The Hough Transform has been used to develop an algorithm for rotation, translation and size-scaling invariant pattern recognition of polygonal objects. In this research the developed system has been successfully applied to the automatic invariant recognition of rectangular chocolates, including identification of defective samples. Since the entire performance of the resulting system is autonomous, the results may be applied to automatic quality control applications in the industry.La Transformada de Hough (TH) ha sido usada para crear un algoritmo de reconocimiento invariante (rotación, traslación y cambio de escala) de objetos poligonales. En esta investigación, el sistema desarrollado ha sido exitosamente aplicado al reconocimiento automático invariante de chocolates rectangulares, incluyendo la identificación de piezas falladas. Como la ejecución total del sistema resultante es totalmente autónoma, los resultados pueden ser aplicados al control automático de calidad en aplicaciones industriales

Montenegro Joo, Javier

English

Revistas de investigacion UNMSM

47SISTEMAS E INFORMÁTICAInd. data 9(2), 2006Hough-transform based algorithm for theautomatic invariant recognition of rectangularchocolates. Detection of defective pieces.(1) Javier Montenegro JooI N T R O D U C T I O NThe Hough transform [1,2] HT, is a distortion tolerant technique that mapsimage-space points into curves in a parameter space (also calledAccumulator space). In this work the Polar, also known as Normal HT isused, this maps image-space points into a parametric Accumulator Spaceby means of the equationBy means of this relation, any binary point  (x,y)  in image space  X-Y  ismapped into a sinusoidal in the accumulator space  r-q , which isdiscretized  in cells  of coordinates (r,q) . The main feature of the HT isthat the N sinusoidals corresponding to a set of N collinear points (xi,yi)meet at a point  (ro,qo) in accumulator space, the values of  ro and qocharacterizing  the original straight line in the image. Every sinusoidalpassing by (r,q)  contributes with 1 to a counting stored in that location.The counting stored in every cell of the accumulator corresponds to thenumber of points that are contained in a straight line characterized by(r,q)  in eq. (1).Montenegro [12] has developed a full interactive Virtual Lab that allows theuser to become acquainted with the Polar Hough Transform (PHT) whilevisualizing it, as well as with other Digital Image Processing topics dealingwith Invariant Pattern recognition.The algorithm being reported in this paper is mainly based on the followingPHT properties, which have been thoroughly exploited:•    When a straight line is displaced to a parallel position in image space, onlya proportional displacement along the r-coordinate takes place inparameter space.•    When a straight line is rotated W0 degrees in image space, its associatedpeak in the accumulator space is shifted W0 degrees along the q axis.•   When an object is uniformly scaled in image space, only the associatedvalues of r change proportionally in the accumulator space.Two researchers have already dealt with invariant pattern recognition inHough space, these are Krishnapuram and Casasent [3], and Sinha et al[4], however none of these two works considered object size scaling. Theseworks use convolution in q-space to achieve the rotational registrationbetween sample objects and templates, an additional processing is thenR e c e p c i ó n :  Agosto  d e  2 0 0 6 /  A c e p t a c i ó n :  Noviembre  d e  2 0 0 6(1)  Director de Virtual Dynamics / Virtual Labs: Science & EngineeringDirector@VirtualDynamics.OrgABSTRACTThe Hough Transform has been used todevelop an algorithm for rotation, translationand size-scaling invariant pattern recognitionof polygonal objects.  In this research thedeveloped system has been successfullyapplied to the automatic invariant recognitionof rectangular chocolates, includingidentification of defective samples. Since theentire performance of the resulting system isautonomous, the results may be applied toautomatic quality control applications in theindustry.Key words: Artificial intelligence, cyberneticvision, pattern recognition, invariant shapeclassification, Polar Hough transform.ALGORITMO BASADO EN LATRANSFORMADA DE HOUGH, PARA ELRECONOCIMIENTO INVARIANTE DECHOCOLATES RECTANGULARES.DETECCIÓN DE PIEZAS FALLADAS.RESUMENLa Transformada de Hough (TH) ha sidousada para crear un algoritmo dereconocimiento invariante (rotación,traslación y cambio de escala) de objetospoligonales.  En esta investigación, elsistema desarrollado ha sido exitosamenteaplicado al reconocimiento automáticoinvariante de chocolates rectangulares,incluyendo la identificación de piezasfalladas. Como la ejecución total del sistemaresultante es totalmente autónoma, losresultados pueden ser aplicados al controlautomático de calidad en aplicacionesindustriales.Palabras Clave: Inteligencia artificial, visióncibernética, reconocimiento del modelo,clasificación invariante de formas,Transformada Polar de Hough.)1(qqr SinyCosx +=48SISTEMAS E INFORMÁTICAInd. data 9(2), 2006>>> Hough-transform based algorithm for the automatic invariant recognition of rectangular chocolates. Detection of defective pieces.necessary to determine the translat ionalcorrespondence.The algorithm developed for the work being reportedhere has the following advantages with respect to thetwo methods above mentioned:•    An algorithm to solve the problem of object sizescaling has been developed and it is successfullyapplied. This algorithm is associated to a lowcomplexity computation and to a short computingtime.•   When training the system there is no need toplace the template object in any particularposition, orientation or size, it is just carelesslythrown into image-space.•   The object to be recognized is rotated and translatedonly once in accumulator space, then a comparisonwith the stored templates is carried out. Thisrepresents a substantial improvement with respectto the many comparisons implied by the methodsused in references 3 and 4.•    The counting stored in the accumulator bins (cells)is used as an evidence of sample-templatematching in the present work.In this report, RTS stands for Rotation, Translation andSize-scalingSTRATEGY OF THE ALGORITHMThis researcher has designed and developed analgorithm [10,11] which consists in taking the   “theobject”  (actually its Hough space features) to a pre-defined  “standard status” in Hough space [9,10,11].In this context, “standard status” must be understoodas a previously defined “object” location, orientation,and size in accumulator space r-q.The algorithm is applied equally to training andrecognition stages. After Hough transforming theimage-space, a sequence of operations andtransformations is carried out in the accumulator, sothat the object is taken to the standard status, then acharacteristic vector T or S, depending whethertemplate or sample, is extracted.  Montenegro [5]has already addressed the use of a pre-defined stan-dard status in Hough space along with Distance-Discriminator Neurons to achieve invariant patternrecognition.At recognition time, the characteristic vectors T oftemplate objects previously extracted at the trainingstage are compared with the vector S of the sampleobject to be recognized.The distance between T and S vectors gives thecorresponding T-S similitude degree.ACHIEVING RTS INVARIANCE INPARAMETER SPACEDuring training or recognition the object is simplythrown to image-space, in no particular position(translation), orientation (rotation), or size (scaling).However, large instances of the training object shouldbe preferred for the sake of improved accuracy.This algorithm operates on a single object at a timethus if several ones appear simultaneously in image-space a pre-processing is necessary to single outindividual samples.THE TRAINING PROCESSThe object is presented only once to the system andafter Hough transforming it, a set of operations takeplace on the accumulator space so as to take thepattern to a pre-defined standard position [7,10,11],in this stage a template vector T is created andinformation about the votations obtained in thecharacteristic (r,q) is stored, this will be used astemplate during the recognition process.  Sometimes,depending on the special geometric characteristicsof the objects used as templates, two template vectorsT1 and T2 may be needed, this just to make sure agood performance at recognition time.THE RECOGNITION PROCESSWhen the system is on recognition mode, the samesteps carried-out at the training process must befollowed for the sample to be recognized. For everyincognito sample a sample-vector S is created withthe corresponding values of (r,q), and associatedvotations.In order to compare sample with template, theEuclidean distance between the two T-S pairs iscomputed.Advanced details of the training and recognitionprocesses may be found in refs. 7 and 11.RESULTS OF THE INVESTIGATIONThe performance evaluation of the developed algorithmhas been previously executed with computer-49SISTEMAS E INFORMÁTICAInd. data 9(2), 2006Figure 1. Chocolates from Chw01 to Chw24 used in the investigation: Flawless:  Chw01 through Chw17.   Flawed: Chw18through  Chw24.Javier Montenegro J. >>>50SISTEMAS E INFORMÁTICAInd. data 9(2), 2006synthesized objects and with complex shapepasteboard pieces [7]. Subsequently the method hasbeen applied to recognize biscuits [8,9]. In all casesthe results show a very good performance of thealgorithm.The work reported in this paper has been performedusing rectangular chocolates whose actual measuresare 4.0 x 6.7 cms, and whose photographs showingevery one of them in different positions, orientationsand sizes (different RTS instances), were scannedand stored in 128 x 128 pixel binary images, see fig.(1). In order to obtain different size samples thephotographic camera was placed at varying distancesfrom the actual objects. To make flawed chocolates,a knife was used.Chart 1 displays the similitude degrees between the24 chocolates and the  9  flawless pieces out of themthat were  carelessly  chosen as templates. Thesamples are identified as Chwnn, where “Ch” standsfor “Chocolate”,  “w” for the commercial brand, and“nn” is a number that runs from 01 through 24.  Piecesfrom Chw01   through Chw17 are flawless, whereaspieces from Chw18 through Chw24 are flawed ones.Since the developed system is prepared to report anull similitude degree for samples with a number ofsides different to that of the template, the flawedobjects used in this research have all the samenumber of sides as that of the template, in this waythe system is forced to achieve a more difficult andambitious task.It may be seen in chart 1 that  as expected,  when  atemplate is also used as a sample the resultingsimilitude degree is  1.00.The same T-S similitude degree is obtained for anypair of objects one of them used as a template in aObjects:  Rectangular chocolates                   Top horizontal row:  templates.      Left vertical column: samples   Chw01 Chw02 Chw03 Chw05 Chw06 Chw07 Chw09 Chw16 Chw17 Chw          01 1.000 0.992 0.987 0.988 0.990 0.995 0.995 0.991 0.979 02 0.992 1.000 0.985 0.988 0.997 0.992 0.989 0.984 0.986 03 0.987 0.985 1.000 0.991 0.984 0.987 0.983 0.989 0.976 04 0.984 0.991 0.979 0.985 0.992 0.987 0.982 0.977 0.992 05 0.988 0.988 0.991 1.000 0.989 0.990 0.983 0.986 0.982 06 0.990 0.997 0.984 0.989 1.000 0.995 0.986 0.982 0.987 07 0.995 0.992 0.987 0.990 0.995 1.000 0.990 0.987 0.982 08 0.998 0.986 0.982 0.985 0.983 0.984 0.987 0.984 0.982 09 0.995 0.989 0.983 0.983 0.986 0.990 1.000 0.990 0.976 10 0.980 0.985 0.972 0.978 0.986 0.982 0.978 0.972 0.985 11 0.980 0.977 0.984 0.981 0.980 0.985 0.977 0.982 0.967 12 0.995 0.987 0.988 0.988 0.985 0.990 0.991 0.991 0.974 13 0.975 0.969 0.975 0.969 0.967 0.972 0.973 0.977 0.955 14 0.966 0.959 0.966 0.960 0.957 0.962 0.967 0.969 0.945 15 0.995 0.992 0.987 0.990 0.995 0.992 0.990 0.987 0.982 16 0.991 0.984 0.989 0.986 0.982 0.987 0.990 1.000 0.972 17 0.979 0.986 0.976 0.982 0.987 0.982 0.976 0.972 1.000 18 0.687-1 0.683-1 0.681-1 0.681-1 0.681-1 0.682-1 0.689-1 0.686-1 0.676-1 19 0.687-1 0.687-1 0.482-2 0.485-2 0.684-1 0.682-1 0.689-1 0.482-2 0.495-2 20 0.682-1 0.682-1 0.674-1 0.674-1 0.679-1 0.677-1 0.684-1 0.679-1 0.679-1 21 0.250-3 0.250-3 0.250-3 0.250-3 0.250-3 0.250-3 0.250-3 0.250-3 0.250-3 22 0.250-3 0.250-3 0.250-3 0.250-3 0.250-3 0.250-3 0.250-3 0.250-3 0.250-3 23 0.689-1 0.684-1 0.694-1 0.689-1 0.684-1 0.689-1 0.689-1 0.694-1 0.674-1 24 0.684-1 0.679-1 0.689-1 0.684-1 0.679-1 0.684-1 0.684-1 0.689-1 0.669-1  Chart 1. Template: Sample normalized Similitude Degrees.Total samples:  24.  Flawless:  Chw01   through Chw17.  Flawed:  Chw18 through Chw24.  In the case of flawed objects, the digit after thehyphen indicates the number of sample peaks out of 2 x 2 searching neighbourhood.>>> Hough-transform based algorithm for the automatic invariant recognition of rectangular chocolates. Detection of defective pieces.51SISTEMAS E INFORMÁTICAInd. data 9(2), 2006moment and as a sample in another moment. Com-pare results from pairs Chw01-Chw02, and Chw02-Chw01, and so forth.It can also be seen in chart 1 that flawless objectshave rather high similitude degrees, while flawedobjects have low similitude degrees, the numbers afterthe hyphen accompanying the flawed pieces similitudedegrees stand for the number of accumulator peaksout of searching window.  It can be seen that the higherthe number of peaks out of searching window, thelower the similitude degree.  Flawless pieces do notreport accumulator peaks out of searching mask.C O N C L U S I O NThe problem of rotation, translation and size-scaling(RTS) invariant pattern recognition of polygonal objectshas been dealt with and an algorithm based on thefundamental properties of the polar HT has beendeveloped and successfully applied to the invariantrecognition of rectangular chocolates.It is important to mention that in the algorithm thathas been designed, the objects are taken to a pre-defined standard status through a set of translation,rotation, and size-scaling transformations which takeplace just once and exclusively in Hough space, inthis way a considerable computing time is saved andthe algorithm computational complexity is low.When dealing with rectangular chocolates thealgorithm successfully identifies flawless pieces,yielding a good similitude degree between templatepattern and samples.  The system also discriminatesagainst flawed pieces.The developed algorithm was initially tested withcomputer-synthesized objects, next with samplesmade with pasteboard, this was followed by itssuccessful application to the recognition of rectangu-lar biscuits and now it has been applied to therecognition of chocolates including discriminationagainst flawed pieces. These results suggest that thisalgorithm may be profitably applied to industrialautomatic quality control of products, maybe forobjects being transported on a conveyor belt.A C K N O W L E D G E M E N TThis work would not have been possible without thedeep and decisive influence of Prof. Luciano daFontoura Costa, from The Cybernetic Vision ResearchGroup, Sao Paulo University, (USP Sao Carlos Bra-sil), who introduced the author to the field of ComputerVision, specifically Pattern Recognition. The authorexpresses his sincere and special gratitude to Prof.da Fontoura Costa for all the time, dedication andvery specially for the transfer of knowledge.BIBLIOGRAPHICAL REFERENCES1.  Illingworth J. and  Kittler J. (1998).  A survey of theHough transform. CVGIP, vol , 44,  pags 87-116.2.  Duda R.O. and  Hart P.E. (1972). Use of the Houghtransform to detect lines  and curves in pictures.Communications of the ACM,  Vol 15,  No  1,  11-15, January.3.   Krishnapuram R. and  Casasent D. (1987).  Houghspace transformations for discrimination anddistortion estimation.  CVGIP,  vol 38,  pags. 299-316.4. Sinha P.K., Chen F.Y., Horne R.E.N. (1993).Recognition and location of  shapes in the Houghpattern space. IEE  Elect. Div. Colloq. on Houghtransform, 1993/106. Savoy place, London, May.5.  Montenegro J.J. - Da Fontoura Costa  L. - KöberleR. (1993). Geometric-Transformation-Invariantpattern recognition with Hough transforms andDistance-Discriminator Neural Networks.Workshop sobre Computacaõ  de altodesempenho para processamento de sinais. SãoCarlos, SP, Brasil.6. Gerig G. and  Klein F. (1986). Fast contouridentification through efficient Hough transform andsimplified  interpretation strategy.  IJCPR-8, Paris,498-500.7.  Montenegro J. J. (1994). Doctoral thesis researchunder  the direction of  Professor Luciano daFontoura Costa (Cybernetic Vision ResearchGroup, USP-SC, Brasil.8.  Montenegro J. J. (2002). Invariant Recognition ofrectangular biscuits through an algorithm operatingexclusively in Hough space. Flawed piecesdetection. Revista de Investigacion de Fisica, Vol5, No 1,2.9.  Montenegro J. J. (1995). Inteligencia Artificial:  Re-conocimiento de objetos en visión  computarizada.Seminario Software Científico, CONCYTEC:National Sci. & Tech Council, Lima Perú.10. Montenegro J. J. (2004). Invariant patternrecognition executed exclusively in the HoughJavier Montenegro J. >>>52SISTEMAS E INFORMÁTICAInd. data 9(2), 2006Space. Revista Electronica-UNMSM, No 13, Aug.200411.  Montenegro J. J. (1998).  A Polar-Hough-TransformBased Algorithm for the Translation, Orientation andSize-Scale Invariant Pattern Recognition ofPolygonal Objects. UMI Dissertations MicroformLD03769. Oct. 199812.  Montenegro J. J.  Imagery,  Digital Image ProcessingVirtual Laboratory.  Virtual Dynamics / Virtual Labs:Science & Engineering.>>> Hough-transform based algorithm for the automatic invariant recognition of rectangular chocolates. Detection of defective pieces.

ALGORITMO BASADO EN LA TRANSFORMADA DE HOUGH, PARA EL RECONOCIMIENTO INVARIANTE DE CHOCOLATES RECTANGULARES. DETECCIÓN DE PIEZAS FALLADAS.

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47SISTEMAS E INFORMÁTICAInd. data 9(2), 2006Hough-transform based algorithm for theautomatic invariant recognition of rectangularchocolates. Detection of defective pieces.(1) Javier Montenegro JooI N T R O D U C T I O NThe Hough transform [1,2] HT, is a distortion tolerant technique that mapsimage-space points into curves in a parameter space (also calledAccumulator space). In this work the Polar, also known as Normal HT isused, this maps image-space points into a parametric Accumulator Spaceby means of the equationBy means of this relation, any binary point  (x,y)  in image space  X-Y  ismapped into a sinusoidal in the accumulator space  ρ-θ , which isdiscretized  in cells  of coordinates (ρ,θ) . The main feature of the HT isthat the N sinusoidals corresponding to a set of N collinear points (xi,yi)meet at a point  (ρo,θo) in accumulator space, the values of  ρo and θocharacterizing  the original straight line in the image. Every sinusoidalpassing by (ρ,θ)  contributes with 1 to a counting stored in that location.The counting stored in every cell of the accumulator corresponds to thenumber of points that are contained in a straight line characterized by(ρ,θ)  in eq. (1).Montenegro [12] has developed a full interactive Virtual Lab that allows theuser to become acquainted with the Polar Hough Transform (PHT) whilevisualizing it, as well as with other Digital Image Processing topics dealingwith Invariant Pattern recognition.The algorithm being reported in this paper is mainly based on the followingPHT properties, which have been thoroughly exploited:•    When a straight line is displaced to a parallel position in image space, onlya proportional displacement along the ρ-coordinate takes place inparameter space.•    When a straight line is rotated Ω0 degrees in image space, its associatedpeak in the accumulator space is shifted Ω0 degrees along the θ axis.•   When an object is uniformly scaled in image space, only the associatedvalues of ρ change proportionally in the accumulator space.Two researchers have already dealt with invariant pattern recognition inHough space, these are Krishnapuram and Casasent [3], and Sinha et al[4], however none of these two works considered object size scaling. Theseworks use convolution in θ-space to achieve the rotational registrationbetween sample objects and templates, an additional processing is thenR e c e p c i ó n :  Agosto  d e  2 0 0 6 /  A c e p t a c i ó n :  Noviembre  d e  2 0 0 6(1)  Director de Virtual Dynamics / Virtual Labs: Science & EngineeringDirector@VirtualDynamics.OrgABSTRACTThe Hough Transform has been used todevelop an algorithm for rotation, translationand size-scaling invariant pattern recognitionof polygonal objects.  In this research thedeveloped system has been successfullyapplied to the automatic invariant recognitionof rectangular chocolates, includingidentification of defective samples. Since theentire performance of the resulting system isautonomous, the results may be applied toautomatic quality control applications in theindustry.Key words: Artificial intelligence, cyberneticvision, pattern recognition, invariant shapeclassification, Polar Hough transform.ALGORITMO BASADO EN LATRANSFORMADA DE HOUGH, PARA ELRECONOCIMIENTO INVARIANTE DECHOCOLATES RECTANGULARES.DETECCIÓN DE PIEZAS FALLADAS.RESUMENLa Transformada de Hough (TH) ha sidousada para crear un algoritmo dereconocimiento invariante (rotación,traslación y cambio de escala) de objetospoligonales.  En esta investigación, elsistema desarrollado ha sido exitosamenteaplicado al reconocimiento automáticoinvariante de chocolates rectangulares,incluyendo la identificación de piezasfalladas. Como la ejecución total del sistemaresultante es totalmente autónoma, losresultados pueden ser aplicados al controlautomático de calidad en aplicacionesindustriales.Palabras Clave: Inteligencia artificial, visióncibernética, reconocimiento del modelo,clasificación invariante de formas,Transformada Polar de Hough.)1(θθρ SinyCosx +=48SISTEMAS E INFORMÁTICAInd. data 9(2), 2006>>> Hough-transform based algorithm for the automatic invariant recognition of rectangular chocolates. Detection of defective pieces.necessary to determine the translat ionalcorrespondence.The algorithm developed for the work being reportedhere has the following advantages with respect to thetwo methods above mentioned:•    An algorithm to solve the problem of object sizescaling has been developed and it is successfullyapplied. This algorithm is associated to a lowcomplexity computation and to a short computingtime.•   When training the system there is no need toplace the template object in any particularposition, orientation or size, it is just carelesslythrown into image-space.•   The object to be recognized is rotated and translatedonly once in accumulator space, then a comparisonwith the stored templates is carried out. Thisrepresents a substantial improvement with respectto the many comparisons implied by the methodsused in references 3 and 4.•    The counting stored in the accumulator bins (cells)is used as an evidence of sample-templatematching in the present work.In this report, RTS stands for Rotation, Translation andSize-scalingSTRATEGY OF THE ALGORITHMThis researcher has designed and developed analgorithm [10,11] which consists in taking the   “theobject”  (actually its Hough space features) to a pre-defined  “standard status” in Hough space [9,10,11].In this context, “standard status” must be understoodas a previously defined “object” location, orientation,and size in accumulator space ρ−θ.The algorithm is applied equally to training andrecognition stages. After Hough transforming theimage-space, a sequence of operations andtransformations is carried out in the accumulator, sothat the object is taken to the standard status, then acharacteristic vector T or S, depending whethertemplate or sample, is extracted.  Montenegro [5]has already addressed the use of a pre-defined stan-dard status in Hough space along with Distance-Discriminator Neurons to achieve invariant patternrecognition.At recognition time, the characteristic vectors T oftemplate objects previously extracted at the trainingstage are compared with the vector S of the sampleobject to be recognized.The distance between T and S vectors gives thecorresponding T-S similitude degree.ACHIEVING RTS INVARIANCE INPARAMETER SPACEDuring training or recognition the object is simplythrown to image-space, in no particular position(translation), orientation (rotation), or size (scaling).However, large instances of the training object shouldbe preferred for the sake of improved accuracy.This algorithm operates on a single object at a timethus if several ones appear simultaneously in image-space a pre-processing is necessary to single outindividual samples.THE TRAINING PROCESSThe object is presented only once to the system andafter Hough transforming it, a set of operations takeplace on the accumulator space so as to take thepattern to a pre-defined standard position [7,10,11],in this stage a template vector T is created andinformation about the votations obtained in thecharacteristic (ρ,θ) is stored, this will be used astemplate during the recognition process.  Sometimes,depending on the special geometric characteristicsof the objects used as templates, two template vectorsT1 and T2 may be needed, this just to make sure agood performance at recognition time.THE RECOGNITION PROCESSWhen the system is on recognition mode, the samesteps carried-out at the training process must befollowed for the sample to be recognized. For everyincognito sample a sample-vector S is created withthe corresponding values of (ρ,θ), and associatedvotations.In order to compare sample with template, theEuclidean distance between the two T-S pairs iscomputed.Advanced details of the training and recognitionprocesses may be found in refs. 7 and 11.RESULTS OF THE INVESTIGATIONThe performance evaluation of the developed algorithmhas been previously executed with computer-49SISTEMAS E INFORMÁTICAInd. data 9(2), 2006Figure 1. Chocolates from Chw01 to Chw24 used in the investigation: Flawless:  Chw01 through Chw17.   Flawed: Chw18through  Chw24.Javier Montenegro J. >>>50SISTEMAS E INFORMÁTICAInd. data 9(2), 2006synthesized objects and with complex shapepasteboard pieces [7]. Subsequently the method hasbeen applied to recognize biscuits [8,9]. In all casesthe results show a very good performance of thealgorithm.The work reported in this paper has been performedusing rectangular chocolates whose actual measuresare 4.0 x 6.7 cms, and whose photographs showingevery one of them in different positions, orientationsand sizes (different RTS instances), were scannedand stored in 128 x 128 pixel binary images, see fig.(1). In order to obtain different size samples thephotographic camera was placed at varying distancesfrom the actual objects. To make flawed chocolates,a knife was used.Chart 1 displays the similitude degrees between the24 chocolates and the  9  flawless pieces out of themthat were  carelessly  chosen as templates. Thesamples are identified as Chwnn, where “Ch” standsfor “Chocolate”,  “w” for the commercial brand, and“nn” is a number that runs from 01 through 24.  Piecesfrom Chw01   through Chw17 are flawless, whereaspieces from Chw18 through Chw24 are flawed ones.Since the developed system is prepared to report anull similitude degree for samples with a number ofsides different to that of the template, the flawedobjects used in this research have all the samenumber of sides as that of the template, in this waythe system is forced to achieve a more difficult andambitious task.It may be seen in chart 1 that  as expected,  when  atemplate is also used as a sample the resultingsimilitude degree is  1.00.The same T-S similitude degree is obtained for anypair of objects one of them used as a template in aObjects:  Rectangular chocolates                   Top horizontal row:  templates.      Left vertical column: samples   Chw01 Chw02 Chw03 Chw05 Chw06 Chw07 Chw09 Chw16 Chw17 Chw          01 1.000 0.992 0.987 0.988 0.990 0.995 0.995 0.991 0.979 02 0.992 1.000 0.985 0.988 0.997 0.992 0.989 0.984 0.986 03 0.987 0.985 1.000 0.991 0.984 0.987 0.983 0.989 0.976 04 0.984 0.991 0.979 0.985 0.992 0.987 0.982 0.977 0.992 05 0.988 0.988 0.991 1.000 0.989 0.990 0.983 0.986 0.982 06 0.990 0.997 0.984 0.989 1.000 0.995 0.986 0.982 0.987 07 0.995 0.992 0.987 0.990 0.995 1.000 0.990 0.987 0.982 08 0.998 0.986 0.982 0.985 0.983 0.984 0.987 0.984 0.982 09 0.995 0.989 0.983 0.983 0.986 0.990 1.000 0.990 0.976 10 0.980 0.985 0.972 0.978 0.986 0.982 0.978 0.972 0.985 11 0.980 0.977 0.984 0.981 0.980 0.985 0.977 0.982 0.967 12 0.995 0.987 0.988 0.988 0.985 0.990 0.991 0.991 0.974 13 0.975 0.969 0.975 0.969 0.967 0.972 0.973 0.977 0.955 14 0.966 0.959 0.966 0.960 0.957 0.962 0.967 0.969 0.945 15 0.995 0.992 0.987 0.990 0.995 0.992 0.990 0.987 0.982 16 0.991 0.984 0.989 0.986 0.982 0.987 0.990 1.000 0.972 17 0.979 0.986 0.976 0.982 0.987 0.982 0.976 0.972 1.000 18 0.687-1 0.683-1 0.681-1 0.681-1 0.681-1 0.682-1 0.689-1 0.686-1 0.676-1 19 0.687-1 0.687-1 0.482-2 0.485-2 0.684-1 0.682-1 0.689-1 0.482-2 0.495-2 20 0.682-1 0.682-1 0.674-1 0.674-1 0.679-1 0.677-1 0.684-1 0.679-1 0.679-1 21 0.250-3 0.250-3 0.250-3 0.250-3 0.250-3 0.250-3 0.250-3 0.250-3 0.250-3 22 0.250-3 0.250-3 0.250-3 0.250-3 0.250-3 0.250-3 0.250-3 0.250-3 0.250-3 23 0.689-1 0.684-1 0.694-1 0.689-1 0.684-1 0.689-1 0.689-1 0.694-1 0.674-1 24 0.684-1 0.679-1 0.689-1 0.684-1 0.679-1 0.684-1 0.684-1 0.689-1 0.669-1  Chart 1. Template: Sample normalized Similitude Degrees.Total samples:  24.  Flawless:  Chw01   through Chw17.  Flawed:  Chw18 through Chw24.  In the case of flawed objects, the digit after thehyphen indicates the number of sample peaks out of 2 x 2 searching neighbourhood.>>> Hough-transform based algorithm for the automatic invariant recognition of rectangular chocolates. Detection of defective pieces.51SISTEMAS E INFORMÁTICAInd. data 9(2), 2006moment and as a sample in another moment. Com-pare results from pairs Chw01-Chw02, and Chw02-Chw01, and so forth.It can also be seen in chart 1 that flawless objectshave rather high similitude degrees, while flawedobjects have low similitude degrees, the numbers afterthe hyphen accompanying the flawed pieces similitudedegrees stand for the number of accumulator peaksout of searching window.  It can be seen that the higherthe number of peaks out of searching window, thelower the similitude degree.  Flawless pieces do notreport accumulator peaks out of searching mask.C O N C L U S I O NThe problem of rotation, translation and size-scaling(RTS) invariant pattern recognition of polygonal objectshas been dealt with and an algorithm based on thefundamental properties of the polar HT has beendeveloped and successfully applied to the invariantrecognition of rectangular chocolates.It is important to mention that in the algorithm thathas been designed, the objects are taken to a pre-defined standard status through a set of translation,rotation, and size-scaling transformations which takeplace just once and exclusively in Hough space, inthis way a considerable computing time is saved andthe algorithm computational complexity is low.When dealing with rectangular chocolates thealgorithm successfully identifies flawless pieces,yielding a good similitude degree between templatepattern and samples.  The system also discriminatesagainst flawed pieces.The developed algorithm was initially tested withcomputer-synthesized objects, next with samplesmade with pasteboard, this was followed by itssuccessful application to the recognition of rectangu-lar biscuits and now it has been applied to therecognition of chocolates including discriminationagainst flawed pieces. These results suggest that thisalgorithm may be profitably applied to industrialautomatic quality control of products, maybe forobjects being transported on a conveyor belt.A C K N O W L E D G E M E N TThis work would not have been possible without thedeep and decisive influence of Prof. Luciano daFontoura Costa, from The Cybernetic Vision ResearchGroup, Sao Paulo University, (USP Sao Carlos Bra-sil), who introduced the author to the field of ComputerVision, specifically Pattern Recognition. The authorexpresses his sincere and special gratitude to Prof.da Fontoura Costa for all the time, dedication andvery specially for the transfer of knowledge.BIBLIOGRAPHICAL REFERENCES1.  Illingworth J. and  Kittler J. (1998).  A survey of theHough transform. CVGIP, vol , 44,  pags 87-116.2.  Duda R.O. and  Hart P.E. (1972). Use of the Houghtransform to detect lines  and curves in pictures.Communications of the ACM,  Vol 15,  No  1,  11-15, January.3.   Krishnapuram R. and  Casasent D. (1987).  Houghspace transformations for discrimination anddistortion estimation.  CVGIP,  vol 38,  pags. 299-316.4. Sinha P.K., Chen F.Y., Horne R.E.N. (1993).Recognition and location of  shapes in the Houghpattern space. IEE  Elect. Div. Colloq. on Houghtransform, 1993/106. Savoy place, London, May.5.  Montenegro J.J. - Da Fontoura Costa  L. - KöberleR. (1993). Geometric-Transformation-Invariantpattern recognition with Hough transforms andDistance-Discriminator Neural Networks.Workshop sobre Computacaõ  de altodesempenho para processamento de sinais. SãoCarlos, SP, Brasil.6. Gerig G. and  Klein F. (1986). Fast contouridentification through efficient Hough transform andsimplified  interpretation strategy.  IJCPR-8, Paris,498-500.7.  Montenegro J. J. (1994). Doctoral thesis researchunder  the direction of  Professor Luciano daFontoura Costa (Cybernetic Vision ResearchGroup, USP-SC, Brasil.8.  Montenegro J. J. (2002). Invariant Recognition ofrectangular biscuits through an algorithm operatingexclusively in Hough space. Flawed piecesdetection. Revista de Investigacion de Fisica, Vol5, No 1,2.9.  Montenegro J. J. (1995). Inteligencia Artificial:  Re-conocimiento de objetos en visión  computarizada.Seminario Software Científico, CONCYTEC:National Sci. & Tech Council, Lima Perú.10. Montenegro J. J. (2004). Invariant patternrecognition executed exclusively in the HoughJavier Montenegro J. >>>52SISTEMAS E INFORMÁTICAInd. data 9(2), 2006Space. Revista Electronica-UNMSM, No 13, Aug.200411.  Montenegro J. J. (1998).  A Polar-Hough-TransformBased Algorithm for the Translation, Orientation andSize-Scale Invariant Pattern Recognition ofPolygonal Objects. UMI Dissertations MicroformLD03769. Oct. 199812.  Montenegro J. J.  Imagery,  Digital Image ProcessingVirtual Laboratory.  Virtual Dynamics / Virtual Labs:Science & Engineering.>>> Hough-transform based algorithm for the automatic invariant recognition of rectangular chocolates. Detection of defective pieces.

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ALGORITMO BASADO EN LA TRANSFORMADA DE HOUGH, PARA EL RECONOCIMIENTO INVARIANTE DE CHOCOLATES RECTANGULARES. DETECCIÓN DE PIEZAS FALLADAS.

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