This paper discusses the use of character images to determine the parameters of an image degradation model. The acute angles in character images provide information used to find the model parameters. Three experiments are conducted to evaluate the use of characters. In the first experiment, large quantities of corners from character images are used to investigate how their contribution affects the mean and the standard deviation of the parameter estimators. In the second experiment, we focus on the relationship between the angles of the corners used in estimation and the estimation results. In the last experiment, we examine how likely the text in a common page would offer a reasonable estimation result compared to the results from experiments 1 and 2

Barney Smith, Elisa H.

Yam, Hok S.

Boise State University - ScholarWorks

Boise State UniversityScholarWorksElectrical and Computer Engineering FacultyPublications and PresentationsDepartment of Electrical and ComputerEngineering1-1-2003Estimating Degradation Model Parameters fromCharacter ImagesHok S. YamBoise State UniversityElisa H. Barney SmithBoise State UniversityThis document was originally published by IEEE in Seventh International Conference on Document Analysis and Recognition, 2003. Proceedings. Copyrightrestrictions may apply.Estimating Degradation Model Parameters from Character ImagesHok Sum Yam and Elisa H. Barney SmithElectrical and Computer Engineering DepartmentBoise State University, Boise, Idaho 83725EBarneySmith@boisestate.eduAbstractThis paper discusses the use of character images todetermine the parameters of an image degradation model.The acute angles in character images provide informationused to ﬁnd the model parameters. Three experiments areconducted to evaluate the use of characters. In the ﬁrstexperiment, large quantities of corners from characterimages are used to investigate how their contributionaffects the mean and the standard deviation of the param-eter estimators. In the second experiment, we focus on therelationship between the angles of the corners used in esti-mation and the estimation results. In the last experiment,we examine how likely the text in a common page wouldoffer a reasonable estimation result compared to theresults from experiments 1 and 2.1. IntroductionDegradations in text images affect character recogni-tion. These degradations are typically introduced throughthe bilevel processes of printing and scanning. It is desir-able to have a calibrated model of the document process topredict how a document image will look after beingsubjected to these printing and scanning processes. Thismodel could be used to generate large training sets ofsynthetic characters with the model parameters matched tothe source document. This would ease the burden of handsegmenting and labeling data. A model will also allowresearchers to conduct controlled experiments to improveOCR performance.The degradation model used for this research is convo-lution followed by thresholding [1]. Several methods tocalibrate this model have been proposed [2, 3, 5, 6]. Thesemethods have included using combinatorial experimentsto try every possible parameter value combination andtaking measurements from specialized test charts such as astar sector test chart or large wedges. A more convenientway to calibrate the model would be to directly use char-acter images rather than using specialized test charts. Todo this we need to be able to use characteristics availablein text images. We also need to know how many textimages are needed to get high enough model calibrationaccuracies and whether the characters available incommon documents are likely to have these characteris-tics.In this paper a model parameter estimation method thatuses the corners is applied to corners existing in textimages. Experiments are run to evaluate how many charac-ters are needed to get an estimate within a given conﬁ-dence level. Analysis is also conducted to see whichcorner angle measures, and thus which characters, aremost useful for providing consistent estimators. Thesystem is presented character samples with an occurrencefrequency similar to what would be expected for a page oftext, in order to simulate estimation from a common textpage.2. Estimation from Corner ImagesThe convolution and thresholding model is parameter-ized by two parameters: the width of the point spreadfunction (PSF), w, and the binarization threshold level, Θ.A corner that is deformed by this model is shown in Figure1. The vertex of the corner will become rounded and theedges of the corner will be displaced from their originalpositions, but will remain parallel to the original corneredges. Parameter estimation is done by relating the cornererosion distance to the amount of rounding seen after acorner is degraded. The black corner erosion distance, db,is [3, 5](1)where ESF (Edge Spread Function) is the cumulativemarginal of the PSF, and fb is the greyscale proﬁle of theblurred corner along the bisector, deﬁned as . (2)For any one measurement from a corner with an angle ofmeasure φ, a locus of (w, Θ) points that could haveproduced the measurement will be available. The angle ofthe wedge is needed to determine this locus of points. Thisangle can be measured from the degraded corner becausethe edges in the degraded corner will be parallel to theoriginal corner edges.db w θ φ;,( ) wESF1– θ( )–φ2--  sin------------------------------- f b1– θ w φ,;( )+=f b d0b w φd,;( ) PSF x d0b–( ) yd xdy x φ2--tan=xφ2--tan∫x 0=∞∫=Proceedings of the Seventh International Conference on Document Analysis and Recognition (ICDAR’03) 0-7695-1960-1/03 $17.00 © 2003 IEEEAuthorized licensed use limited to: Boise State University. Downloaded on April 28, 2009 at 16:30 from IEEE Xplore.  Restrictions apply.A white corner on a black background will suffer adegradation similar to the degradation for a black corner.The white corner erosion distance, dw, can be related to theblack corner erosion distance, db, bydw (w, Θ; φ)= db(w, 1-Θ; φ) . (3)These two erosion distances can be combined and theintersection of the loci of (w, Θ) points will yield anunique estimate of the unknown parameters to the model.The noise that is introduced into the image through spatialquantization and sensor noise will yield errors in measure-ments of the erosion distances. Also measurements of theoriginal corner angle may be in error. This yields the needto use erosion distances from many corners and to averagethe intersection locations to decide on a ﬁnal estimate ofthe model parameters.3. Estimation from Character ImagesThree different experiments were conducted to evaluatethe feasibility of using text images to estimate modelparameters. The ﬁrst experiment considers how thenumber of corners used in the estimation process affectsthe ﬁnal parameter estimate. The second experimentconsiders how the angle measure of the corner affects theestimates. The third experiment considers the naturalfrequency distribution of the characters on the page toevaluate whether enough of each corner is likely to beavailable to use in estimation.We restrict our analysis to sans-serif fonts so thatstraight edges meet at the corners. The exact font detailsare not necessary because the angle of the corner ismeasured from the resulting image. The sans-serif fontsgive some a priori information on the general shape of thecharacter and the existence of ‘simple’ corners. The char-acters kvwxyzAKVWXYZ were chosen for use in theseexperiments because they contain acute angles for bothexterior (black) and interior (white) corners. Samples fromthe 12 point font Arial are used in these experiments.We use photo typeset images to separate the effects ofprinting from the effects of scanning. Each page consistsof between 21 and 26 samples of each character. The char-acters were well spaced on the page to aid in segmenta-tion. We scanned a page of text 10 times. Each time, weslightly moved the page (no more than 5 degree skewrange) before it was scanned to make more variation in thesample images. Results in this paper focus on using twodifferent thresholds to convert the grey-scale images tobilevel images. Some characters were not consideredbecause they contained missing pixels inside the characterstrokes or broken strokes. For the threshold 64, 5438 whitecorners and 5288 black corners were generated. For thethreshold 125, 5990 white corners and 6132 black cornerswere generated. Fewer corners were found for threshold64 due to a larger amount of noise resulting in rejectingsome character images. For all thresholds there werenearly equal numbers of black and white wedges.To measure the corner erosion, each corner in the char-acter image was located and lines were ﬁt to the strokeedges. The lines associated with each corner are parallel tothe original stroke if they are sufﬁciently far from thecorner apex, allowing measurement of φ. Sufﬁciently far isdeﬁned by the width of the point spread function, which isnot known. The PSF was assumed to be a bivariate Gaus-sian density function with standard deviation w. Edgepoints at or close to the corner apex were not used to ﬁt thelines. These lines were extrapolated to ﬁnd their intersec-tion and the distance from that intersection point to thenearest pixel in the image is used to measure the erosiondistance db or dw.3.1 Experiment 1: Number of CornersThe ﬁrst experiment was intended to see how thenumber of corners used in estimation affects the mean andstandard deviation of the estimation results. Because char-acter images have more noise from measurement errors(pixel drop out, errors in edge ﬁnding, etc.) than testcharts, using character images requires more samples thanwould be needed if specialized test charts were used. Nbcorners were randomly chosen from the black cornerpopulation, and Nw from the white corner population. Themean of the intersections between Nb black and Nw whiteloci were used to determine the parameter estimate. Thisestimation was repeated 100 times and the average andsample standard deviation of the 100 resulting estimateswere recorded. The values of N that were chosen wereN=Nb=Nw= {5, 10, 20, 50, 100, 200}. Because of the rela-tionship in Equation 3, the loci from white and blackcorners have different orientations.As shown in Figure 2a, the average of the estimates ofthe width of the PSF is nearly constant as N increases. TheFigure 1: A degraded corner will have arounded apex and the edges will be parallel to theoriginal stroke edges. This can occur in threepossible ways relative to the original corner.dbφp1p0φp2Original CornerThree possible Eroded CornersProceedings of the Seventh International Conference on Document Analysis and Recognition (ICDAR’03) 0-7695-1960-1/03 $17.00 © 2003 IEEEAuthorized licensed use limited to: Boise State University. Downloaded on April 28, 2009 at 16:30 from IEEE Xplore.  Restrictions apply.sample standard deviation decreases rapidly as Nincreases. These phenomena can also be found for thebinarization threshold in Figure 2b. A minimum of N=100samples are required to have the standard deviations forestimates of both w and Θ less than 4% of the mean.The width of PSF supposedly remains the same with allthresholds, since the characters were scanned from thesame scanner. However, the estimates at these thresholdsdiffer by about 0.2 pixels. The theory expects somethreshold dependent bias to exist if the assumed PSF shapedoes not match the actual PSF shape of the scanner [3].This small error is negligible. These estimation results willbe used to compare with the next experiment.3.2 Experiment 2: Angle MeasureA study was done to see how using erosion measure-ments from corners of different angle measures wouldaffect the estimation results. The angles were grouped into10 degree ranges. Histograms showing the frequency ofoccurrence of angles in these ranges are shown in Figure3. The frequency for a threshold of 125 is shown, but thehistogram looks similar for other thresholds.Estimates were calculated based on selecting data fromthese ranges. For each pair of ranges, all the black cornersin the range were compared with all the white cornersfrom the other range. The estimation results over all theangle combinations at threshold 125 are shown in Figure4. The cross symbol represents the best guess of the actualPSF width and binarization threshold based on resultsfrom experiment 1. No single angle combination wasfound to be the best indicator of that estimate. Also therewas no predominant bias evident. Use of multiple anglewidths is needed to reach that estimate. Some anglecombinations contribute more than the others. Table 1shows the sample variance in the Nb x Nw intersectionscalculated for each pair of angle ranges. The sample vari-ance on the estimates is low for small white and for largeblack corners.3.3 Experiment 3: Typical PagesIf model parameters are to be estimated from charactersin documents, the availability of suitable data from thesedocuments must be analyzed. The letter occurrencefrequency in English language documents was determinedfrom a sample of 2,194,661 characters gathered fromscientiﬁc and technical documents at ISRI [10]. CharacterFigure 2: Results as N varies. Sample mean and sample standard deviation of (a) PSF width at thresh-olds 64 and 125, (b) binarization threshold at thresholds 64 and 125.(a) (b)Figure 3: Histograms of corner angle occur-rence.Proceedings of the Seventh International Conference on Document Analysis and Recognition (ICDAR’03) 0-7695-1960-1/03 $17.00 © 2003 IEEEAuthorized licensed use limited to: Boise State University. Downloaded on April 28, 2009 at 16:30 from IEEE Xplore.  Restrictions apply.frequencies from our dataset are shown in the Table 2. Inthe same table, the expected number of each character on apage of 1000 characters is estimated.The next experiment was to sample P={1, 2, 5} sets ofcharacters to estimate the expected number of suitablecharacters on P pages of 1000 characters. Each setrandomly selects 56 characters from our dataset with thedistribution in Table 2. All the corners present in these56xP characters were used to estimate the model parame-ters (w, Θ). As shown in Table 2, some characters havehigher frequencies of occurrence than the others. Somecharacters such as K, X, and Z do not occur frequentlyenough so their expected number was set to 1 to assuretheir presence in the sample.This experiment was repeated 100 times. Each set of 56characters contains a total of 211 corners; 109 corners(51.7%) are white and 102 corners (48.3%) are black. Theresults are shown in Figure 5. Again the sample mean doesnot change signiﬁcantly, and the standard deviationdecreases gradually. The averages of the estimates aresimilar to the averages in experiment 1. The width esti-mates differ by 5% and the threshold estimates by lessthan 1%, even though some of the corners that wereneeded to get the original results come from charactersthat occur infrequently.4. ConclusionsThree experiments to estimate scanner parameters usingcharacter images were presented. From these experimentsthe number of corners needed for a ‘good’ estimate of themodel parameters were estimated. A minimum of N=100corners is required to return a good estimation result forthis scanner, noise level and printing process. The effect ofthe angle measure on the estimation value and variancehas also been studied. The corners available from charac-ters on a typical page of text serve as a potential estimationFigure 4: Estimation results obtained by combinations of angle ranges.Line:dashdot 40-50 degree B with each Wdashed 50-60 degree B with each Wsolid 60-70 degree B with each Wdotted 70-80 degree B with each WSymbols:Star 10-20 degree W with each BSquare 20-30 degree W with each BDiamond 30-40 degree W with each BCircle 40-50 degree W with each BTriangle 50-60 degree W with each BPentagon 60-70 degree W with each BHexagon 70-80 degree W with each BTable 1:  Sample standard deviation of estimates as a function of corner angle.Black Corners Black Corners40-50 50-60 60-70 70-80 40-50 50-60 60-70 70-80White Corners10-20 0.256 0.204 0.215 0.211 0.2281 0.1766 0.1731 0.174720-30 0.246 0.184 0.193 0.191 0.2176 0.1576 0.1527 0.153730-40 0.253 0.191 0.200 0.198 0.2182 0.1607 0.1576 0.158640-50 0.336 0.263 0.272 0.266 0.2044 0.1903 0.1929 0.194250-60 0.306 0.239 0.249 0.244 0.2195 0.1979 0.1981 0.199960-70 0.266 0.211 0.219 0.216 0.2350 0.1941 0.1937 0.195670-80 0.321 0.251 0.256 0.251 0.2037 0.1969 0.2079 0.2096σˆw σˆΘProceedings of the Seventh International Conference on Document Analysis and Recognition (ICDAR’03) 0-7695-1960-1/03 $17.00 © 2003 IEEEAuthorized licensed use limited to: Boise State University. Downloaded on April 28, 2009 at 16:30 from IEEE Xplore.  Restrictions apply.mechanism. Calibration of the degradation model from thesource image opens the way for using the degradationmodel to improve character recognition and documentanalysis.5. AcknowledgementPortions of this work were completed with fundingfrom NSF-EPSCoR grant #9720634 and the BSU FacultyResearch Grant program.6. References[1] Henry S. Baird, “Document image defect models,” in H.S.Baird, H. Bunke and K. Yamamoto (eds.), StructuredDocument Image Analysis, Springer-Verlag, June 1992.[2] Henry S. Baird, “Calibration of document image defectmodels,” Proc. of Second Annual Symposium on DocumentAnalysis and Information Retrieval, Las Vegas, Nevada,April 1993, pp. 1-16.[3] Elisa H. Barney Smith, “Optical Scanner CharacterizationMethods using Bilevel Scans,” Ph.D. thesis, RensselaerPolytechnic Institute, December 1998.[4] Elisa H. Barney Smith, “Characterization of Image Degra-dation Caused by Scanning,” Pattern Recognition Letters,Volume 19, Number 13, 1998, pp. 1191-1197.[5] Elisa H. Barney Smith, “Estimating scanning characteristicsfrom corners in bilevel images,” Proceedings SPIEDocument Recognition and Retrieval VIII, Volume 4307,San Jose, CA 2001, pp. 176-183.[6] Elisa H. Barney Smith, “Scanner parameter estimationusing bilevel scans of star charts,” Proceedings Internationalconference on Document Analysis and Recognition 2001,Seattle, WA, 2001, pp. 1164-1168.[7] Tin Kam Ho and Henry S. Baird, “Large-Scale SimulationStudies in Image Pattern Recognition,” IEEE Transactionson Pattern Analysis and Machine Intelligence, Vol. 19, No.10, October 1997, pp. 1067-1079.[8] Theo Pavlidis, Minghua Chen, and Eugene Joseph,“Sampling and Quantization of Bilevel Signals,” PatternRecognition Letters, Vol. 14, July 1993, pp. 559-562.[9] Prateek Sarkar, George Nagy, Jiangying Zhou, DanielLopresti, “Spatial Sampling of Printed Patterns,” IEEETransactions on Pattern Analysis and Machine Intelligence,Vol. 20, No. 3, March 1998, pp. 344-351.[10] ISRI data complements of Tomas Nartkar and Ron Young.Table 2: Character occurrence frequencies in ISRIdataset.CharacterFrequency ofoccurrence in ISRIsample (%)Number of members insample page of 1000charactersk 0.276 3w 0.888 9v 0.891 9x 0.232 2y 1.122 11z 0.107 1A 0.616 6K 0.031 1(force)M 0.562 6W 0.290 3V 0.158 2X 0.006 1(force)Y 0.095 1Z 0.035 1(force)Figure 5: Estimation results as P increases with ISRI character occurrence frequencies.1 2 5 1 2 5Proceedings of the Seventh International Conference on Document Analysis and Recognition (ICDAR’03) 0-7695-1960-1/03 $17.00 © 2003 IEEEAuthorized licensed use limited to: Boise State University. 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Estimating Degradation Model Parameters from Character Images

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Estimating Degradation Model Parameters from Character Images

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