IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE VOL XX NO XX APRIL

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. XX, NO. XX, APRIL 2008 1 Improving Zernike Moments Comparison for Optimal Similarity and Rotation Angle Retrieval Jérôme Revaud, Guillaume Lavoué and Atilla Baskurt Abstract—Zernike moments constitute a powerful shape descriptor in terms of robustness and description capability. However the classical way of comparing two Zernike descriptors only takes into account the magnitude of the moments and loses the phase information. The novelty of our approach is to take advantage of the phase information in the comparison process while still preserving the invariance to rotation. This new Zernike comparator provides a more accurate similarity measure together with the optimal rotation angle between the patterns, while keeping the same complexity as the classical approach. This angle information is particularly of interest for many applications, including 3D scene understanding through images. Experiments demonstrate that our comparator outperforms the classical one in terms of similarity measure. In particular the robustness of the retrieval against noise and geometric deformation is greatly improved. Moreover, the rotation angle estimation is also more accurate than state of the art algorithms. Index Terms—Zernike moments, scene analysis, 3D object recognition, shape F 1 INTRODUCTION Zernike moments are widely used to capture global features of an image in pattern recognition and im- age analysis. Firstly introduced in computer vision by Teague [1], this shape descriptor has proved its superiority over other moment functions [2], [3] regarding to its description capability and ro- bustness to noise or deformations.

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• zernike moments

Sujets

• Analysis
• Maxima and minima
• Function

Informations

• Publié par: profil-urra-2012
• Nombre de lectures: 24
• Langue: English
• Poids de l'ouvrage: 1 Mo

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Abstract —Zernike moments constitute a powerful shape descriptor in terms of robustness and description capability. However the classical way of comparing two Zernike descriptors only takes into account the magnitude of the moments and loses the phase information. The novelty of our approach is to take advantage of the phase information in the comparison process while still preserving the invariance to rotation. This new Zernike comparator provides a more accurate similarity measure together with the optimal rotation angle between the patterns, while keeping the same complexity as the classical approach. This angle information is particularly of interest for many applications, including 3D scene understanding through images. Experiments demonstrate that our comparator outperforms the classical one in terms of similarity measure. In particular the robustness of the retrieval against noise and geometric deformation is greatly improved. Moreover, the rotation angle estimation is also more accurate than state of the art algorithms.

Jérôme Revaud, Guillaume Lavoué and Atilla Baskurt

1 I Zernike moments are widely used to capture global  process seems a natural way to improve the similar- features of an image in pattern recognition and im-  ity measure in terms of robustness against geomet- ageanalysis.Firstlyintroducedincomputervision t ri h c at d c e a f s o e rm th a e tio re n su o l r tin no g is c e om pa p r a t r ic at u o la r r i l s y. n H ot o i w n e v v a e r r ia i n n t by Teague [1], this shape descriptor has proved itssuperiorityoverothermomentfunctions[2], a a n n y gl m e o b re et t w o ee r n ot t at h i e on t , w u o nl p e a s t s te t r h n e si i s n- k pl n a o n w e n. ro F ta o t r i t o u n - [3] regarding to its description capability and ro-  nately in this paper we show that the moment bustness to noise or deformations. Hence rotation invariantpatternrecognitionusingZernikemo- a p n h g a l s e es in c a a n n o a p ls ti o m b al e w u a se y. d Fi t n o d r i e n t g rie b v ot e h t i h n i f s or ro m t a a t t i i o o n n ments has been extensively studied [4], [5]. Even very recently, a lot of authors have been working  (i.e. a robust rotation-invariant similarity measure on these moments, particularly to improve their  together with the optimal angle of rotation) can computation time [6], [7], [8], [9] or their accuracy  be of great interest for many applications includ- [10]. ing image registration [11], motion estimation in PracticallyoneZernikemomentisacomplex r v e i c d o e g o n a iz n i d ng pa t r h ti e cu o l b a j r e l c y ts sc c e o n m e p u o n s d i e n r g st t a h n e di i n m g a : g in e d a e n e d d number that contains two different values: magni- tude and phase , however, the usual way (i.e. used in  then extracting their in-plane orientation angles all existing algorithms) of comparing two Zernike  may help to compute their precise 3D pose and descriptorsonlyconsidersthemomentsmagni- t 3 h D us en t v o ir u o n n d m e e rs n t t. an A d l a ot cc o u f ra w te o l r y k t h h a e s c b o e r e r n es d p o o n n e di f n o g r tudes (as it brings invariance to rotation). In the angle/similarity recognition using keypoint-based context of 2D and 2D-3D indexing and recogni-  local descriptors like SIFT [12], however, this kind tion, this loss of information is not harmless when comparing two different patterns, and can induce  of tools works only on textured objects and fails erroneous results and impreciseness, as it will be  to describe smooth shapes or drawings (i.e. sketch) furtherillustrated. f c o a r se i s n , st g a l n o c b e a . l I s n h s a u p c e h d h e a s r c d rip d t e o s r c s ri l p i t k i e on Z /r e e r c n o ik g e niti m o o n - Using the phase information of Zernike moments  ments are particularly robust, that is the reason why Emails: {jerome.revaud, glavoue, abaskurt} @insa-lyon.fr t 2 h D e / y 3 h D av o e bj r e e c c t en r t e l c y o b g e n e it n io u n se t d h f r o o r u r g o h ta s ti k o e n tc i h n e v s ar [ i 1 a 3 n ] t , The authors are with LIRIS, UMR 5205 CNRS, INSA-Lyon, F-69621 Villeurbanne, France. [14]. It appears quite relevant to compute the in-

Index Terms —Zernike moments, scene analysis, 3D object recognition, shape ✦

Improving Zernike Moments Comparison for Optimal Similarity and Rotation Angle Retrieval

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. XX, NO. XX, APRIL 2008 1