Fast algorithm for skew detection. Adnan Amin, Stephen Fischer, Tony Parkinson, and Ricky Shiu

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1 Fast algorithm for skew detectio Ada Ami, Stephe Fischer, Toy Parkiso, ad Ricky Shiu School of Computer Sciece ad Egieerig Uiversity of New South Wales, Sydey NSW, 2052 Australia ABSTRACT Documet image processig has become a icreasigly importat techology i the automatio of office documetatio tasks. Automatic documet scaers such as text readers ad OCR (Optical Character Recogitio) systems are a essetial compoet of systems capable of those tasks. Oe of the problems i this field is that the documet to be read is ot always placed correctly o a flat-bed scaer. This meas that the documet may be skewed o the scaer bed, resultig i a skewed image. This skew has a detrimetal effect o documet aalysis, documet uderstadig, ad character segmetatio ad recogitio. Cosequetly, detectig the skew of a documet image ad correctig it are importat issues i realisig a practical documet reader. I this paper we describe ew algorithms for skew detectio ad skew correctio. We the compare the performace ad results of this skew detectio algorithm to other published methods from O Gorma, Hids, Le, Baird, ad Postl. Fially, we discuss the theory of skew detectio ad the differet approaches take to solve the problem of skew i documets. The skew correctio algorithm we propose has bee show to be extremely fast, with ru times averagig uder 0.25 CPU secods to calculate the agle o a DEC 5000/20 workstatio. Keywords: skew detectio, documet aalysis, Hough trasform, coected compoets, projectio profile, least square method 1. INTRODUCTION Over the past two decades, may people have attempted to solve the problem of skewed documets usig several differet methods. Applyig the Hough Trasform to a set of poits to determie straight lies i the image has bee a popular approach. Srihari ad Govidaraju 1 use the Hough Trasform o all black pixels, while Hids et al. 2 reduce the data with the use of horizotal ad vertical ru legth computatios. Le et al. 3 apply this trasform oly to the bottom pixels of a coected compoet. A theoretically idetical method is the use of projectio profiles, where a histogram is created at each possible agle ad a cost fuctio is applied to this histogram. The skew agle is the agle at which this cost fuctio is maximised. Baird 4 uses coected compoet aalysis ad creates a projectio profile usig a sigle poit to represet each coected compoet. Postl 5 briefly discusses a method which maximises a give fuctio, called the premium, with respect to the agle by simulatig sca lies. Ishitai 6 detects the skew agle by maximisig the deviatio from the mea of the pixel couts i the projectio profiles. Akiyama ad Hagita 7 describe a method that is extremely fast, where the documet is segmeted ito vertical partitios, ad projectio profiles are created for each partitio. The skew agle is the calculated by determiig the average shift i zero crossigs betwee partitios. Hashizume et al. 8 propose a method that computes the earest eighbour of each character ad creates a histogram of these values to detect the skew agle. Liu et al. 9 use a similar techique to Hashizume et al., i which they detect ad remove the characters with asceders or desceders ad the calculate the icliatio betwee adjacet base poits of coected compoets. These two methods rely o the

2 iformatio that i-lie spacig is less tha betwee-lie spacig. O Gorma 10 discusses skew correctio i the framework of his docstrum aalysis. Here, the skew agle is determied by fidig the earest eighbours for a coected compoet ad determiig the most commo agle betwee eighbourig coected compoets. This method geerally searches for the 5 earest eighbours, which i a ormal situatio will correspod to the coected compoets o either side, above, ad below the coected compoet i questio, as well as oe extra i case there is oise of some sort. O Gorma s method ca be see as a geeralisatio of the previous methods, although the data is used to extract additioal iformatio about the image as well. Two other methods are ot so easily grouped together. Postl 5 uses a 2-dimesioal Fourier trasform, from which the premium fuctio ca the be calculated ad maximised. Smith 11 discusses a algorithm that groups the coected compoets ito lies, movig from left to right across the documet, ad uses a cotiually updated estimate of the skew agle to place compoets i the correct lie Overview 2. NEW SKEW DETECTION ALGORITHM The proposed skew detectio algorithm attempts to determie the skew agle of the etire documet by idetifyig blocks of text, such as paragraphs or captios for pictures, ad calculatig a skew agle for each block. The skew agle for the etire page is the determied by choosig the most frequet agle, after applyig a weightig factor to each agle to accout for the umber of poits used i its calculatio. I each text block, we attempt to isolate the last lie ad determie its agle. We first use the Hough Trasform to estimate the agle, ad the obtai a more precise figure by applyig the Least Squares formula to determie the slope of the lie that best fits the poits used. Sice the Hough Trasform is computatioally expesive, we reduce the amout of data to be used i the calculatio by groupig the pixels ito coected compoets which will geerally represet characters, although oise may break a character ito two or more pieces or joi a group of characters ito oe coected compoet. Completely correct segmetatio of characters is ot vital to the algorithm, ad, ideed, experimets have show that there is a wide margi for error i the segmetatio process where the skew results are uaffected. As the experimetal results later i the paper show, this method is accurate for documets skewed at agles up to 45. At greater agles, the idetified bottom lie may i fact be oe of the edges of the block of text. The other costrait of this method is that it fails i some cases where part of the documet is cut off, because the calculated bottom lie may be i fact simply the bottom-most characters that were scaed. Obviously if there are may blocks o the page, the this costrait will ot be a problem Preprocessig Before ay skew agle ca be calculated, the image must be scaed. I these tests we use images that are scaed at 300 dots per ich (dpi). The test pages were stored as grey-level images so that data loss due to scaig was miimised. Sice most of the algorithms i the experimet were desiged for biary images, where each pixel is either black or white, a global threshold for the image must be chose, separatig the backgroud from the data. We use a modified versio of Otsu s thresholdig method 12, where we create a histogram of all pixel values. After smoothig the histogram, it is ispected for local maxima. I a grey-scale image, there will geerally be two peaks - oe correspodig to the text ad oe correspodig to the backgroud. After fidig these peaks, we apply Otsu s formulas to fid a appropriate threshold poit.

3 2.3. Coected Compoet Aalysis After the preprocessig is completed, the coected compoets must be determied. Coected compoets are rectagular boxes boudig together regios of coected black pixels. The objective of the coected compoet stage is to form rectagles aroud distict compoets o the page, whether they be characters or images. These boudig rectagles the form the skeleto for all future aalysis o the page. The algorithm used to obtai the coected compoets is a simple iterative procedure which compares successive scalies of a image to determie whether black pixels i ay pair of scalies are coected together. Boudig rectagles are exteded to eclose ay groupigs of coected black pixels betwee successive scalies, Figure 1 demostrates this procedure. (a) -- scalie i -- boudig rectagles (b) -- scalies i ad i boudig rectagles (c) -- scalies i, i + 1 ad i boudig rectagles Figure 1: The process of buildig coected compoets from image scalies. Each scalie i Figure 1 is 14 pixels i width (ote that a pixel is represeted by a small rectagular block), the boudig rectagles i Figure 1(a) just eclose the black pixel of that scalie, but for each successive scalie the boudig boxes icrease to iclude the black pixels coected to the previous scalie. Figure 1(c) also poits out that a boudig box stops growig i size oly whe there are o more black pixels o the curret scalie joied oto black pixels of the previous scalie Groupig After the cc's have bee determied the ext step is to group eighbourig coected compoets of similar dimesios. All the cc's of documets fall ito oe of three categories, oise, small or large depedig o their size. The oise cc s are the removed from ay further skew calculatio ad the other cc's are the merged i accordace to the category they fall uder. Mergig requires the use of a prefixed threshold (differet for each category) so as to provide a meas of determiig the eighbourhood of a group. The groupig algorithm takes oe cc at a time ad tries to merge it ito a group from a set of existig groups. If it succeeds the group's dimesios are altered so as to cater for the ew cc, that is the group ecompassig the rectagle is expaded so as to accommodate the ew cc alog with the existig cc's already formig the group. A possible merge is foud whe the cc ad a group (both of the same category) are i close proximity to each other. Whe a cc is foud to be ear a group, its distace from each cc i the group is the checked util oe is foud that is withi the predefied threshold distace or all cc s have bee checked. If such a cc is foud, the the cc is defied to be i the eighbourhood of the group ad is merged with that group. If the cc ca ot be merged with ay of the existig groups the a ew

4 group is formed with its sole member beig the cc which caused its creatio. Figure 2 demostrates the coditios ecessary for a cc to be merged ito a existig group. As ca be see i Figure 2, the small cc (hashed) is merged ito the left group ad the group dimesios icrease to accommodate the ew cc. Both larger cc s are ear the group of large cc s, but oly the lower oe is close to a idividual cc. Therefore, a ew group is created for the upper cc, ad the lower oe is merged ito that group. (a) (b) Figure 2: Mergig criteria of a cc ito a existig group As ca be see from Figure 2(a), the eighbourhood of a group (represeted by the grey shaded regio surroudig each group) is the extet of the regio of ifluece which the group possesses over a cc. I other words if the cc lays withi the group's eighbourhood it is merged ito the group (the dashed rectagles i the group represet previous cc's that have bee successfully merged ito the group). If the cc does ot fall withi the group's eighbourhood the it's ot merged ito the group. Furthermore, cc's from differet categories are ot merged together, thus as ca be see from Figure 2(a) the large (hashed) cc s are ot merged with the group to the right (eve though they fall i its regio of ifluece) sice they are much larger tha the cc's which comprise that group Skew Estimatio To estimate the skew agle for each group, we divide each group ito vertical segmets of approximately the width of oe coected compoet ad store oly the bottom rectagle i each segmet. This process allows us to store primarily the bottom row of text i each group, with other radom coected compoets where there are gaps i the bottom row. We the apply the Hough Trasform to the poit at the cetre of each rectagle, mappig the poit from the (x,y) domai to a curve i the (ρ,θ) domai accordig to equatio (1). ρ = x cos θ + y si θ, for 0 θ < π (1)

5 The Hough Trasform has several iterestig properties: 1. Poits i the (x,y) domai map to curves i the (ρ,θ) domai. 2. Poits i the (ρ,θ) domai map to lies i the (x,y) domai, where ρ is the perpedicular distace of the lie from the origi, ad θ is the agle from the horizotal of the perpedicular lie. 3. Curves that cross at a commo poit i the (ρ,θ) domai map to colliear poits i the (x,y) domai. 13 Whe the Hough Trasform has bee applied to each poit, the resultat graph is examied to fid the poit at which the most curves cross. This poit will correspod to a lie of coected compoets, which should represet the bottom row of text. The extra coected compoets that were mapped ito the (ρ,θ) domai will ot cross at the same poit ad are excluded from further calculatio of the agle Skew Calculatio If more tha oe curve crosses at this poit i the graph, we the determie the slope of a straight lie that best approximates these poits, which represet the coected compoets of the bottom row of text, usig the least squares method. Least squares is a statistical method for fidig the equatio (lie, quadratic, etc.) of best fit give a set of poits. We determie the equatio of best fit for a lie y = a + bx, (2) where the coefficiets a ad b are computed usig the formulae 14 : b = xi yi - x 2 i - x i xi y 2 i (3) a = y i - b x i (4) give that (x i, y i ) is a poit from a set of samples {(x i, y i ), 2,..., )}. Aalogously, the cc's associated with each lie segmet costitute the sample space. Oce agai these cc's are deoted as poits, ad otig that each lie segmet maitais a set of poits, i.e. {(x i, y i ), 2,..., )}, the above equatios are applied to determie the equatio of the lie of best fit for a give lie segmet. Give that the equatio derived is of the form give i equatio (2), we ca determie the agle α which the lie makes with respect to the horizotal by usig equatio (5) α = ta -1 (b) (5) where b represets the gradiet of the lie. The slope of the calculated lie gives the optimal skew agle for the group. After we calculate a agle for each group, we group them i sets of 0.5, weightig the

6 agle by the umber of coected compoets used i its calculatio. We the determie which partitio cotais the most agles, ad average these values to determie the skew agle, α Baird s algorithm 3. OTHER SKEW DETECTION ALGORITHMS Baird s algorithm detects the skew agle by usig the projectio profile techique. The method is said to work o a wide variety of layouts, icludig multiple colums, sparse tables, variable lie spacigs, mixed fots, ad a wide rage of poit sizes. Baird 15 claims that his method is oe of the fastest ad most accurate skew detectio algorithms. First, Baird applies a coected compoet aalysis to the documet. The midpoit of the bottom of each coected compoet is the projected oto a imagiary accumulator lie perpedicular to differet projectio agles. Large coected compoets like images will be igored durig the projectio process; while the other coected compoets such as the characters, character fragmets ad margi oise are projected oto the accumulator lie. Although the oise ad character fragmets are the sources of skew detectio error, Baird claims that they will ot oticeably affectig the detectio of skew agle. For each projectio directio, the sum of squares of the accumulated values of each bi is calculated, although Baird otes that ay positive super-liear fuctio provides the same result. The agle at which the fuctio is maximised correspods to the skew agle. For highest accuracy, he states that the skew agle should be limited to ±15.0. The accuracy depeds o the agular resolutio of the projectio profile Hids et al. algorithm Hids et al. 2 applies the vertical rulegth aalysis for the image. A gray scale burst image is created from the black rulegths that are perpedicular to the text lies by placig the legth of the ru i the ru s bottom most pixel. The Hough trasform is the applied to each of these burst images. Rulegths with values betwee 1 ad 25 are beig applied with the Hough trasform. Ulike the stadard approach of icremetig the accumulator cells by oe, the cells are icremeted by the value of the burst image. Sice the Hough trasform is computatioally expesive ad is slowed by oise, this algorithm reduces the amout of data withi a documet image through the computatio of its vertical black rulegths. This algorithm de-emphasises the oise ad emphasises the cotributio of the bottoms of the lies of text. This method is said to work up to ±45. The accuracy depeds o the agular resolutio of the Hough trasform O Gorma s algorithm O Gorma 10 discusses his skew detectio method as part of a structural page layout aalysis system, which detects the i-lie ad betwee-lie spacigs, ad locates text lies ad blocks as well as calculatig the skew agle. This meas that computig time for determiig skew is ot ecessarily optimum. The method ivolves a bottom-up earest eighbour clusterig. The followig steps take place: 1. Preprocessig is used to remove oise. O'Gorma's ow method to reduce the salt ad pepper oise is the k-fill filter. This removes "small" (determied by chose dimesio of k pixels) regios o text edges ("spurs") or i backgroud ad likewise it fills i small holes. The scheme is iterative ad each iteratio

7 cosists of two subiteratios doig o-fills ad off-fills respectively. Sice the filter is quite slow ad a completely clea documet is ot ecessary for skew estimatio, the filter process was ot used i testig. 2. The ext stage of preprocessig is to fid the coected compoets (cc s). 3. The fudametal stage of this method is to fid the k earest eighbours () for each of the cc s (or more precisely the boudig boxes) ad to form a suitable data structure cotaiig the results. A few prelimiaries are used to speed up the process, such as sortig poiters to cc's i order of x-positios ad cuttig off the search whe the x-distace exceeds the k-th closest distace already foud. The cetroids of each box are used, ad the five earest eighbours are idetified, as recommeded by O Gorma. The reaso is that most commoly (except ear the edges of the image or text areas), the four earest eighbours are those immediately to the left, right, up ad dow directios (imagiig that the image is suitably orieted), ad a fifth is for eve better coverage of the directed eighbours (such as betwee words). Now this data is plotted o a polar diagram usig radial relative distace ad agle (k X poits, where is the umber of cc s) ad it is called the "docstrum" by aalogy with a power spectrum. Now the blob cocetratios o the (almost symmetric) docstrum represet the iter-character spacig alog the lie ad also less itese blobs alog the same axis represet the iter-word spacig, while the blobs alog the perpedicular axis represet the iter-lie spacig. The itegratio of the docstrum over distace ad agle produces two histograms. These are respectively, the agle histogram ad the distace histogram. The agle histogram has a peak ad after suitable smoothig directly gives the first rough estimatio of the skew agle, at least modulo 90 deg. The actual orietatio readily follows due to the text cocetratio properties which appear as two mai peaks o the distace histogram i.e. iter-character spacig is less tha iter-lie spacig ad also the blob itesity is higher alog the lies whe compared to itesity across the lies. I fact, the distace histogram is separated ito two histograms, give the rough skew, so that each has a sigle peak represetig the two basic text spacigs. Note that this method works for ay skew agle, but it does ot distiguish upside dow text. 4. Usig the rough skew, the cc data is rotated to approximately the correct orietatio, ad usig the estimatios of iter-character ad iter-lie spacig, the lie segmets of text are ext costructed. Least squares lies are fitted to the cetroids of the cc's makig up the segmets ad a more accurate skew estimate is made as a correctio to the rough skew. 5. Further costructio gives the text lies from the lie segmets. Agai, least squares lies are fitted to the cetroids to give the fial weighted estimate of the image skew agle Postl s algorithms Postl 5 discusses two methods for skew determiatio. Postl calls his first method the "simulated skew sca" method. It amouts to maximisig a chose cost fuctio as the slope of the projectio profile is varied. The cost fuctio is the total variatio of the projectio profile i.e. the sum of the squares of the successive differeces of the projectio profile bi heights. Postl's secod method ivolves takig a two-dimesioal Fourier trasform of the pixel desity distributio. I practice, this is a discrete trasformatio usig the chose bi widths. The projectio profile ca be expressed as the (sigle) itegral alog the radius vector of the Fourier trasform with a imagiary expoetial kerel. Hece the two cocepts are directly related ad ay suitable cost fuctio ca be employed for the optimisatio ad determiatio of the skew agle. The derivative of the projectio profile correspods to the successive differeces betwee bis i the discrete aalogue of Postl. The power spectrum is give by the magitude of the trasformed fuctio Z squared i.e. Z 2. Postl

8 suggests that the zeroth momet of the power spectrum take alog the radius vector at the chose slope agle, which becomes the sum of squares of the projectio profile bi heights. Put aother way, this cost fuctio is equivalet to the variace of the projectio profile bi heights as the secod cetral momet is obtaied by subtractig the mea squared, which is just a costat. This latter cost fuctio, derived from the Fourier versio suggested by Postl, correspods to a cost fuctio used by may other authors, although without the Fourier coectio Le et al. algorithm This algorithm 3 applies the coected compoet aalysis to the origial image. Large coected compoets, which are classified as images, or small coected compoets, which are classified as oise or character fragmets, are excluded from the calculatio i order to help miimise the skew agle error. Next, it extracts the pixels of the last black rus of each coected compoets. Fially, the Hough trasform is applied to each of these extracted pixels ad the skew agle is chose from the Hough accumulator array by searchig for maxima. This method has bee tested with a large image database which cotais several thousads of images ad claims a accuracy of about EXPERIMENTAL RESULTS Over 120 ucostraied documet images were used i the experimets. These images were chose from a wide rage of sources icludig techical reports, Arabic, Chiese ad Eglish magazies ad busiess documets, busiess cards, Australia Telecom Yellow pages ad badly degraded photocopies. These images cotai a wide variety of layouts, icludig sparse textual regios, dese textual regios, mixed fots, multiple colums, tabular ad eve for documets with very high graphical cotets. Figure 3 shows two sample test images. I additio to our method, we tested the above algorithms by usig 40 ucostraied images, checkig for both speed ad accuracy. The experimet is performed by rotatig the origial uskewed image at several kow agles up to 45 ad the ruig each method to calculate the skew agle. The skew detectio error is the differece betwee the rotatio agle ad the detected skew agle. The time take is measured from the ed of ay preprocessig required, such as thresholdig, to the completio of skew agle detectio. I order to obtai a more accurate measuremet of the processig time, we ra the test 10 times o each image for each algorithm. The miimum of these 10 periods was determied ad used to calculate the average time take i the skew detectio process. A give algorithm was oly tested o agles up to its stated detectio agles, ad algorithms such as O Gorma s docstrum method were oly tested o text images if it was give as a restrictio. Whe testig the algorithms, we compared several factors: CPU speed, the average absolute skew agle error ad the percetage of images whose skew was correctly detected withi The figure of 0.25 was chose because i a documet with 8 poit text, the boudig boxes of lies of text will begi to overlap at about this agle. If the documet is skewed less tha 0.25, documet aalysis methods will almost certaily fuctio properly. I additio, we looked at the percetage of images whose skew was correctly detected withi 0.5 ad 1. Table 1 shows the relative accuracy ad speed for each algorithm. The first colum shows the average speed i CPU secods to calculate the skew agle. The secod colum shows the average absolute deviatio from the theoretical skew agle. The last three colums show the percetage of images for which the skew agle was correctly determied withi 0.25, 0.5, ad 1.0, respectively.

9 Percetage of tests withi error tolerace Average CPU secods Average error < 0.25 degrees < 0.5 degrees < 1 degree LSM (Least Square Method) Baird Le Hids Postl O'Gorma Table 1: Experimetal Results Clearly, Baird s algorithm is faster tha the other methods, ad our method is the secod fastest. Whe comparig accuracy, our algorithm returs the smallest average error of ay tested algorithm. O the other had, Le s algorithm calculated almost 95% of the skew agles withi 0.25, while ours ad D Amato s methods calculated 75% ad 78%, respectively. However, Baird s algorithm does ot perform as well i this area. O Gorma s method did very poorly i computig the skew agle, possibly because of the iaccuracy i calculatig the earest eighbours i the lie. Figure 3 shows a rutime compariso of the algorithms. it ca be see that Postl s method took a log time to determie the skew agle. This aomaly is because the method is highly depedet o a proper threshold calculatio. If the threshold is set high eough that some oise is icluded i the image, the Fourier trasform takes much loger to ru. Other methods are less affected because the oise is filtered out before skew calculatio, primarily by coected compoet aalysis. We are i the process of implemetig additioal algorithms for compariso. We have already implemeted Srihari s method 1 usig the Hough Trasform. Sice this algorithm applies the Hough Trasform to each pixel, we foud it prohibitively slow to test. Furthermore, the algorithm is limited to text images oly. Figure 4 shows two sample images from the test database. 4(a) is a joural article that cotais images ad lie drawigs as well as text. 4(b) is the table of cotets from a magazie, which has multiple fots ad text sizes, pictures ad graphics. Figure 5(a) ad 5(b) illustrates the two images after skew correctio. This rage of images comprise the test images used i this experimet. 5. CONCLUSION This paper preseted a ew skew detectio algorithm. I additio we have implemeted other wellkow published algorithms ad compared them for speed ad accuracy. To date, there has ot bee a method that is both more accurate ad faster tha our algorithm. There is a fudametal tradeoff betwee speed ad accuracy i ay such algorithm, ad we believe that our method maages to balace the two criteria well. Sice we use the Hough Trasform, we ca detect large skew agles i a documet, ad tests show that the method is accurate for agles of up to 45.

10 Ru Times Time (CPU secods) LSM Baird Le Hids Postl O'Gorma Test Images Figure 3: Ru time compariso

11 (a) (b) Figure 4: 2 sample images. 4(a) is skewed at (b) is skewed at (a) (b) Figure 5: Skew corrected images of Figure 4 6. REFERENCES 1. S.N. Srihari ad V. Govidaraju, Aalysis of Textual Images Usig the Hough Trasform, Machie Visio ad Applicatios, Vol. 2, pp , S.C. Hids, J.L. Fisher, ad D.P. D Amato, A Documet Skew Detectio Method Usig Rulegth Ecodig ad the Hough Trasform, Proceedigs, 10th Iteratioal Coferece o Patter Recogitio, pp , 1990.

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