Bull, DR

Canagarajah, CN

Hill, PR

English

Content-based retrieval is ultimately dependent on the features used for the annotation of data and its efficiency is dependent on the invariance and robust properties of these features. For texture-based features an important form of invariance is rotational invariance. Novel rotationally invariant texture-based features are introduced that are extracted from a polar Fourier transform (PFT). The PFT is similar to the discrete Fourier transform in two dimensions but uses transform parameters radius and angle rather than the Cartesian co-ordinates. The PFT is discretised appropriately across the angular and radial frequency space with the transform magnitudes forming the rotationally invariant features. These features although rotationally invariant, capture the angular distribution together with the radial distribution of frequency within texture. Preliminary results show the method to give better results than rotationally variant and invariant Gabor filter scheme

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                          Hill, P. R., Canagarajah, C. N., & Bull, D. R. (2001). Rotationally invarianttexture based features. In ICIP 2001. (Vol. 2, pp. 141 - 144). Institute ofElectrical and Electronics Engineers (IEEE). 10.1109/ICIP.2001.958444Link to published version (if available):10.1109/ICIP.2001.958444Link to publication record in Explore Bristol ResearchPDF-documentUniversity of Bristol - Explore Bristol ResearchGeneral rightsThis document is made available in accordance with publisher policies. Please cite only the publishedversion using the reference above. Full terms of use are available:http://www.bristol.ac.uk/pure/about/ebr-terms.htmlTake down policyExplore Bristol Research is a digital archive and the intention is that deposited content should not beremoved. However, if you believe that this version of the work breaches copyright law please contactopen-access@bristol.ac.uk and include the following information in your message:• Your contact details• Bibliographic details for the item, including a URL• An outline of the nature of the complaintOn receipt of your message the Open Access Team will immediately investigate your claim, make aninitial judgement of the validity of the claim and, where appropriate, withdraw the item in questionfrom public view.ROTATIONALLY INVARIANT TEXTURE BASED FEATURES P.R. Hill, C.N. Canagarajah and D.R. Bull The University of Bristol, Bristol, UK ABSTRACT Content-based retrieval is ultimately dependent on the fea- tures used for the annotation of data and its efficiency is dependent on the invariance and robust properties of these features. For texture based features an important form of invariance is rotational invariance. In this paper novel rota- tionally invariant texture based features are introduced that are extracted from a Polar Fourier Transform (PFT). The PFT is similar to the Discrete Fourier Transform in two di- mensions but uses transform parameters radius and angle rather than the Cartesian co-ordinates. The PFT is discre- tised appropriately across the angular and radial frequency space with the transform magnitudes forming the rotation- ally invariant features. These features although rotationally invariant, capture the angular distribution together with the radial distribution of frequency within texture. Preliminary results show the method to give better results than rotation- ally variant and invariant Gabor filter schemes. 1. INTRODUCTION The ability to effectively retrieve images or video accord- ing to their content is still an unfulfilled goal for multimedia applications and therefore a currently active research area. Content-based retrieval is dependent on the features used for the annotation of data and its efficiency is dependent on the ability of extracted features to facilitate meaningful re- sponses to a range of queries. For texture based features, this ability is to a large extent, dependent on the invari- ance and robust properties of the features. These proper- ties include the invariance to scale, rotation, illumination transforms and robustness against noise. Inclusion of these properties should ensure that the features capture a more ab- stract representation of the texture separate from the circum- stances in which it is found. This paper focuses on texture features that have been developed to be invariant to a trans- formation of a texture by rotation. Rotational invariance of texture features can be separated into two different classes: Isotropic and Anisotropic. Isotropic rotational invariant fea- tures are formed from averaged measures of some property (such as frequency content) in all directions. This is the most obvious way of obtaining rotationally invariant fea- tures. However in order to produce a richer representation 0-7803-6725-1/01/$10.00 02001 IEEE the angular distribution of such a property can be charac- terised whilst remaining rotationally invariant. This type of rotational invariance is known as anisotropic. 2. REVIEW Several methods have been proposed to extract rotation- ally invariant texture based features without using spatial- frequency analysis including circularly symmetric autore- gressive (CSAR) models [ 11 and iterative morphological de- compositions [2]. However, most attention has been fo- cused on spatial-frequency analysis methods such as wavelet and pyramid decompositions as in general they have pro- duced the best results. The steerable pyramid [3, 4, 51 is a spatial-frequency decomposition that has been utilised to produce isotropic and anisotropic rotationally invariant tex- ture based features. It has the advantage over a normal wavelet type decomposition in that the output subbands can be adjusted to analyse many different orientations at each scale. Unfortunately this transform has the disadvantage of being considerably overcomplete with the amount of over- completeness increasing with the number of analysed ori- entations. The more common dyadic wavelet decomposi- tions used in many compression applications have also been used to extract texture features that are rotationally invari- ant. This has been done by simple combinations of subband energy measures [6] or by the modelling of the variation in the energy of each subband using Markov models [7]. These methods however lack the directional selectivity of the steerable pyramid. Wu and Wei [SI have used a clas- sical dyadic wavelet decomposition on a spiral-resampling lattice. The phase (and therefore the rotation) of the spi- ral is removed in the decomposition thus enabling rotation- ally invariant measures to be produced from the resulting subbands. The filter separability and iterative nature of the dyadic wavelet transform necessary for computationally ef- ficient decomposition produces frequency analysis in octave bands. This may be considered to be too coarse for accurate texture analysis. Non-separable wavelets have been used [9] to produce more flexible isotropic and anisotropic rotation- ally invariant features over greater radial frequency ranges. This paper is organised as follows. Initially the proper- ties of the Polar Fourier Transform are investigated together 141 Authorized licensed use limited to: UNIVERSITY OF BRISTOL. Downloaded on February 25, 2009 at 06:22 from IEEE Xplore.  Restrictions apply.a) 2D Fourier Transform b) Polar Fourier Transform Fig. 1. Spatial visualisations of positions in FFT and PFT transform space with visualisations of the analysis functions. The texture classification experiments using the developed features are then described together with the experimental results. 3. THE POLAR FOURIER TRANSFORM (PFT) The traditional discrete Fourier transform in two dimensions takes the form shown in equation 1. The parameters map- ping the transform domain are the vertical and horizontal Cartesian frequency parameters and figure l a  shows the real parts of several two dimensional spatial basis functions and their corresponding position in transform space. This trans- form domain can therefore be considered as analysing the frequency content in lerms of such orientated complex si- nusoidal gratings. 1 *--l F ( W z , W y )  = N2 1; f ( G Y ) e z P [ - j 2 n ( w z z  + W y Y ) I N l  x=l) (1) The parameters that map the transform domain of the PFT are the frequency parameters relating to the angular and radial frequency i.e. w,. and w e  in equation 2. Points in the transform space therefore correspond to complex spiral- type basis functions as depicted in figure lb. The magnitude of the complex output of the PFT can be used to form ro- tationally invariant texture based features. However, when applied directly to the spatial domain, the PlT is not invari- ant to translations. The PET transformation is only applied after an initial FFT is performed on the texture in order to remove translation dependence. 1 N-l F(wl-9 w e )  = ~2 f(z, y ) e w  [-j(r x wrr/N + wee)] (2) The features are therefore extracted as represented by figure 2. i.e. the features are formed from the magnitudes of the PFT output after an FFT transformation. When dis- cretising the parameters, we only needs to take even val- ues as the frequency plane is symmetric. The discretisa- tion of the w,. parameter is discretionary but would be ex- pected to produce the best results when considering an even or logarithmic spread. The best results were in fact pro- duced from an empirically derived and small set (see sec- tion 4). These features are not only rotationally invariant but also characterise the angular frequency distribution of the texture i.e. they have anisotropic rotational invariance. A similar method is used in pattern recognition called the Fourier-Mellin transform [ 101 where the rotational invari- ance is achieved by resampling on a log-polar lattice in be- tween two FFT transforms. However, developing texture features obtained directly from the PFT obviates the need for the interpolation necessary for the translation to log- polar (or just polar) coordinates. This interpolation may be considered to introduce unnecessary errors due to the nec- essary averaging operations and also the variations in cov- erage for different radii. 2=0 4. EXPERIMENTAL RESULTS Sixteen textures were taken from the Brodatz texture al- bum [ l l] to test the classification performance of the de- veloped features. These textures (shown in figure 3) were 142 Authorized licensed use limited to: UNIVERSITY OF BRISTOL. Downloaded on February 25, 2009 at 06:22 from IEEE Xplore.  Restrictions apply.Texture Area Feature Extraction Technique PFT derived features at each scale Rotationally variant Gabor filters Rotationally invariant Gabor filters 2D-FFT U Correct Classification Rate (%) 89.58 70.53 82.89 Power Spectrum output for each 0, andme combination Polar Fourier Transform Fig. 2. Extraction of texture features from the Polar Fourier Transform chosen to represent textures that contained a range of peri- odic, stochastic and directional elements. The textures were scanned as eight-bit raw grey level images of size 256 x 256 pixels. Fig. 3. 16 Brodatz textures used in texture classification experiments One version of each texture class was used for training at angles of 0", 30", 45" and 60". Seven different versions of each texture were used for classification and presented at an- gles 20", 70", go", 120", 135" and 150'. This gave 42 clas- sifications per texture arid 672 in all. Each training texture was tiled into 16 x 16 squares with feature values being ex- tracted from the PFT decomposition of each tile leading to a mean vector and covariance matrix for each texture class. The four angles of training were used to enable the mean feature vector and the covariance matrix to be properly es- timated under texture rotation. Similarly, the mean feature vectors were extracted from the test textures from the PFT transform of tiled 16 x 16 squares. Textures were classified Feature Vector Table 1. Classification performance of wavelet features on rotated images: decomposition on 16 x 16 areas, best per- forming feature sets for each method. 5. CONCLUSION Traditional texture based features for retrieval often do not exhibit rotational invariance as can be seen from the results for the rotationally variant Gabor filters in table 1. Con- I 43 Authorized licensed use limited to: UNIVERSITY OF BRISTOL. Downloaded on February 25, 2009 at 06:22 from IEEE Xplore.  Restrictions apply.versely, many rotationally invariant texture based features do not characterise the angular distribution of frequency con- tent within the texture i.e. they have isotropic rotational in- variance. The features here developed from the PFI’ are not only rotationally invariant but also characterise the angular frequency content of the texture i.e. they have anisotropic rotational invariance. However, one disadvantage of using the magnitude of the PFT output (as described above) is the removal of radial phase information that would provide ex- tra useful information for classification. Indeed although the PFT magnitude output does produce rotationally invari- ant features in general it does not capture an intuitively un- derstandable representation of frequency content. This may not prove to be a disadvantage but may have implications for content based retrieval of natural images where there will be a significantly higher number of textures to distinguish. It does however effectively characterise the frequency content of the image / texture in a rotationally invariant fashion as is demonstrated in the above results. The classification per- formance in the conducted tests of a feature vector formed from rotational harmonics extracted from a PFT decompo- sition was over 5% better than an alternative rotationally in- variant method based 011 circularly symmetric Gabor filters. Using the PIT within this type of method may be extended into an analogous transform of the Fourier-Mellin transform where by the axes of thle PFT are not just polar but log po- lar. Theoretically this s’hould produce scale and rotationally invariant texture based features. This should be a valuable extension to this work. Experience has shown that classification results can be extremely dependant on the choice of test conditions and image set. It is therefcre difficult to claim a definitive im- provement on previous rotational invariant characterisation methods. However the PFT method provides a flexible ap- proach for generating aniostropic rotationally invariant fea- tures that could be potentially integrated with scale invariant features. 6. REFERENCES [I]  R.L. Kashyap anid A. Khotanzad, “A model-based method for rotation invariant texture classification,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 8, no. 4, pp. 472-481, July 1996. [2] W.K. Lam and C.K. Li, “Scale invariant texture clas- sification by iterative morphological decomposition,” IEE Electronics Letters, vol. 32, no. 6,  pp. 534-535, March 1996. [4] W.T. Freeman E.P. Simoncelli, “A flexible architec- ture for multi-scale derivative computation,” IEEE 111- ternational Conference on Image Processing, October 1995. [5] R. Goodman H. Greenspan, S. Belongie and P. Perone, “Overcomplete steerable pyramid filters and rotation invariance,” Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 222- 228, June 1994. [6] R. Porter, Texture Class$cation and Segmentation, Ph.D. thesis, The University of Bristol, November 1997. [7] J-L Chen and A. Kundu, “Rotation and gray scale transform invariant identification using wavelet de- composition and hidden markov model,” IEEE Truns- actions on Pattern Analysis and Machine Intelligence, vol. 16, no. 2, February 1994. [8] W-R Wu and S-C Wei, “Rotation and gray-scale transform-invariant texture classification using spi- ral resampling, subband decomposition, and hidden markov model,” IEEE Transactions on Image Pro- cessing, vol. 5,  no. 10, October 1996. [9] P. Scheunders S. Livens P. Vautrot, G. Van De Wouwer and D. Van Dyck, “Non-separable wavelets for rotation-invariant texture classification and segmenta- tion,” IEEE Transactions on Pattern Analysis and Ma- chine Intelligence, vol. 8, no. 4, pp. 472-481, July 1998. [lo] M Daoudi S. Derrode and E Ghorbel, “Invariant content-based image retrieval using a complete set of fourier-mellin descriptors,” ”ICMCS”,  vol. 2, pp. 534-535, 1999. [ 111 P. Brodatz, Textures, A Photographic Album for Artists and Designers, Dover Publications, New York, 1966. [3] E.H. Adelson E.I! Simoncelli, W.T. Freeman and D.J. Heeger, “Shiftable multi-scale transforms,” IEEE Transactions on Information Theory, vol. 38, no. 2, pp. 587-607, March 1992. 144 Authorized licensed use limited to: UNIVERSITY OF BRISTOL. Downloaded on February 25, 2009 at 06:22 from IEEE Xplore.  Restrictions apply.

A flexible architecture for multi-scale derivative computation,”

A model-based method for rotation invariant texture classification,”

Invariant content-based image retrieval using a complete set of fourier-mellin descriptors,”

Non-separable wavelets for rotation-invariant texture classification and segmentation,”

Overcomplete steerable pyramid filters and rotation invariance,”

Rotation and gray scale transform invariant identification using wavelet decomposition and hidden markov model,”

Rotation and gray-scale transform-invariant texture classification using spiral resampling, subband decomposition, and hidden markov model,”

Scale invariant texture classification by iterative morphological decomposition,”

Shiftable multi-scale transforms,”

Texture Class$cation and Segmentation,

Rotationally invariant texture based features

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Rotationally invariant texture based features

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