The Polar Hough Transform has been used to create a system for rotation, translation and sizescaling automatic invariant pattern recognition of polygonal objects, and it has been successfully applied to the invariant recognition of L-shaped metallic corner-fasteners. Since the performance of the developed system is autonomous it may be applied to automatic quality control and automatic classification in the industry.La Transformada polar de Hough ha sido usada para crear un sistema para reconocimiento invariante automático de objetos poligonales, el cual opera independientemente de la posición, orientación y tamaño de los objetos y, ha sido exitosamente aplicado al reconocimiento de sujetadores metálicos esquineros(forma de L). Como el sistema es autónomo, podría ser aplicado a la automatización del control de calidad y de la clasificación, en la industria

Montenegro Joo, Javier

English

Revistas de investigacion UNMSM

SISTEMAS E INFORMÁ TICA88 Ind. data 10(1), 2007 ABSTRACT The Polar Hough Transform has been used to create a system for rotation, translation and size-scaling automatic invariant pattern recognition of polygonal objects, and it has been successfully applied to the invariant recognition of L-shaped meta l l i c  corner - fas teners .  S ince the performance of the developed system is autonomous it may be applied to automatic quality control and automatic classification in the industry. Key Words: Artificial intelligence, computational vision, vybernetic vision, invariant pattern recognition, invariant shape classification, Polar Hough transform, automatic quality control.R E C O N O C I M I E N T O  A U T O M Á T I C O  INVARIANTE DE SUJETADORES METÁ LICOS  E S Q U I N E R O S ,  B A S A D O  E N  L A  TRANSFORMADA DE HOUGH.RESUMENLa Transformada Polar de Hough ha sido usada para crear un sistema para reconocimiento invariante automático de objetos poligonales, el cual opera independientemente de la posición, orientación y tamaño de los objetos y, ha sido exitosamente aplicado al reconocimiento de sujetadores metálicos esquineros (forma de L).  Como el sistema es autónomo, podría ser aplicado a la automatización del control de calidad y de la clasificación, en la industria. Palabras Clave:  Inteligencia artificial, visión c o m p u t a c i o n a l ,  v i s i ó n  c i b e r n é t i c a ,  reconocimiento invariante, reconocimiento invariante de sujetadores, Transformada Polar de Hough, control automático de calidad.INTRODUCTION The Hough transform [1,4]  HT, is a powerful distortion and noise tolerant  technique thatmaps image-space points (x,y) into curves in a parameter   or accumulator space. In the present work the polar, also known as Normal HT is used. It maps image-space points into a parametric accumulator space by virtue of the equation                             By means of this relation, any binary point  (x,y)  in image space  X-Y  is mapped into a sinusoidal in the accumulator  space  - , which is   discretized  in cells  of coordinates .  The main feature of the HT is  that the N sinusoidals corresponding to a set of N collinear points (x ,y)  i ii=1,2,…,N   meet at a point   in the accumulator, the values of   o  and   characterizing the original straight line in the image. Every sinusoidal passing by contributes with 1 to a counting stored in that   location . The counting stored in every cell of the accumulator  corresponds to the number of points that are contained in a line characterized by  in eq.(1). Due to spatial discretization, lines in  image space - when Hough transformed- are usually scattered to neighbouring cells in parameter space. Montenegro [15] has created Imagery, a full interactive Virtual Lab that allows the user to learn about the Polar Hough Transform in real time while it is executed on user defined points and lines. This Virtual Lab includes also many other topics of Digital Image Processing and Pattern Recognition. MAIN HT PROPERTIESThe work reported here is based on the following fundamental HT properties: When a straight line is displaced to a parallel position in image space, only   a proportional displacement along the -coordinate   takes place in parameter space. When a straight line is rotated   degrees in image space, its 0associated peak in the accumulator space is shifted    degrees along 0  the     axis. When an object is uniformly scaled in image space, only the associated values of  change proportionally in accumulator space.(   ,   )(   ,    )   (  ,   ) (  ,  )(   ,   )(1) Javier Montenegro Joo )1( SinyCosx Recepción: Febrero de 2007 / Aceptación: Mayo de 2007(1) Director de Virtual Dynamics / Virtual Labs. Science & Engineering, EE.UU.E-mail: Director@virtualdynamics.orgHough-transform based automatic invariant recognition of metallic corner-fasteners.o o  o SISTEMAS E INFORMÁ TICA89Ind. data 10(1), 2007PREVIOUS RELATED WORKS Abundant literature dealing with general behaviour of the HT can be easily found in journals, however articles like this, reporting applications of the polar HT to pattern recognition in Hough's accumulator space are rather scarce and to the knowledge of this author only two researchers have already dealt with invariant pattern recognition in Hough space; these are  Krishnapuram and Casasent [3] , and Sinha et al [5], however neither of these two works considered object size-scaling. These authors use convolution in -space to achieve the rotational registration between sample objects and templates, an additional processing is then necessary to determine the translational correspondence.THE PRESENT WORK The system being described in this report is based on an algorithm endowed with the following advantages with respect to the two methods just mentioned lines above:An algorithm to solve the problem of object size-scaling is developed and it is successfully applied. This algorithm is associated to a low complexity computation and to a short computing time.When training the system there is no need to place the template object in any particular position, orientation or size, it is simply placed at random in image-space.The Hough space features of the object to be recognized are rotated and translated only once in accumulator space, then a comparison with the stored templates is accomplished.  This represents a substantial improvement respectively to the many comparisons implied by the methods used in the two works above mentioned.In the present work the counting stored in the accumulator bins is used as an evidence of sample-template matching.STRATEGY OF THE ALGORITHM This author has designed and developed an algorithm which operates exclusively on accumulator space    and  consists in taking the Hough space features of  the object  to a pre-defined standard  status  in Hough  space. In this context, “standard status” must be understood as a previously defined spatial distribution and normalized intensity of peaks in the accumulator [6,7,9,12]. The scaling problem is solved taking into account the fact that whatever the object size, the proportion among its side-lengths is translation, orientation and size-scale invariant, in this way the normalized intensity stored in the accumulator bins is always the same for any given object. The algorithm is applied equally to training and recognition stages. After Hough transforming the image-space, a sequence of operations and transformations take place in the accumulator so that the object's Hough space features are taken to the previously defined standard status, then a characteristic vector T or S, depending whether template or sample, is extracted. ACHIEVING INVARIANCE IN THE ACCUMULATOR (PARAMETER) SPACE All operations leading to achieve invariance respect to position, orientation and size-scaling, are carried out in the accumulator or parameter space.In both cases, during training and recognition the object is randomly placed on image-space in no par t icu lar  pos i t ion,  or ienta t ion,  or  s ize.     Notwithstanding, large instances of the training object should be preferred for the sake of improved accuracy.The algorithm being reported operates on a single object at a time, thus if several ones appear simultaneously in image-space a pre-processing is Figure 1.  L-shaped metallic corner-fasteners used in woodwork to maintain firm wooden jointures with four screws. This image shows four of the twenty sample photographs used in the research.Javier Montenegro J.  >>>SISTEMAS E INFORMÁ TICA90 Ind. data 10(1), 2007            Figure 2.   L-shaped  metallic corner-fasteners  (used to keep  firm  rectangular wooden joints with four screws).  Twenty Binarized photographs.necessary to single out individual samples. Below is included a short description of training and recognition processes, a broader description of these stages appear in [7,9,12].  THE TRAINING PROCESSThe pattern used to train the system is placed only once on image space and after Hough transforming it, a set of operations is carried out on the accumulator space so as to take the pattern to a pre-defined standard position [7,9,12,13,14], in this stage a template vector T is created and information about the votations accumulated in the characteristic peaks () of the template pattern is stored, this will be used as template during the recognition process.  Sometimes, depending on the special geometric features of the objects used as templates, two template vectors T  and T  may be needed, this just to 1 2make sure a good performance at recognition time.THE RECOGNITION PROCESSWhen the system is on recognition mode, the same steps carried-out at the training process must be followed for the sample to be recognized. For every incognito sample a sample-vector S is created with the corresponding values of (), and associated votations. In order to compare sample with template, the Euclidean distance between the two T-S pairs is computed.THE RESEARCH The performance evaluation of the system has been previously executed with computer-synthesized objects and with complex-shape pasteboard pieces [7,8,12].   Subsequently the method has been applied to recognize biscuits [7,8,13] and rectangular chocolates and to discriminate flawed rectangular  chocolates against flawless pieces. In all cases the results show a very good performance of the     algorithm [7,8,14].  This research was made with L-shaped metallic corner-fasteners used in woodwork to keep firm wooden jointures like the corner in a wooden box, see Figure 1. The twenty instances of the L-shaped metallic patterns used in the investigation are shown in Figure 2. Grey-scaled photographs were taken, scanned and converted to binary images, which were Hough-transform based automatic invariant recognition of metallic corner-fasteners.SISTEMAS E INFORMÁ TICA91Ind. data 10(1), 2007similitude degree is obtained for any pair of objects one of them used as a template in a moment and as a sample in another moment.  Compare results from pairs  mf01 - mf02,    and  mf04  - mf06  and so forth.The digits after the hyphen in chart 1 stand for the number of accumulator peaks out of searching window.   It can be seen that the higher the number of peaks out of searching window, the lower the similitude degree and vice versa.  CONCLUSION The problem of rotation, translation and size-scaling invariant pattern recognition of polygonal objects has been dealt with and an system (algorithm) based on the fundamental properties of the polar HT has been developed and successfully applied to the invariant recognition of  L-shaped  jointure fasteners. It is important to mention that in the designed algorithm   the Hough space features of the objects are taken to a pre-defined standard status through a set of translation, rotation, and size-scaling transformations which take place just once and exclusively in accumulator space, in this way a considerable computing time is saved and the algorithm complexity is low. In this research only the four longest sides of the corner-fasteners were used to characterize the samples by means of its associated four Hough space features.  Obviously if considering the six object sides the sample classification would be more accurate, but in this case some pre-processing in order to discard or refill the holes in the samples before Hough Top horizontal row  templates             Left vertical column: samples mf-01 mf-02 mf-03 mf-04 mf-05 mf-06 mf-07       1 mf-01 1.000 - 0 0.984 - 0 0.966 - 0 0.982 - 0  0.984 - 0 0.934 - 0 0.984 - 02 mf-02 0.984 - 0 1.000 - 0 0.737 - 1 0.979 - 0 0.972 - 0 0.937 - 0 0.730 - 13 mf-03 0.966 - 0 0.737 - 1 1.000 - 0 0.982 - 0 0.725 - 1 0.967 - 0 0.972 - 04 mf-04 0.982 - 0 0.979 - 0 0.982 - 0 1.000 - 0 0.972 - 0 0.952 - 0 0.977 - 05 mf-05 0.984 - 0 0.972 - 0 0.725 - 1 0.972 - 0 1.000 - 0 0.929 - 0 0.987 - 06 mf-06 0.934 - 0 0.937 - 0 0.967 - 0 0.952 - 0 0.929 - 0 1.000 - 0 0.939 - 07 mf-07 0.984 - 0  0.730 - 1 0.972 - 0 0.977 - 0 0.987 - 0 0.939 - 0 1.000 - 0       8 mf-08 0.742 - 1 0.744 - 1 0.737 - 1  0.747 - 1  0.731 - 1  0.724 - 1  0.734 - 19 mf-09 0.961 - 0 0.963 - 0 0.985 - 0  0.979 - 0  0.956 - 0  0.970 - 0  0.964 - 010 mf-10 0.730 - 1 0.964 - 0  0.746 - 1 0.735 - 1 0.722 - 1 0.740 - 1 0.730 - 111 mf-11 0.742 - 1 0.732 - 1 0.735 - 1 0.737 - 1 0.740 - 1 0.722 - 1 0.747 - 112 mf-12 0.950 - 0  0.952 - 0 0.981 - 0 0.967 - 0 0.944 - 0 0.985 - 0 0.954 - 013 mf-13 0.934 - 0 0.732 - 1 0.957 - 0 0.952 - 0  0.924 - 0 0.989 - 0 0.929 - 014 mf-14 0.977 - 0 0.722 - 1 0.954 - 0 0.959 - 0 0.986 - 0 0.922 - 0 0.982 - 015 mf-15 0.982 - 0 0.970 - 0 0.730 - 1 0.989 - 0 0.977 - 0 0.947 - 0 0.981 - 016 mf-16 0.957 - 0 0.960 - 0 0.747 - 1 0.974 - 0  0.952 - 0 0.976 - 0 0.730 - 017 mf-17 0.975 - 0 0.742 - 1 0.986 - 0 0.992 - 0 0.969 - 0 0.959 - 0 0.975 - 018 mf-18 0.950 - 0 0.952 - 0 0.981 - 0 0.967 - 0 0.944 - 0 0.985 - 0 0.954 - 019 mf-19 0.954 - 0 0.957 - 0 0.742 - 1 0.972 - 0 0.950 - 0 0.980 - 0 0.954 - 020 mf-20 0.947 - 0 0.949 - 0 0.974 - 0 0.965 - 0 0.942 - 0 0.987 - 0 0.947 - 0Chart 1.  Total samples:  20.   The digit after the hyphen indicates the number of sample peaks out of a 2x2 searching mask.                      passed as input to the system.  As it can be seen in the photographs, in Figure 2, input images are noise free and object edges are well defined, the metallic fasteners are six-sided and have four holes, which are used to fix them with four screws to the wooden boards making a rectangular corner.  The next section justifies the use of only four Hough space features instead of six (six sides) when dealing with the L-shaped fasteners.FOUR INSTEAD OF SIX HOUGH SPACE FEATURESThe obvious choice is to attempt to recognize the six-sided L-shaped fasteners by its corresponding six Hough space features, however when operating in this way sometimes the screw holes in the fasteners contributed to spurious accumulator peaks which   this research  to characterize the metallic fasteners. RESULTSChart 1 displays the similitude degrees between 20 samples and the 7 pieces out of them that were randomly chosen as templates. The objects are identified as mfnn where “mf” stands for “metallic fastener” and nn ranges from 01 through 20.   It may be seen in chart 1 that, as expected, when a template is also used as a sample the resulting similitude degree is 1.00.  (See the unitary diagonal in the upper portion of the chart). The same T-S Javier Montenegro J.  >>>SISTEMAS E INFORMÁ TICA92 Ind. data 10(1), 2007transformation might be necessary, in this manner the interference introduced by the holes may be eliminated at a cost of an increase in computing resources (time and processing).SYSTEM WEAKNESSES Even though the HT is noise and distortion tolerant per se, the system reported here is sensitive to both of them.  Seeing that the developed algorithm considers the counting stored in the accumulator bins, any noise particles aligned with the sample sides in image space may introduce spurious counting in the accumulator, thus altering the results of the scaling normalization stage.  Sampling variations, like those introduced by mechanical vibrations when input sample photographs are obtained may be responsible for distorted object sides, thus introducing spurious peaks in parameter space. A pre-processing based on repeated sampling to overcome these problems is proposed by Zhou and Lopresti [11], bear in mind however that any solution to solve problems like these has in general a non-negligible runtime cost.ACKNOWLEDGEMENT                                           The author expresses his heartfelt and special gratitude to Prof. Luciano da Fontoura Costa from The Cybernetic Vision Research Group, Sao Paulo University, (USP Sao Carlos Brasil), who introduced the researcher to the field of Computer Vision, specifically Pattern Recognition, for the dedication, the time and very specially for the transfer of knowledge.  Working with Prof. Luciano was a very pleasant and enriching experience, this research would not have been possible without his deep and decisive influence.                                  BIBLIOGRAPHICAL REFERENCES 1. Duda R.O and Hart P.E. (1972) Use of the Hough transform to detect lines and curves in pictures. Communications of the ACM, Vol 15, No 1, 11-15. USA. 2. Gerig G. and  Klein F. (1986). Fast contour identification  through efficient Hough transform and simplified  interpretation strategy. IJCPR-8, Paris, Francia. pags. 498-500,  3. Krishnapuram R. and  Casasent D. (1987). Hough space transformations  for discrimination and distortion estimation.  CVGIP,  vol 38,  pags. 299-316. 4. Illingworth J. and  Kittler J.  (1988). A survey of  the Hough transform.  CVGIP, vol , 44,  pags 87-116.5. Montenegro J.J. - Da Fontoura Costa  L. - Köberle  R. (1993). Geometric-Transformation-Invariant Pattern Recognition with Hough Transforms and Distance-Discriminator Neural Networks. Workshop Computacaõ de alto desempenho para processamento de sinais. São Carlos, SP, Brasil.6.  Montenegro J. J. (1994). Doctoral thesis research project under the direction of Prof. Luciano da  Fontoura Costa (Cybernetic Vision Research Group, USP-SC, Brasil).  7. Montenegro J.J. (1995). Inteligencia Artificial: Reconocimiento de Objetos en Visión Computarizada. Seminario Software Científico, CONCYTEC, Lima  Perú.  8. Montenegro J. J. (2004). Invariant pattern recognition executed exclusively in the Hough Space. Revista de Electronica,  UNMSM, No 13, Lima, Perú.9. Montenegro J.J. (2002). Invariant recognition of rectangular biscuits through an algorithm operating exclusively in Hough Space. Flawed pieces detection.  Rev. Inv. Fisica. Vol 5, Lima, Perú.10. Montenegro J.J., (2006). Hough Transform based Algorithm for the automatic Invariant Recognition of Rectangular Chocolates. Detection of defective pieces. Industrial Data, Vol 9, No 2, Lima, Perú.12. Sinha P.K., Chen F.Y., Horne R.E.N. (1993) Recognition and location of shapes in the Hough pattern space. IEE Elect. Div. Colloq. on Hough transform, 1993/106. Savoy place, London, UK.13. Yuen S. Y.  and  Ma C.H. (1997).  An investigation of the nature of parameterization for the Hough transform. Pattern Recognition, Vol  30,  No 6.14. Zhou, J. and Lopresti, D. (1997). Improving classifier performance through repeated sampling. Pattern Recognition, Vol. 30, No. 10.Hough-transform based automatic invariant recognition of metallic corner-fasteners.

Reconocimiento automático invariante de sujetadores metálicos e squineros, basado en la transformada de Hough.

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Reconocimiento automático invariante de sujetadores metálicos e squineros, basado en la transformada de Hough.

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