Correlative features for the classification of textural images

Transcription

1 Correlatve features for the classfcaton of textural mages M A Turkova 1 and A V Gadel 1, 1 Samara Natonal Research Unversty, Moskovskoe Shosse 34, Samara, Russa, Image Processng Systems Insttute - Branch of the Federal Scentfc Research Centre Crystallography and Photoncs of Russan Academy of Scences, Molodogvardeyskaya str. 151, Samara, Russa, Abstract. The work s amed to study varous correlatve mage features n order to solve the classfcaton problem of textural mages, wth further selecton of the most nformatve features for ncreasng the relablty of classfcaton. In the present paper seres of experments are performed on a set of 4480 real dgtal mages from the open Kylberg Texture Dataset v A set of programs necessary for computatons was developed. The autocorrelatve mage features are calculated, and the approxmatng coeffcents from the regresson equaton are obtaned. Due to the removal of the least nformatve features, the share of correctly recognzed mages ncreased n 1.04 tmes and amounted to 90.11% for 8 mage classes. 1. Introducton At present, the task of computer vson and, consequently mage recognton, cause a partcular nterest n many areas of scence and technology. Identfyng a number of characterstc features whch help to classfy a texture s essental for the textural mages recognton. A varety of parameters can act as the mage features. Optmal and unversal descrptors development contnues. Among the most common classfcaton sgns for textural mages are morphologcal features, fractal dmenson, Markov s parameters, samples of the autocorrelaton functon and others [1]. At the begnnng of the classfcaton process each mage can be characterzed by a large number of parameters. Snce the classfer for solvng the classfcaton problem s not deal, the error t ntroduces essentally depends on the qualty of the feature space. Thus, for proper classfcaton, t s necessary to reduce the subset of features by removng unnformatve and redundant features, thereby reducng the dmensonalty of the feature set. Usage of the optmal feature subset wll ncrease the relablty, at the same tme reducng the computatonal complexty and tme for classfcaton. Despte the urgency of the data processng problem, an optmal method for dentfyng and selectng features has not been found yet. In paper [] a novel feature selecton strategy resstant to problems wth asymmetrc data and based on Genetc Programmng s proposed. It works well wth both balanced and unbalanced data. The results of the experments made possble reducng the sze of the feature space up to 83%, whch allow one to ncrease the effectveness of the learnng process. More detals about the process of selectng features and usng the samples of the correlaton functon as characterstcs are descrbed n [3]. A two-stage feature selecton approach whch makes full use of nteractons s proposed n [4]. On the frst stage, the problem of feature selecton s decomposed nto the sum of nformaton nteracton. Then, hgher-order nteractons are used to select nteracton-preservng feature subset. On the second stage, the desgn of experments s employed to dentfy sgnfcant nteractons from the subset of

2 features. A flexble algorthm for selectng a subset of features under user control based on clusterng was developed n work [5]. Ths s a two-step hybrd process whch reduces the computatonal complexty of the feature selecton, especally for large sets of features. In [6] the feature selecton s carred out n two stages: n the frst step, the correspondence of each objectve functon feature s evaluated. If the attrbute s rrelevant, then t s dscarded. In the second step, the number of features s mnmzed by removng duplcate or low-performance functons. In [7] the process of selectng features s carred out usng a heurstc evolutonary algorthm, whch s the example of competton n a trbe. The man dea of the method s that only the most sgnfcant sgns wn and partcpate n the classfcaton. In ths paper, there s a data set consstng of dfferent classes of textural mages. A number of features s formed for each mage, based on the readngs of the correlaton functon and the coeffcents from the regresson equatons. A flterng method wth a marked set of tranng data s used for the feature selecton. A measure of the Eucldean dstance s chosen as a search strategy.. Texture descrptors.1. Autocorrelaton functon as a characterstc of a texture mage To form a set of texture mage features we use the often applcable texture descrptor the autocorrelaton functon, as n [8]: 1 ρ(x, y) = I(, j)i( + x, j + y) ( 1 I(, j) ) 1 (1) (N x )(N j y ) N N j j N Nj =1 j=1 where I(, j) pxel value, N N j sze of mage, ρ(0,0) 1 [1]. It was shown n [9] that lnear combnatons of autocorrelaton functon counts are the best sgns n the class of quadratc features. The coeffcents of the autocorrelaton functon determne the relatonshp of the pxels n the mage. As the dstance between ponts ncreases, the correlaton weakens and the value of the coeffcents does not make a sgnfcant contrbuton to the calculatons. Before the study begns, t s necessary to normalze the autocorrelaton functon to get rd of the hgh-frequency nose nfluence. Thus, we obtan an expresson for the coeffcents of the autocorrelaton functon... Regresson equaton coeffcents as a characterstc of the texture mage The autocorrelaton functon ρ(x, y) obtaned n the prevous secton can be unnecessarly complcated for descrbng the texture. However, f the exstng functon s approxmated by a parametrc functon, then ts parameters can be used as a more relable texture descrptor. Suppose that the autocorrelaton functon at a pont (x, y ) s known and s equal to ρ. Let us approxmate a functon by the followng regresson equatons: ρ 1 (x, y) = exp(a 1 x + a y + a 3 ), () ρ (x, y) = exp (b 1 x + y + b ), (3) where a 1, a, a 3, b 1, b the coeffcents to be found. We take the logarthm of () and (3) and obtan: ln(ρ 1 (x, y)) = a 1 x + a y + a 3, (4) ln (ρ (x, y)) = b 1 x + y + b. (5) The total error for (4) and (5), respectvely, s: E 1 = (ln(ρ 1 (x, y )) ρ ) = (a 1 x + a y + a 3 ρ ), E = (ln(ρ 1 (x, y )) ρ ) = (b 1 x + y + b ρ ). It s necessary to select the parameters a 1, a, a 3, b 1, b n such a way for the error to be mnmal. To do ths we take the partal dervatve wth respect to each parameter and equate t to zero, obtanng a system of lnear equatons wth respect to unknown parameters: 15

3 E 1 a 1 = 0 (a 1 x + a y + a 3 ρ )x = 0, E 1 a = 0 (a 1 x + a y + a 3 ρ )y = 0, E 1 { Solvng the resultng system of lnear equatons: a 3 = 0 (a 1 x + a y + a 3 ρ ) = 0. 4 a 1 x + a x y + a 3 x = ρ x, a 1 x y 4 + a y + a 3 y = ρ y, x + a y + a 3 1 = ρ, { we obtan expressons for the coeffcents a 1, a, a 3 that are used n the regresson equaton (). Smlarly, we obtan values for the coeffcents b 1, b from equaton (3) [1]. 3. Expermental studes 3.1. Input data As the nput data set 8 classes of textural mages from the open mage database Kylberg Texture Dataset v. 1.0 are used [10]. Each class contans 160 unque monochrome photographs wthout rotatons measurng pxels. All mages are normalzed wth a mean value of 17 and a standard devaton of 40 (Fgures 1a and 1b). a) b) Fgure 1. Examples of mages on whch experments were performed: seat (a), pearl sugar (b). For each mage a vector of 30 features s constructed. The frst 5 features are formed as the samples of the correlaton functon ρ(x, y) (1), x = 0,, 4 y = 0,, 4 but nstead of the value ρ(0, 0) 1 the count ρ( 1, 1) s used. Features 5-7 are the coeffcents a 1, a, a 3 from the regresson equaton (), 8 and 9 are the coeffcents b 1, b from equaton (3). The form of the regresson equatons () and (3) for the specfc values obtaned durng the computatonal experment s shown n Fgures a-b and 3a-b, respectvely. The values of the coeffcents from the regresson equatons () and (3) are presented n table 1. Table 1. The values of the coeffcents of the regresson equatons for the graphs presented n Fgures 1a and 1b. Coeffcents a 1 a a 3 b 1 b Seat Pearl sugar

4 a) b) Fgure. The graph of the regresson equatons (): for Fgure 1a (a), for Fgure 1b (b) a) b) Fgure 3. The graph of the regresson equatons (3): for Fgure 1a (a), for Fgure 1b (b) Also, the "Class" feld s added to the characterstcs vector, whch has a range of values from 1 to 8 and wll be used for the model tranng. 3.. The scheme of the computatonal experment Before the begnnng of the research t s necessary to scale out the feature set, snce the numercal values are presented n dfferent scales, accordng to the followng formulas. To normalze the sample t s necessary to dvde each feature x nto the sample rate: K x = x ( x k k=1 ) 1/, = 1,, K where K s the total number of features. For standardzaton, we use the formula: x = (x M())R(, ) 1/, = 1,, K where M() s the mean value and R(, ) s the standard devaton. To classfy mages, t s necessary to form a tranng sample. In ths paper we form t accordng to the prncple of leave-one-out cross-valdaton:at each teraton step of the tranng there s a sample of K 1 elements, where K s the total sample sze. Due to ths, we ncrease the accuracy of classfcaton (t s defned as the rato of the number of correctly defned classes to ther total number), although we ncrease the computatonal complexty of the algorthm. We dstrbute an mage wth an unknown class to a partcular group based on the nearest neghbour, fndng the vector closest to the desred vector by the set of characterstcs. Durng the frst computatonal experment we form the tranng sample consstng of the object by the cross-valdaton method. We successvely determne the class of each mage not ncluded n the tranng sample. As a feature set, we use all the 30 features n the frst case, n the second only features wth numbers 0-4, n the thrd 5-9. Durng the second computatonal experment, the tranng sample s formed n a smlar way, but the attrbute space s formed by the full search method 17

5 as a subset of the cardnaltes one and three, as well as the random search method wth capactes of four and fve. To compare the results of computatonal experments we wll classfy the vectors for each mage and evaluate the qualty crteron J, assgned as the proporton of correctly recognzed objects to ther total number. Object classfcaton should be carred out n ts characterstc space, obtaned accordng to the requrements of the computatonal experments descrbed above Results of experments The obtaned results for the classfcaton of texture mages n accordance wth the task of the frst computatonal experment are presented n table. Table. Results of the frst computatonal experment. Number of features Cardnalty Relablty, % Tme, s 0, 1,, , 1,, , 6, 7, 8, Table shows that the hghest proporton of correctly classfed objects s acheved usng a full set of features. However, n ths case, the presence of non-nformatve features s possble, whch wll reduce the relablty of the classfcaton. Also, a large subset of characterstcs sgnfcantly ncreases the computatonal complexty of the algorthm and, as a consequence, ncreases the calculaton tme. Therefore, t s necessary to select features, whch wll reduce re-tranng, ncrease relablty and shorten the classfcaton tme. The most nformatve features for the classfcaton problem were sgns under numbers 4, 0 and 5. The ndvdual qualtes of the fve best attrbutes are gven n table 3. Table 3. Indvdual qualtes of features. Number of features Relablty, % We form feature subsets of cardnalty three by the method of complete enumeraton. The average tme necessary for classfyng the mages usng the generated subsets was 7.36 seconds. Table 4 shows that the frst two best subsets of the features consst of only the samples of the correlaton functon, the thrd one also ncludes a sgn derved from the coeffcent of the regresson equaton. The relablty of the classfcaton usng the most effectve feature subset of cardnalty three s 1.13 tmes lower than the classfcaton usng the full feature set. However, the tme spent on classfcaton s tmes lower. Table 4. The feature selecton result usng a subset of cardnalty three. Number of features Relablty, % 4, 14, , 4, , 19, We use the method of random search to construct subsets of cardnaltes four and fve. The classfcaton usng a feature subset of cardnalty four s 1.05 tmes as low as the classfcaton proposed n the frst computatonal experment. However, when usng a subset of cardnalty fve relablty of classfcaton s 1.04 tmes hgher. 18

6 Table 5 shows that n the formaton of a characterstc subset the most nformatve features also partcpate: n the subset of cardnalty four are the sgn at number four, n the subset of cardnalty of fve, the sgn wth the number zero and four. The average classfcaton tme was and seconds when usng subsets of cardnaltes four and fve, whch gves a gan n tme of and tmes, respectvely. Table 5. The feature selecton results usng subsets of cardnaltes four and fve. Number of features Relablty, % 4, 14, 8, , 14, 19, , 19, 6, ,, 3, 5, ,, 3, 5, ,, 3, 4, Thus, after carryng out seres of experments, the usage of the feature subset of cardnalty fve was the most effectve, wth the help of whch t was possble to acheve a qualty classfcaton of more than 90%. Also the need to reduce feature set by removng the least nformatve ones was confrmed expermentally. 4. Concluson In the recent work, the objects were classfed on the base of the calculated features. A number of features were formed usng the samples of the correlaton functon and the coeffcents from the regresson equatons. The selecton of features was carred out wth the methods of complete and random search. The features that are the most nformatve and necessary n the constructon of the classfer were revealed, they turned out to be the readngs of the correlaton functon ρ(1, 0), ρ(0, 1), ρ(1, 1). Ther ncluson n a varety of attrbutes for further classfcaton wll ncrease ts relablty, allowng one to remove less nformatve features. The features, whch are coeffcents from the regresson equatons, were not among the top ten, whch ndcates ther lttle nformaton n the task of classfyng mages. Among the features that have the least mpact on the classfcaton process, are the coeffcents a 3 and a from the regresson equatons ρ 1 (x, y) = exp (a 1 x + a y + a 3 ) and ρ (x, y) = exp (b 1 x + y + b ), as well as the correlaton functon ρ(0,). The hghest relablty of the mage classfcaton, whch amounted to 90.11% was acheved wth the use of a feature subset of cardnalty fve, whch ncluded the samples of the correlaton functon ρ(0,1), ρ(0,3), ρ(0,4) and the coeffcents a 1 and b from the regresson equatons. In ths way, the hypothess about the need to exclude the least nformatve features from the set was expermentally confrmed. When usng the full set of attrbutes for mage classfcaton, the acheved relablty was 86.83%, whch s 1.04 tmes as low as the maxmum relablty obtaned n the course of the computatonal experment. Also, the tme spent on classfcaton decreased by tmes by reducng the cardnalty of feature set. 5. References [1] Petrou M 006 Image processng: Dealng wth texture (John Wley & Sons, Ltd) [] Vegas F, Rocha L, Goncalves M, Mourao F, Salles T, Andrade G and Sandn I 018 A Genetc Programmng approach for feature selecton n hghly dmensonal skewed Neurocomputng [3] Gadel A V, Zelter P M, Kapshnkov A V and Khramov A G 014 Computed tomography texture analyss capabltes n dagnosng a chronc obstructve pulmonary dsease Computer Optcs 38(4) [4] Tang X, Da Y, Sun P and Meng S 018 Interacton-based feature selecton usng Factoral Desgn Neurocomputng

7 [5] Goswam S, Das A K, Chakrabart A and Chakraborty B 017 A feature cluster taxonomy based feature selecton technque Expert System wth Applcatons [6] Rahmanna M and Morad P 017 OSFSMI: Onlne Stream Feature Selecton Method based on Mutual Informaton Appl. Soft Comput [7] Maa B and Xa Y 017 A trbe competton-based genetc algorthm for feature selecton npattern classfcaton Appl. Soft Comput [8] Gadel A V 015 A method for adjustng drected texture features n bomedcal mage analyss problems Computer Optcs 39() DOI: / [9] Gadel A V 016 Matched polynomal features for the analyss of grayscale bomedcal mages Computer Optcs 40() 3-39 DOI: / [10] Kylberg G 011 The Kylberg Texture Dataset v. 1.0: External report (Blue seres) Centre for Image Analyss, Swedsh Unversty of Agrcultural Scences and Uppsala Unversty 35 Acknowledgments The work was partally funded by the Russan Foundaton of Basc Research grant р_а, by the Federal Agency for Scentfc Organzatons under agreement No. 007-GZ/Ch3363/6 and by the Russan Federaton Mnstry of Educaton and Scence. 0