture analysis methods. he relations and summarized in Figure. Figure. L in the field of texture analysis operators. he Original L he loal inary pattern (L) operator was first introdued as a omplementary measure for loal image ontrast (Ojala et al. 996). he first inarnation of the operator worked with the eight-neighors of a pixel, using the value of the enter pixel as a threshold. An L ode for a neighorhood was produed y multiplying the thresholded values with weights given to the orresponding pixels, and summing up the result (Figure 2). Sine the L was, y definition, invariant to monotoni hanges in gray sale, it was supplemented y an orthogonal measure of loal ontrast. Figure 2 shows how the ontrast measure (C) was derived. he average of the gray levels elow the enter pixel is sutrated from that of the gray levels aove (or equal to) the enter pixel. wo-dimensional distriutions of the L and loal ontrast measures were used as features. he operator was alled L/C. example thresholded weights Figure 2. Calulating the original L ode and a ontrast measure attern L C ( )/5 - (5+2+)/3 4.7

2 Derivation he derivation of the L follows that represented y Ojala et al. (22). Let us define texture as the joint distriution + > image pixels: of the gray levels of ( ) t( g g,..., g ),, p where g orresponds to the gray value of the enter pixel of a loal neighorhood. g p ( p,..., ) orrespond to the gray values of equally spaed pixels on a irle of radius R ( R > ) that form a irularly symmetri set of neighors. Figure 3 illustrates three irularly symmetri neighor sets for different values of and R. Without losing information, Figure 3. Cirularly symmetri neighor sets. g an e sutrated from g p : t( g g g,..., g g )., p Assuming that the differenes are independent of g, the distriution an e fatorized: ( g ) t( g g g g ). t,..., p Sine t ( g ) desries the overall luminane of an image, whih is unrelated to loal image texture, it an e ignored: t( g g,..., g p g ). Although invariant against gray sale shifts, the differenes are affeted y saling. o ahieve invariane with respet to any monotoni transformation of the gray sale, only the signs of the differenes are onsidered: ( s( g g ) s( g g )), t,..., p where s ( x), x, x <.

3 Now, a inomial weight unique L ode: L ( g g ), R s p 2. p p 2 is assigned to eah sign ( ) s g p g, transforming the differenes in a neighorhood into a Non-parametri Classifiation riniple In lassifiation, the dissimilarity etween a sample and a model L distriution is measured with a non-parametri statistial test. his approah has the advantage that no assumptions aout the feature distriutions need to e made. Originally, the statistial test hosen for this purpose was the ross-entropy priniple introdued y Kullak (968) (Ojala et al. 996). Later, Sokal & Rohlf (969) have alled this measure the G statisti: G S M ) 2 S log 2[ S log S S log M ], M where S and M denote (disrete) sample and model distriutions, respetively. S and proaility of in in the sample and model distriutions. is the numer of ins in the distriutions. he G statisti an e used in lassifiation in a modified form: L M ) S log M. M orrespond to the Model textures an e treated as random proesses whose properties are aptured y their L distriutions. In a simple i lassifiation setting, eah lass is represented with a single model distriution M. Similarly, an unidentified sample texture an e desried y the distriution S. L is a pseudo-metri that measures the likelihood that the sample S is from lass i. he most likely lass C of an unknown sample an thus e desried y a simple nearest-neighor rule: C arg min i i L M ). Apart from a log-likelihood statisti, L an also e seen as a dissimilarity measure. herefore, it an e used in onjuntion with many lassifiers, like the k-nn lassifier or the self-organizing map (SOM). he log-likelihood measure works well in many situations, ut may e unstale with small sample sizes. With small samples, the Chi square distane usually works etter (Ahonen et al. 24): 2 χ M ) ( S M ) S + M 2. Almost equivalent auray an e ahieved with the histogram intersetion, with a signifiantly smaller omputational overhead: H M ) min(, ). S M

4 Rotation Invariane o remove the effet of rotation, eah L ode must e rotated ak to a referene position, effetively making all rotated versions of a inary ode the same. his transformation an e defined as follows: { ROR( L, i) i,,..., } ri L, R min, R where the supersript ri stands for rotation invariant. he funtion ( x i) numer x i times to the right ( i < ). ROR, irularly shifts the it inary he onept of uniform patterns was introdued in Mäenpää et al (2). It was oserved that ertain patterns seem to e fundamental properties of texture, providing the vast majority of patterns, sometimes over 9%. hese patterns are alled uniform eause they have one thing in ommon: at most two one-to-zero or zero-to-one transitions in the irular inary ode. o formally define the uniformity of a neighorhood G, a uniformity measure U is needed: U p p p ( G ) s( g g ) s( g g ) + s( g g ) s( g g ). atterns with a U value of less than or equal to two are designated as uniform. For a value an e alulated effiiently as follows: U p ( x) F x xor ROR( x, ), ( p), where x is a inary numer. he funtion ( x i) ( x, i) ROR( x, i) and. F riu F, extrats the i th it from a inary numer x : it inary numer, the U he rotation invariant uniform ( 2 ) pattern ode for any uniform pattern is alulated y simply ounting ones in the inary numer. All other patterns are laeled misellaneous and ollapsed into one value: L riu2, R ( g g ), U ( G ) s p p +, otherwise. 2 In pratie, L is est implemented y reating a look-up tale that onverts the asi L odes into their riu2, R riu2 L orrespondents.

5 Contrast and exture atterns exture an e regarded as a two dimensional phenomenon haraterized y two orthogonal properties: spatial struture (patterns) and ontrast (the strength of the patterns). Rotation invariant loal ontrast an e measured in a irularly symmetri neighor set just like the L: ( g p µ ) 2, R, where g p. p p o VAR µ VAR,R is, y definition, invariant against shifts in the gray sale. A rotation invariant desription of texture in terms of texture patterns and their strength is otained with the joint distriution of L and loal variane, denoted as L VAR. riu 2, R 2, R2 Multi-Resolution L Comining Operators A straightforward way of enlarging the spatial support area is to omine the information provided y N L operators with varying and R values. his way, eah pixel in an image gets N different L odes. he aggregate dissimilarity etween a sample and a model an e alulated as a sum of the dissimilarities etween the marginal distriutions: L N N n L n n ( S, M ), n n where S and M orrespond to the sample and model distriutions extrated y the n th operator. Of ourse, the Chi square distane or histogram intersetion an also e used instead of the log-likelihood measure. Filtering and Cellular Automata he L operator an e omined with multi-sale filtering in a straightforward way. Using Gaussian low-pass filters, eah sample in the neighorhood an e made to ollet intensity information from an area larger than the original single pixel. he length of the final feature vetor soon eomes a limiting fator in using a large numer of different sales. he aility to enode a large neighorhood ompatly while preserving important information is a ruial issue in uilding a multisale extension of the L operator. Cellular automata may provide a solution to this prolem. he relation etween multi-sale L and ellular automata may not e quite ovious. It eomes so if we think of the thresholded irular neighorhoods as one-dimensional irular inary signals. In Figure 4, two L odes are dressed to form the two topmost rows of a two-dimensional pattern. he notation of time in the evolution of the ellular automaton pattern is thus replaed y the radius of the irular neighorhood. Sine the rows are treated irularly, the reakpoint (dashed line) plays no role. his property has an important onsequene: the ellular automata are always invariant with respet to rotation, irrespetive of the L version used as the input signal. Any numer of L sales an e added to the pattern. he prolem of enoding a neighorhood now eomes one of finding a rule that most proaly produed the oserved pattern, i.e. inversion. 8, R

6 he inversion prolem an e solved with a simple algorithm ased on majority voting (Mäenpää 23). Aritrarily large inary neighorhoods an thus e enoded with the input signal ( its) and a ellular automaton rule (eight its). he marginal distriutions of the input signal and the ellular automaton rule ode an e used as a texture desriptor. he L, onatenated with the marginal distriution of the ellular automaton odes dedued from S o-entri L, R odes is denoted y LCA, S. Figure 4. urning a multi-resolution L into a two-dimensional pattern. Opponent Color L he opponent olor L (OCL) operator was developed as a joint olor-texture operator for omparing gray-sale and olor texture features (Mäenpää et al. 22). he mehanism with whih the OCL feature is extrated is motivated y Jain & Healey (998). Also the use of the term opponent olor follows the onvention adopted y them: all pairs of olor hannels are alled opponent olors. In the opponent olor L, the L operator is applied on eah olor hannel separately. In addition, eah pair of olor hannels is used in olleting opponent olor patterns so that the enter pixel for a neighorhood and the neighorhood itself are taken from different olor hannels. Referenes Ahonen, Hadid A & ietikäinen M (24) Fae reognition with loal inary patterns. Computer Vision, ECCV 24 roeedings, Leture Notes in Computer Siene 32, Springer, Jain A & Healey G (998) A multisale representation inluding opponent olor features for texture reognition. IEEE ransations on Image roessing, 7(): Kullak S (968) Information theory and statistis. Dover uliations, New York. Mäenpää (23) he loal inary pattern approah to texture analysis extensions and appliations. Dissertation, Ata Univ Oul C 87, University of Oulu, 78 p + App.

7 Mäenpää, Ojala, ietikäinen M & Soriano M (2) Roust texture lassifiation y susets of loal inary patterns. ro. 5th International Conferene on attern Reognition, arelona, Spain, 3: Mäenpää & ietikäinen M (24) exture analysis with loal inary patterns. In: Chen CH & Wang S (eds) Handook of attern Reognition & Computer Vision, 3rd ed, World Sientifi, Singapore, in press (invited hapter). Mäenpää, ietikäinen M & Viertola J (22) Separating olor and pattern information for olor texture disrimination. ro. 6th International Conferene on attern Reognition, August 5, Vol., Ojala, ietikäinen M & Harwood D (996) A omparative study of texture measures with lassifiation ased on featured distriution. attern Reognition, 29():5-59. Ojala, ietikäinen M & Mäenpää (22) Multiresolution gray-sale and rotation invariant texture lassifiation with loal inary patterns. IEEE ransations on attern Analysis and Mahine Intelligene, 24(7): Sokal R & Rohlf F (969) iometry. W.H. Freeman.