A Comparative Study of Color Edge Detection Techniques

Transcription

1 CS31A WINTER-1314 PROJECT REPORT 1 A Comparative Study of Color Edge Detectio Techiques Masood Shaikh, Departmet of Electrical Egieerig, Staford Uiversity Abstract Edge detectio has attracted the attetio of may researchers ad is oe of the most importat areas i low level computer visio. I recet years, the focus of edge detectio has shifted from grayscale sigle compoet images to multicompoet color images that utilize the iter-spectral correlatio of the eighborig color samples to elimiate color artifacts ad icrease the accuracy of edge detectio process. This project presets the study of color edge detectio based o vector order statistics operators. Variatios are itroduced i the vector order statistics color edge operator to improve oise performace ad we demostrate their ability to atteuate oise with added algorithm complexity. We preset a performace evaluatio framework to assess the quality of color edge detectors ad compare it with the Cay edge detector which is the optimal edge detector used for grayscale images. The edge detectors are evaluated with subjective ad objective tests usig statistical idices by comparig it with huma groud truth images extracted from the BSDS300 dataset. Idex Terms color edge detectio, computer visio, vector techiques, performace evaluatio 1 INTRODUCTION T he capability to idetify ad segmet edges alog with texture regios i a image is critical to the aalysis of atural scees. It has bee kow for a log time that edges cotai most of the iformatio i a image while beig represeted far more compactly tha the image itself. For this reaso edge detectio is perhaps the most basic (ad therefore most widely studied) problem i computer visio. It is theorized [1] to be the first step i cotour detectio ad image segmetatio, the partitioig of a image ito meaigful regios, which ca the be aalyzed idepedetly to recogize differet parts of a scee, ad hopefully the cotext of the scee as a whole. The subject of color image processig i computer visio has gaied icreasig attetio recetly because color images covey more iformatio about objects i a scee tha gray-scale images ad this iformatio ca be used to further refie the performace of a imagig system. The multicompoet ature of a color image, however, adds cosiderable complexity to the processig system. Oe of the challeges facig color image processig is to extract the additioal color iformatio without icurrig large complexity i the system. I moochrome images, a edge usually correspods to object boudaries or chage i physical properties of the image such as (illumiatio) lumiace. I this sese, a color image (multi-spectral) cotais more detailed edge iformatio. Moreover, edge detectio with moochromatic images may fail i certai applicatios sice o edges will be detected i moochrome images if eighborig objects have differet hue ad saturatio while their itesity values are same. Psychological research has cocluded that color plays a importat role i decidi object ad scee cotours i huma visual system []. Sice the capability to distiguish betwee differet objects is crucial for applicatios such as object recogitio image segmetatio ad scee uderstadig, the additioal boudary iformatio provided by color is of paramout importace. Color edge detectio also outperforms moochrome edge detectio i low cotrast images [3]. There is thus a strog motivatio to develop efficiet color edge detectors that provide high quality edge maps. Numerous approaches of differet complexities to color edge detectio have bee proposed. I this project we preset the study of color edge detectors based o vector order statistics class [4]. It is importat to idetify their stregths ad weakesses i choosig the best color edge detector for a applicatio. The major performace issues cocerig edge detectors are their ability to extract edges accurately, their robustess to oise, ad their computatioal efficiecy. To provide a fair assessmet, it is ecessary to have a set of effective performace evaluatio frameowork. Though umerous evaluatio methods for edge detectio have bee proposed, there has ot bee ay stadardized objective or subjective evaluatio method. While objective evaluatio ca provide aalytical data for compariso purposes, it is ot sufficiet to represet the complexity of the huma visual systems. I most computer visio applicatios, huma evaluatio is the fial step. Hece i this project, both types of evaluatio methods are utilized for comparig various edge detectors. We start with a overview of techiques used i moochrome edge detectio i Sectio. The edge detector illustrated ad described i this sectio is the Cay Edge Detector [5] which is the optimal edge detector ad the most widely used for moochrome images. Sectio 3 gives a overview of color edge detectio techiques, where early approaches exteded from moochrome Staford Uiversity

2 CS31A WINTER-1314 PROJECT REPORT edge detectio, as well as more recet vector space approaches ad differece vector approaches [6] are addressed. Color edge detectio based o vector-order statistics method [4] ad a family of edge detectors based o this class is studied i detail i Sectio 4. Sectio 5 gives details of quatative performace evaluatio procedure usig BSDS300 [7] dataset for statistical evaluatio of edge detectors. The evaluatio results from both objective ad subjective tests are listed i Sectio 6 followed by our coclusios i Sectio 7. MONOCHROME EDGE DETECTION I moochrome grayscale images, edges are commoly defied as sharp itesity discotiuities, as physical edges ofte coicide with places of strog illumiatio ad reflectio chages. Hece the most commo method of edge detectio i gray-scale images use some form of differetial operators that detect itesity discotiuities. Aother group of gradiet-based edge operators locates a edge by fidig the zero crossig of the secod derivative of the image itesity fuctio. The zero crossig carries the iformatio about the local extremum of the first derivative ad idicates a poit of rapid chage of the itesity fuctio. By detectig zero crossigs, edges of oe pixel thickess ca be obtaied, which is hardly possible with the differetial based methods..1 Cay Edge Detectio Algorithm The Cay Edge Detector proposed by Joh F. Cay i 1986 [5] is oe of the most widely used image processig tools i computer visio for detectig edges i moochrome images. The algorithm rus i 5 separate steps: 1. Smoothig Images take from a camera will cotai some amout of oise. To prevet that oise to be mistake for edges, oise must be reduced. Therefore the image is first smoothed by applyig a Gaussia filter. The kerel of a Gaussia filter with a stadard deviatio of σ = 1.4 is show i Equatio (1) g (1) Fidig Gradiets The Cay algorithm basically fids edges where the grayscale itesity of the image chages the most. These areas are foud by determiig gradiets of the image. The gradiet of the image f(x, ca be computed by covolvig it with the first derivative of the the Gaussia filter used i step 1 i x ad y directios as give by equatio () ad (3) x x y f x ( x, f ( x, exp () y x y f y ( x, f ( x, exp (3) The gradiet magitudes (also kow as the edge stregths) ca the be determied as a Euclidea distace measure as show i Equatio (4). It is sometimes simplified by applyig Mahatta distace measure as show i Equatio (5) to reduce the computatioal complexity. The Euclidea distace measure has bee used i our implemetatio. x y f f ( x, f ( x, (4) f f ( x, f ( x, (5) x y Image of the gradiet magitude ofte idicate the edges quite clearly. However, the edges are typically broad ad thus, do ot idicate exactly the orietatio of the edge. To determie this, the directio of the edges must be computed as show i Equatio (6). f y ( x, arcta (6) f ( x, x 3. No-Maxima Suppressio The purpose of this step is to covert the blurred edges i the image of the gradiet magitudes to sharp edges. Basically this is doe by preservig all local maxima i the gradiet image, ad deletig everythig else. The algorithm for each pixel i the gradiet image is: a. Roud the gradiet directio to earest 45 degree correspodig to the use of 8- coected eighborhood. b. Compare the edge stregth of the curret pixel with the edge stregth of the pixel i the positive ad egative gradiet directio, i.e. if the gradiet directio is orth (Theta = 90 degree), compare with pixels i orth ad south. c. If the edge stregth of the curret pixel is largest; preserve the value of the edge stregth. If ot, suppress (i.e. remove) the value. 4. Mi-Max Thresholdig The edge-pixels remaiig after the o-maximum suppressio step are (still) marked with their stregth pixel by pixel. May of these will probably be true edges i the image, but some may be caused by oise or color variatios for istace due to rough surfaces. The simplest way to discer betwee these would be to use a threshold, so that oly edges stroger that a certai value would be preserved. The Cay edge detectio algorithm uses mimax thresholdig. Edge pixels stroger tha the max threshold are marked as strog; edge pixels weaker tha the mi threshold are suppressed ad edge pixels betwee the two thresholds are marked as weak.

3 MASOOD SHAIKH: A COMPARATIVE STUDY OF COLOR EDGE DETECTION TECHNIQUES 5. Hysteresis Edge Trackig Strog edges are iterpreted as certai edges, ad ca immediately be icluded i the fial edge image. Weak edges are icluded if ad oly if they are coected to strog edges. The logic is of course that oise ad other small variatios are ulikely to result i a strog edge (with proper adjustmet of the threshold levels). Thus strog edges will (almost) oly be due to true edges i the origial image. The weak edges ca either be due to true edges or oise/color variatios. The latter type will probably be distributed idepedetly of edges o the etire image, ad thus oly a small amout will be located adjacet to strog edges. Weak edges due to true edges are much more likely to be coected directly to strog edges. Edge trackig is implemeted by groupig the edge pixels ito a group of 8-coected eighbourhood. The group that cotais atleast oe strog edge pixel is preserved, while other groups are suppressed. Figure 1 shows the output of various stages of the Cay edge detectio algorithm applied o the moochrome (lumiace) compoet of a color image take from the BSDS300 dataset. (a) (b) 3.1 Techiques exteded from moochrome edge detectio I a moochrome image, a edge is defied as a itesity discotiuity. I the case of color images, the additioal variatio i color must also be cosidered. Early approaches to color edge detectio are extesios of moochrome edge detectio. These techiques are applied to the three color chaels idepedetly ad the the results are combied usig certai logical operatio. Several stadard techiques ca be applied i this way [8]. Oe of the represetative classes of edge detectio is the Sobel operator. It ca be realized by covolvig the image with the followig two covolutio masks: g x g y These two masks are applied to each color chael idepedetly ad the sum of the squared covolutio gives a estimated gradiet i each chael. A pixel is regarded as a edge poit if the maximum of the gradiet magitude values i the three chaels exceeds a predetermied threshold. Aother operator that ca also be used i a similar fashio is the eight-eighbor Laplacia operator [8]. The Laplacia covolutio mask is defied as follows: g 18 (7) Agai, the Laplacia mask is applied to the three color chaels idepedetly ad edge poits are located by thresholdig the maximum gradiet magitude. Aother group of edge detectors commoly used i moochrome edge detectio is based o secod derivative operators, ad they ca also be exteded to color edge detectio i the same way. A secod derivative method ca be implemeted based o the precedig operator. The Mexica hat operator uses covolutio masks geerated based o the egative Laplacia derivative of the Gaussia distributio: (c) (d) x y x y f ( x, exp 6 (8) (e) Fig. 1. (a) Origial image 1003.jpg (481x31) from BSDS300. (b) Gray-scale Gaussia filtered image (c) Gradiet of the Gaussia filter output. (d)norm of the Gradiet. (e) After o-maxima suppressio ad hysteresis trackig (f) Groud truth image. 3 OVERVIEW OF COLOR EDGE DETECTION TECHNIQUES (f) Edge poits are located if zero-crossig occur i ay oe color chael. Oe commo problem with the precedig approaches is that they failed to take ito accout the correlatio amog the color chaels, ad as a result, they are ot able to extract certai crucial iformatio coveyed by color. For example, they ted to miss edges that have the same stregth but i opposite directio i two of their color compoets. Cosequetly, the approach to treat the color image as vector space has bee proposed. 3. Vector Space Approach Various approaches proposed cosider the problem of color edge detectio i vector space. Color images ca be viewed as a -D three-chael vector field [9], which ca be characterize by a discrete iteger fuctio f(x,. The value of this fuctio at each poit is defied by a 3-D

4 4 CS31A WINTER-1314 PROJECT REPORT vector i a give color space. I the RGB color space, the fuctio ca be writte as f(x, = (R(x,, G(x,, B(x,), where (x, refers to the spatial dimesios i the -D plae. Most existig edge detectio algorithms use either first or secod differece betwee eighborig pixels for edge detectio. A sigificat chage gives rise to a peak i the first derivative ad zero-crossig i the secod differece, both of which ca be idetified fairly easily. Some of these operators are cosidered i the followig Vector Gradiet Operators The vector gradiet operator employs the cocept of a gradiet operator [10], except that istead of scalar space the operator operates i a -D three-chael color vector space. There are several ways of implemetig the vector gradiet operator. Oe simple approach is to employ a 3 x 3 widow cetered o each pixel ad the obtai eight distace values (D 1, D,..., D8) by computig the Euclidea distace betwee the ceter vector ad its eight eighborig vectors. The vector gradiet Γ is the chose as max : k,...8 D k Aother approach called vector directioal gradiet employs directioal operators [11]. Let the image be a vector fuctio f(x, = (R(x,,G(x,,B(x,), ad let r, g, ad b be the uit vectors alog the R, G, ad B axes, respectively. The horizotal ad vertical directioal operators ca be defied as: R G B u r g b (10) x x x R G B v r g b (11) y y y g xx g yy g xy R G B u u (1) x x x R G B v v (13) y y y R R G G B B (14) x y x y x y The the maximum rate of chage of f ad the directio of the maximum cotrast ca be calculated as: 1 g xy arcta (15) g g xx yy g g cos g g 1 F( ) xx yy xx yy gxy si (16) Edges ca the be obtaied by thresholdig [F(θ)] 1/. This approach of vector gradiet operator was further exteded by Ruzo ad Tomasi [1] i their compass operator, where it was assumed that edges occur whe there are local statistical differeces i the distributio of color image samples. To locate edges, a circular operatio mask, (9) called a compass, which measures the differece betwee the distributios of the pixels betwee two halves of a circular widow, is utilized. The orietatio producig the maximum differece is the directio of the edge, ad the differece betwee the distributios yields a measure of the edge stregth. Ulike the gradiet operator exteded from the metioed moochrome edge detectio, the vector gradiet operator ca extract more color iformatio from the image because it cosiders the vector ature of the color image. O the other had, the vector gradiet operator is very sesitive to small texture variatios. This may be udesirable i some cases sice it ca cause cofusio i idetifyig the real objects. The operator is also sesitive to Gaussia ad impulse oise. 3.3 Differece Vector Operators The class of differece vector operators [6] ca be viewed as first derivative like operators. This group of operators is extremely effective from the poit of view of the computatioal aspects. I this approach, each pixel represets a vector i the RGB color space, ad a gradiet is obtaied i each of the four possible directios (0, 45, 90, ad 135 degree) by applyig covolutio kerels to the pixel widow. The a threshold ca be applied to the maximum gradiet vector to locate edges. The gradiets are defied as: f (17) Y 0deg 0deg X0deg f (18) Y 90deg 90deg X90deg f (19) Y 45deg 45deg X45deg f (0) Y 135deg 135deg X135deg DV max f f (1), f, f, 0 deg 90deg 45deg 135deg where. deotes the L orm, ad X ad Y are three dimesioal vectors used as covolutio kerels. The variatios i the defiitios of these covolutio kerels give rise to a umber of operators. The basic operator of this group employs a 3 x 3 widow ivolvig a ceter pixel ad eight eighborig pixels. Let each pixel deote v(x,, ad the covolutio kerels for the ceter pixel v(x0,y0) i all four directios are defied as: X 0deg ( 1 0 0deg 1 y0 v x, y ), Y v( x, ) () X v x, y ), Y v( x, y ) (3) X 45deg ( deg deg ( deg 0 y1 v x, y ), Y v( x, ) (4) X v x, y ), Y v( x, y ) (5) 135deg ( deg 1 1 This operator requires the least amout of computatio amog the edge detectors cosidered so far. However, like with the vector gradiet operator, the differece vector operator is also sesitive to impulsive ad Gaussia

5 MASOOD SHAIKH: A COMPARATIVE STUDY OF COLOR EDGE DETECTION TECHNIQUES oise [6]. As a result, more complex operators with subfilterig are desiged. A larger widow size is required i this case to allow more data for processig. Although there is o upper limit o the size of the widow, usually a 5 x 5 widow is preferred sice the computatioal complexity is directly liked to the size of the widow. I additio, whe the widow becomes too large it ca o loger represet the characteristics of the local regio. 4 VECTOR ORDER STATISTICS OPERATORS 4.1 Itroductio Oe importat family of operators for image processig is based o order statistics [4]. It has played a importat role i moochrome image processig ad it is also exteded to color image filterig ad edge detectio. This approach is ispired by the morphological edge detectors that have bee proposed for the moochrome images. This class of color edge detectors is characterized by liear combiatios of the sorted vector samples. Differet sets of coefficiets of the liear combiatio give rise to differet edge detectors that vary i performace ad efficiecy. The primary step i order statistics is to arrage a set of radom variables i ascedig order accordig to certai criteria. I color space, sice we are dealig with -D, multichael variables, there is o uiversal way of defiig a orderig. A umber of ways have bee proposed to perform multivariate data orderig [13] ad they ca be classified ito margial orderig (M-orderig), reduced aggregate orderig (R-orderig), partial orderig (P-orderig), ad coditioal orderig (C-orderig). I M-orderig, the ordered vectors do ot co respod to the origial vectors, ad P-orderig is difficult to implemet for digital image processig. C- orderig cosiders oly oe color compoet. R-orderig is hece more appropriate for color image processig. R- orderig reduces each multichael variable to a scalar value accordig to a distace criterio. Let the image vectors i a widow W deote X i, i=1,,..., ad D(Xi,Xj) be a measure of distace betwee vectors Xi ad Xj. The reduced scalar quatity associated with Xi is defied as d i k 1 D( X, X ), i 1,,... (6) i j The arragemet of di i ascedig order (d (1) <d () <... <d () ) correspods to the same orderig to the multivar ate variables: X (1) () ( ) X... X (7) I the ordered sequece, X (1) is the vector media ad vectors appearig at high raks are referred to as outliers because they diverge the most from the data populatio. 4. Edge Detectors The vector rage (VR) edge detector is the simplest color edge detector based o order statistics. It expresses the deviatio of the vector outlier i the highest rak from the vector media i W as follows: ( ) (1) VR D( X, X ) (8) where VR is small i a uiform area sice all vectors are close together, ad it gives large output whe discotiuities exist. Edges ca be obtaied by thresholdig the VR outputs. The VR detector, though simple ad efficiet, is sesitive to oise, especially to impulsive oise. It will respod to a oise pixel at the ceter of W with pixels. To improve oise performace, a more geeral class of operators, vector dispersio edge detector (VDED), is defied as a liear combiatio of the ordered vectors: VDED ( i) ix (9) i1 where. deotes the appropriate orm. Note that VR is a special case of VDED with α 1 = -1, α = 1 ad α i = 0, i =,..., -1. The precedig equatio ca be further geeralized by employig several sets of coefficiets ad combiig the resultig vector magitude i a suitable way. The coefficiets ca be chose i a way to atteuate oise. Oe proposed class of operator is the miimum vector dispersio (MVD) detector, ad it is defied as: l ( i) ( j 1) X MVD mi j DX, i1 l j 1,,..., k, k, l (30) The choice of k ad l deped o, the size of W. These two parameters cotrol the trade-off betwee complexity ad oise atteuatio. This more computatioally ivolved operator ca improve edge detectio performace i the presece of both impulsive ad Gaussia oise. By their ature, impulsive oise differs from the rest of the pixels by a large amout. Therefore, after orderig, the impulsive oise pixels have the highest raks, X (-k+), X (k+3)...,x (). Sice the distace betwee these oise pixels ad the rest of the pixels are large, Equatio (30) ca be reduced to the form stated above. Notice that oe of the oise pixels appears at this equatio, ad thus would ot affect the edge detectio process. The MVD is also robust i Gaussia oise due to the l-poits average term. A alterative desig of the geeralized VDED operators utilizes the adaptive earest-eighbor (NN) filter. The coefficiets are chose to adapt to local image characteristics. Istead of costats, the coefficiets are determied by a adaptive weight fuctio for each widow W. The operator is defied as the distace betwee the outlier ad the weighted sum of all the raked vectors: ( ) ( i) NNVR DX, wi X (31) i1 The weight fuctio wi is determied adaptively usig trasformatios of a distace criterio at each image locatio ad it is ot uiquely defied. There are two costraits o the weight fuctio:

6 6 CS31A WINTER-1314 PROJECT REPORT 1. Each weight coefficiet is positive, wi > 0.. The weight fuctio is ormalized, w i i1 1 Sice the operator should also atteuate oise, it is importat to assig a small weight to the pixels with high raks i.e. outliers. A possible weight fuctio ca be defied as follows: ( ) ( i) d d wi ( ) ( j) (3) d d j1 Oe special case for this weight fuctio occurs i highly uiform areas where all pixels have the same distace. The precedig weight fuctio ca ot be used sice the deomiator is zero. Sice o edge exists i this area, the differece measure of NNVR is set to zero. The MVD operator ca also be icorporated with the earest eighbor filter to further improve its performace i the presece of impulse oise as follows: ( j1) ( i) MVD mi j DX, wi X i1 j 1,,..., k, k (33) A fial aotatio o the class of vector order statistic operators cocers the distace measure D(Xi,Xj). By covetio, the Euclidea distace measure L orm is adopted. The use of L1 orm ca also be cosidered because it reduces the computatioal complexity by computig the absolute values istead of squares ad square root, ad it shows o otable deviatio i performace. A few other distace measures ca also be cosidered i the attempt to locate a optimal measure, amely, the Mahatta distace metric, the Caberra metric, the Czekaowski coefficiet, ad the agular distace measure. 5 QUANTATIVE PERFORMANCE EVALUATION PROCEDURE There are two schools of thought with regards to the evaluatio of computatioal visio algorithms i geeral. The first maitais that visio algorithms should be evaluated evaluated i the cotext of particular task as suggested by [14]. I the cotext of edge detectio ad other low-level visio tasks this traslates to measurig how much a particular algorithm cotributes to the success of higher-level procedures that carry out the low level operatio, for example, image segmetatio ad object recogitio. The secod school of thought holds that visio algorithms ca be evaluated i terms of their performace with regard to some suitably defied groud truth data as described by [15]. I this project we adopt this latter philosophy, ad preset the results of evaluatig the performace of the edge detectio algorithms described above o a set of real ad sythetic images for which the groud truth is kow. This has bee made possible by the itroductio of the Berkeley Segmetatio Database (BSDS300) [7]. The curret public distributio of the BSDs300 cotais 300 colour images of size pixels. For each of these images, the database provides betwee 4 ad 9 huma segmetatios i the form of label maps. The segmetatios are provided separately for the grayscale ad colour versios of each image, ad the complete database is split i two sets. A traiig image set cosistig of 00 images ad their correspodig segmetatios, ad a testig data set cosistig of the remaiig 100 images ad their huma segmetatios. The BSDS300 was origially desiged for evaluatio of image segmetatio algorithms. Sice edge detectio or boudary markig is a essetial part of the heriarchical image segmetatio algorithms, we ca derive the groud truth data for edge detectio from the huma segmetatio label maps available i this data set as described i the ext sub-sectio. Apart from the BSDS300, we also icluded a few machie geerated sythetic images that particularly used differet gradiet of colors i the image segmets to effectively evaluate the performace of the color edge detectors. 5.1 Extractig Groud Truth Edges from Huma Segmetatio The segmetatios from the huma groud truth data i the BSDS300 are stored as labeled images where pixels withi the same regio have idetical labels. To extract the edges from the labeled images we could, as a first approach, simply mark as a edge ay pixels that have a eighbor with a differet label. This, however, yields edges that are two pixels thick. Thick edges create two problems. First, very thi or very small regios will disappear altogether, havig bee replaced by solid clusters of edge pixels withi which the regio-structure of the image is lost. Secodly, thick edges complicate the matchig procedure betwee the edge detectio algorithm ad groud truth data ad are likely to itroduce uwated artifacts i the resultig performace parameters (e.g precisio/ recall scores). We could also attempt to mark pixels uiformly o oe side (e.g. to the left ad above) of edge boudaries but this also itroduces artifacts. To elimiate these problems, we first geerate edge maps that have twice the resolutio of the segmetatios. I these higher-resolutio images, edges ca be accurately localized to lie betwee the pixels correspodig to the origial regios i the low resolutio segmetatio. The procedure for geeratig the super-sampled edges is simple: We super-sample each idividual regio i the origial segmetatio ad fid its edge i the higher resolutio image. The fial edge map is the formed by dow-scalig the super-sampled image. Figure shows segmetatio, the boudaries extracted by markig as boudary ay pixels that have eighbors with a differet label, the super-sampled edge map ad the dowsampled edge map that is used as the fial groud truth image.

7 MASOOD SHAIKH: A COMPARATIVE STUDY OF COLOR EDGE DETECTION TECHNIQUES (a) (b) I a similar way, Recall is defied as the proportio of pixels i edge detected output image for which we ca fid a suitable match i the groud truth image, TP RC (38) N I The figure of merit of Pratt [16] is aother useful measure for assessig the performace of edge detectors. This measure uses the distace betwee all pairs of poits correspodig to quatify, with precisio, the differece betwee the edges. The figure of merit is defied as: 1 FOM max( N, N ) I B N B i1 1 1 d i (39) (c) Fig.. (a) Origial image BSDS jpg (481x31). (b) Segmetatio labels as give by huma aotatio (c) Edges geerated by markig every pixel that has at least oe eighbour with a differet label (superscaled edges are pixels thick). (d) Dow-sampled (481x31) image. Edges are ow more accurately localized. 5. Performace Parameters Compariso of a edge map, obtaied by the edge detectio algorithm, to its groud truth map is achieved by the measuremet of the statistical parameters of the matchig algorithm. These statistical parameters iclude metrics such as the umber of correctly detected edge pixels, called Total Positives (TP), the umber of pixels erroeously classified as edge pixels, called False Positives (FP), the amout of edge pixels that were ot classified as edge pixel, called False Negatives (FN) ad the Precisio ad Recall scores. From these measures, we compute the followig statistical metrics: The percetage of pixels that were correctly detected (Pco): P TP co max( N, N ) (34) I B where N I represets the umber of edge pixels of the groud truth image ad N B represets the umber of edge pixels actually detected by the algorithm. The percetage of pixels that were ot detected, i.e. the percetage of false egatives (Pd): FN Pd (35) max( N, N ) I B The percetage of pixels that were erroeously detected as edge pixels, i.e. the percetage of false positives (Pfa): FP Pfa (36) max( N, N ) I B Precisio is defied as the proportio of edge pixels i groud truth image for which we ca fid a matchig edge pixel i the edge detected output im age, TP PR (37) N B (d) where N I ad N B are the poits of edges i the edge detected image ad groud truth image, respectively, d i is the distace betwee a edge pixel ad the earest edge pixel of the groud truth ad α is a empirical calibratio costat ad was used α=1/9, optimal value established by Pratt [16]. The figure of merit of Pratt s FOM is a idicator of the quality of edge, ad reflects the overall behavior of the distaces betwee the edges, beig a relative measure, which varies i the rage [0, 1], where 1 represets the optimal value, i.e., the edges detected exactly coicide with the groud truth. 5.3 Matchig Strategy To compute the statistical parameters described above, we eed a method for determiig correspodece betwee edge pixels i the groud truth image ad the correspodig output image of edge detectio algorithm. We used the followig steps i the matchig strategy: a) Cout the edge pixels i the edge detected output image that exactly match with the groud truth image. These are correct idetificatios ad are termed as True Positives. b) Elimiate the correctly idetified edge pixels from the edge detected output image ad the groud truth image. For the remaiig edge pixels, cout the edge pixels i the detected image that are at a Euclidea distace of sqrt() (i.e. close viciit from the groud truth edge pixel. These are the edge pixels that are just oe pixel away from the groud truth edge pixel. These are locatioal errors ad are termed as local positives. We take Total Positives as the sum of true positives ad the local positives i our metric calculatios. 6 EXPERIMENTAL RESULTS AND OBSERVATIONS A total of 4 edge detectio algorithms from the class of the vector order statistic operators are implemeted ad their performaces are evaluated alog with the Cay edge detector implemetatio. Table 1 provides a list of the 4 edge detectors. As stated above, we have used real images from the BSDS300 dataset that provide huma groud truth edge data for experimetatio. Apart from

8 8 CS31A WINTER-1314 PROJECT REPORT these real images, we have used machie geerated sythetic images ad some radom images i the subjective ad quatitative evaluatio. Edge Detector Table 1 Edge Detectors for Evaluatio Descriptio Cay Moochrome edge detectio VR VR operator (W:3x3) with L 1 orm MVD MVD operator (W:3x3) with k=, l=3 NNMVD NNMVD operator (W:3x3) with k=3 NNVR NNVR operator (W:3x3) 6.1 Subjective Evaluatio Figure 3 shows the applicatio of the edge detectio algorithms from Table 1 o real image from the BSDS300 dataset alog with its huma groud truth edge data. Similarly Figure 4 shows the respose of edge detectio algorithms o a machie geerated sythetic image. The subjective evaluatio of edge detectors ca be based o several criterios: ease i recogizig objects, cotiuity of edges, thiess of edges ad performace i suppressig oise. (a) (b) A few observatios ca be draw from the visual ipsectio of the edge maps produced from various edge detectors applied to real ad sythetic images: The performace of Cay, NNVR ad NNMVD edge detectors is same i the sese that they produce more or less similar edge maps. For large color variatios NNVR ad NNMVD perform better tha Cay as see i case of sythetic image (Figure 4) VR ad MVD perform superior as compared to the other edge detectors as they produce more promiet edges. The MVD edge detector produce thier edges ad is less sesitive to small texture variatios because of the averagig operatio which smooths out small variatios. MVD edge detector is more sesitive to color variatios ad hece ca produce edges with very small color gradiets as well. This ca be further cotrolled by properly choosig the threshold value. 6. Statistical Evaluatio As described i sectio 5., compariso of a edge map obtaied by the edge detectio algorithm, with its groud truth map is achieved by the measuremet of the statistical parameters such as percetage of correctly detected edge pixels (Pco), percetage of erroeously classified edge pixels (Pfa), percetage of pixels ot detected as edge pixels (Pf), Precisio ad Recall scores ad Pratt s figure of merit (FOM). Table ad 3 gives the statistical parameters calculated for edge detectio from real image ad sythetic image. (c) (d) Table Statistical Edge Parameters for jpg image Params Cay VR MVD NNMVD NNVR Pco 31.6% 4.5% 8.3%.6%.5% Pf 68.4% 8.7% 4.0% 77.4% 77.5% Pfa 46.1% 75.5% 71.7% 36.4% 38.0% Precisio 40.7% 4.5% 8.3% 38.3% 37.% Recall 31.6% 46.1% 40.%.6%.5% FOM 4.8% 50.% 51.3% 3.6% 3.6% (e) (f) Table 3 Statistical Edge Parameters for sythetic image Params Cay VR MVD NNMVD NNVR Pco 40.1% 84.6% 8.3% 35.9% 40.% Pf 59.9%.5% 17.7% 64.1% 59.8% Pfa 3.0% 15.4% 0.3% 0.% 0.3% Precisio 93.0% 84.6% 99.7% 99.6% 99.3% Recall 40.1% 97.1% 8.3% 35.9% 40.% FOM 39.7% 98.5% 8.5% 35.8% 40.0% (g) (h) Fig. 3. (a) Origial image jpg (481x31) from BSDS300. (b) Gray-scale image. (c) Huma groud truth image. (d) Cay Edge Output. (e) VR Edge Output. (f) MVD Edge Output. (g) NNMVD Edge Output. (h) NNVR Edge Output.

9 MASOOD SHAIKH: A COMPARATIVE STUDY OF COLOR EDGE DETECTION TECHNIQUES From the results i Table ad Table 3, few coclusios ca be draw: For real color images, Cay ad MVD edge detectors have higher percetage of correctly detected edge pixels as compared to VR, NNVR ad NNMVD. But at the same time VR ad MVD has smaller Pf scores which idicate that Cay edge detector has higher percetage of pixels that were ot detected as true edges. I terms of Pratt s FOM, VR ad MVD have better scores amog all the edge detectors sice they both detect edge pixels that are closer to the real groud truth edge pixels. For the sythetic color image with large color variatio, VR ad MVD has huge performace gai i terms of correctly detected edge pixels as compared to Cay, NNVR ad NNMVD. Moreover, MVD, NNVR ad NNMVD have a very high precisio score amog all the edge detectors while VR has the best FOM score. Clearly we observe that for color images with large color variatio, color edge detectors give better quality performace as compared to moochrome edge detectio techiques like Cay edge detector. For statistical evaluatio we used L orm for all the distace calculatios ad a costat widow size of 3 x 3. If computatioal complexity permits, the we ca use a larger widow size like 5 x 5 ad some more accurate distace measures such as Caberra metric ad agular distace measure. (g) (h) Fig. 4. (a) Origial sythetic image 0004.ppm (400 x 400). (b) Grayscale image. (c) Groud truth image. (d) Cay Edge Output. (e) VR Edge Output. (f) MVD Edge Output. (g) NNMVD Edge Output. (h) NNVR Edge Output. 6.3 Noise Performace A umber of edge detectio experimets have bee coducted usig various oise distributios at various oise levels to cotamiate the test image. I each case, FOM has bee measured ad used as the performace criterio. We cosidered Gaussia oise distributio, but other forms of oise corruptio such as Gaussia Impulsive oise, expoetial or correlated oise ca also be used. For the corruptio of the sythetic image, the oise process i each chael has bee cosidered as a idepedet process. While i case of real image, the oise process has bee cosidered as a correlated process sice there is some idicatio that this type of correlatio may exist i real color images. The oise performace of the color edge detectors are show graphically i Figure 5. The edge detectio output o a BSDS300 real image corrupted with Gaussia oise is depicted i Figure 6. (a) (b) (c) (e) (d) (f) Fig. 5a. FOM plots of color edge detectors uder oise corruptio for sythetic image. A few observatios ca be made from the results : The Cay, VR ad NNVR edge detectors are very sesitive to Gaussia oise. As observed VR fires idiscrimiately for Gaussia oise corruptio sice it just takes the differece betwee the first ad the last vector sample i the ordered vector space. Cay edge detector ca produce better oise performace with added complexity by icreasig the variace σ i the Gaussia filterig stage. MVD ad NNMVD vector order statistics edge

10 10 CS31A WINTER-1314 PROJECT REPORT detectors show more robustess i the presece of oise because of the iheret averagig operatio i the desig of these detectors. We ca also cofirm that oise performace improves with icrease i the complexity of these edge detectors, which are cotrolled by the two parameters k ad l. As observed from the FOM plots (Figure 5) of real ad sythetic color images, MVD edge detector has superior performace amog all edge detectors i various oise distributios. (g) Fig. 6. (a) Origial image jpg (481x31) from BSDS300 corrupted with Gaussia oise. (b) Gray-scale image. (c) Groud truth image. (d) Cay Edge Output. (e) VR Edge Output. (f) MVD Edge Output. (g) NNMVD Edge Output. (h) NNVR Edge Output. (h) Fig. 5b. FOM plots of color edge detectors uder oise corruptio for real image. 7 CONCLUSION The problem of color edge detectio has bee studied usig vector order statistics i this project. A family of color edge detectors based o vector order statistics has bee proposed because these are effective with multichael data ad are computatioally efficiet. The desig parameters of this class of edge detectors ca be appropriately choose for better oise suppressio at the cost of icreasig complexity. The performace of all edge detectors was evaluated both subjectively ad objectively usig various statistical parameters. The Miimum Vector Dispersio (MVD) color edge detector scores high poits i objective tests ad the edge maps produced by this edge detector are perceived favorably by huma eyes uder subjective evaluatio. Differet visio applicatios have differet requiremets o edge detectio, ad though some of the geeral characteristics of color edge detectors were addressed, it is still better to select edge detector that is optimum for a particular applicatio. (a) (c) (e) (b) (d) (f) REFERENCES [1] J. Thomas Alle ad T. Hutsberger, Comparig Color Edge Detectio ad Segmetatio Methods, IEEE Proceedigs Southeastco, pg. 7, Sessio 11C5, [] K. N. Plataiotis ad A. N. Veetsaopoulos, Color Image Processig ad Applicatios, Spriger, 000. [3] P. Adroutsos, D. Adroutsos, K.N. Plataiotis, ad A.N. Veetsaopoulos. Colour Edge Detectors: A Overview ad Compariso, IEEE Proceedigs, pg. 607, [4] P.E. Trahaias ad A.N. Veetsaopoulos, Vector order Statistics Operators as Color Edge Detectors, IEEE Trasactio o Systems, Ma ad Cyberetics-Part B: Cyberetics, Vol. 6, No. 1, pg. 137, February [5] J. Cay, A computatioal approach to edge detectio,, Patter Aalysis ad Machie Itelligece, 8(6): , November [6] I. Pitas ad A.N. Veetsaopoulos. Edge detectors based o oliear filters, IEEE Tras. Patter Aal. Machie Itell., vol. PAMI-8, o. 4, pp , July [7] Marti, D., & Fowlkes, C. (001). The Berkeley segmetatio database ad bechmark, Computer Sciece Departmet, Berkeley Uiversity. bsds/.001

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