## Wavelet-Based Texture Retrieval Using Generalized Gaussian Density and Kullback-Leibler Distance (2002)

### Cached

### Download Links

- [lcavwww.epfl.ch]
- [infoscience.epfl.ch]
- [www.ifp.uiuc.edu]
- [www.ifp.illinois.edu]
- [lcavwww.epfl.ch]
- DBLP

### Other Repositories/Bibliography

Venue: | IEEE Trans. Image Processing |

Citations: | 157 - 4 self |

### BibTeX

@ARTICLE{Do02wavelet-basedtexture,

author = {Minh N. Do and Martin Vetterli},

title = {Wavelet-Based Texture Retrieval Using Generalized Gaussian Density and Kullback-Leibler Distance},

journal = {IEEE Trans. Image Processing},

year = {2002},

volume = {11},

pages = {146--158}

}

### Years of Citing Articles

### OpenURL

### Abstract

We present a statistical view of the texture retrieval problem by combining the two related tasks, namely feature extraction (FE) and similarity measurement (SM), into a joint modeling and classification scheme. We show that using a consistent estimator of texture model parameters for the FE step followed by computing the Kullback--Leibler distance (KLD) between estimated models for the SM step is asymptotically optimal in term of retrieval error probability. The statistical scheme leads to a new wavelet-based texture retrieval method that is based on the accurate modeling of the marginal distribution of wavelet coefficients using generalized Gaussian density (GGD) and on the existence a closed form for the KLD between GGDs. The proposed method provides greater accuracy and flexibility in capturing texture information, while its simplified form has a close resemblance with the existing methods which uses energy distribution in the frequency domain to identify textures. Experimental results on a database of 640 texture images indicate that the new method significantly improves retrieval rates, e.g., from 65% to 77%, compared with traditional approaches, while it retains comparable levels of computational complexity.

### Citations

8889 |
Elements of Information Theory
- Covet, Thomas
- 1991
(Show Context)
Citation Context ... FEBRUARY 2002 weak law of large number, the ML selection rule (1) is equivalent to maximizing This can be seen as equivalent to minimizing the Kullback–Leibler distance (KLD) or the relative entrop=-=y [19]-=- between the two PDFs and Under the same asymptotic condition ( is large), if the FE step uses a consistent estimator, which ensures the estimated parameter converges to the true parameter , then the ... |

2491 | A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
- Mallat
- 1989
(Show Context)
Citation Context ... marginal density of coefficients at a particular subband produced by various type of wavelet transforms may be achieved by adaptively varying two parameters of the generalized Gaussian density (GGD) =-=[29]-=-, [30], [7], [31], which is defined as (12) where is the Gamma function, i.e., , . Here models the width of the PDF peak (standard deviation), while is inversely proportional to the decreasing rate of... |

1801 |
Ten lectures on wavelets
- Daubechies
- 1992
(Show Context)
Citation Context ...iscriminating textures. In this experiment, we employed the conventional pyramid wavelet decomposition with three levels using the Daubechies’ maximally flat orthogonal filters of length 8 ( filters=-=) [35]-=-. From a single image in the database (of size 128 128), two GGD parameters were estimated from each of nine wavelet subbands (except for the lowest band or scale coefficients which corresponds to the... |

1334 | On information and sufficiency - Kullback, Leibler - 1951 |

1212 | Contentbased image retrieval at the end of the early years
- Smeulders, Worring, et al.
- 2000
(Show Context)
Citation Context ...interact with these collections and to do so in a timely manner. As a result, content-based image retrieval (CBIR) from unannotated image databases has been a fast growing research area recently: see =-=[1]-=- for a recent extensive review on the subject. We consider a simple architecture of a typical CBIR system (Fig. 1), where there are two major tasks. The first one is feature Manuscript received Decemb... |

918 |
Query by image and video content: The QBIC system
- Flickner, Sawhney, et al.
- 1995
(Show Context)
Citation Context ...tion problems where the normalized factors are computed using a training set of feature vectors from each class. Furthermore, the commonly used inverse variance weighted Euclidean distance as in CBIR =-=[15]-=- is questionable in the case of a feature component that has small global variance, thus leading to a large weight in the overall distance. By contrast, it can be argued that a small variation compone... |

875 |
Receptive fields, binocular interaction and functional architecture in the cat's visual cortex
- Hubel, Wiesel
- 1962
(Show Context)
Citation Context ...uency domain identifies a texture. Besides providing acceptable retrieval performance from large texture databases, those approaches are partly supported by physiological studies of the visual cortex =-=[9]-=-, [10]. Furthermore, as wavelets are a core technology in the next generation of still image coding format, JPEG-2000 [11], the choice of wavelet features enables the implementation of retrieval syste... |

853 |
Fundamentals for Statistical Signal Processing: Estimation Theory
- Kay
- 1993
(Show Context)
Citation Context ... estimated parameter converges to the true parameter , then the distance (2) can be computed using the estimated model parameters and . For such consistent estimator, we could employ the ML estimator =-=[20]-=-, which means that for the query image, it computes In summary, by combining FE and SM into a joint modeling and classification scheme, the optimum ML selection rule can be asymptotically realized (as... |

747 |
Texture features for browsing and retrieval of image data
- Manjunath, Ma
- 1996
(Show Context)
Citation Context ... experiments, a simulated query image is any one of 640 images in our database. The relevant images for each query are defined as the other 15 subimages from the same original VisTex image. Following =-=[6]-=- we evaluated the performance in terms of the average rate of retrieving relevant images as a function of the number of top retrieved images. The new approach is compared with the traditional methods ... |

659 | VisualSEEk: A fully automated contentbased image query system - Smith, Chang - 1996 |

659 | Non-Uniform Random Variate Generation - Devroye - 1986 |

575 | Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by twodimensional visual cortical filters - DAUGMAN - 1985 |

489 | Photobook: Content-based manipulation of image databases - Pentland, Picard, et al. - 1996 |

395 | Pyramid-based texture analysis/synthesis
- HEEGER, BERGEN
- 1995
(Show Context)
Citation Context ...on which suggests that two homogeneous textures are often difficult to discriminate if they produce similar marginal distributions of responses from a bank of filters [26]. In fact, Heeger and Bergen =-=[27]-=- successfully synthesized many natural looking 2 This is an abuse of terminology since strictly speaking v norm is not an energy function. Sometimes it is chosen due to its simplicity. Results from se... |

360 |
Textural features corresponding to visual perception
- Tamura, Mori, et al.
(Show Context)
Citation Context ...e one hand, the ultimate goal is to define similarity functions that match with human perception, but how humans judge the similarity between images is a topic of ongoing research. Perceptual studies =-=[12]-=-, [13] identified texture dimensions by conducting experiments that asked observers to group textures according to perceived similarity. The detected perceptual criteria and rules for similarity judgm... |

333 | NaTra: A Toolbox for Navigating Large Image Databases. Paper presented at the - Ma, Manjunath - 1997 |

277 | Fast multiresolution image querying
- Jacobs, Finkelstein, et al.
- 1995
(Show Context)
Citation Context ...efficient transforms [2]–[8]. Furthermore, since wavelets are used in major future image compression standards [11] and are also shown to be prominent in searching for images based on color and shap=-=e [23]-=-, [24], a wavelet-based texture retrieval system can be used effectively in conjunction with a compression system and retrieval systems using other image features (see Fig. 2). Using the assumption th... |

272 | Texture classification and segmentation using wavelet frames - Unser - 1995 |

268 |
Filtering for texture classification: A comparative study
- Randen, Husoy
- 1999
(Show Context)
Citation Context .... In this work, we focus on the use of texture information for image retrieval. Some of the most popular texture extraction methods for retrieval are based on filtering or wavelet-like approaches [2]�=-=��[8]-=-. Essentially, these methods measure energy (possibly weighted) at the output of filter banks as extracted features for texture discrimination. The basic assumption of these approaches is that the ene... |

231 |
Texture analysis and classification with tree-structured wavelet transform
- Chang, Kuo
- 1993
(Show Context)
Citation Context ...ts on images of size 128 2 128. (a) lowpass filter. Wavelet uses an orthogonal filter bank with length lowpass and highpass filters. For the number of decomposition levels, our experiments agree with =-=[3]-=- that the size of the smallest subimages should not be less than 16 16 so the estimated energy values or model parameters would be robust. Hence for the input image size 128 128, a maximum of three le... |

221 |
Two-dimensional spectral analysis of cortical receptive field profiles
- Daugman
- 1980
(Show Context)
Citation Context ... domain identifies a texture. Besides providing acceptable retrieval performance from large texture databases, those approaches are partly supported by physiological studies of the visual cortex [9], =-=[10]-=-. Furthermore, as wavelets are a core technology in the next generation of still image coding format, JPEG-2000 [11], the choice of wavelet features enables the implementation of retrieval systems tha... |

200 | random fields and maximum entropy: Towards a unified theory for texture modeling
- Zhu, Wu, et al.
- 1998
(Show Context)
Citation Context ...t the th subband, typically the following two values are used as features: and (10) (11) On the other hand, statistical approaches treat texture analysis as a probability inference problem (e.g., see =-=[25]-=-). A natural extension of the energy method is to model a texture by the marginal densities of wavelet subband coefficients. This is justified by recent psychological research on human texture percept... |

181 | Analysis of multiresolution image denoising schemes using generalized Gaussian and complexity priors
- Moulin, Liu
- 1999
(Show Context)
Citation Context ... of coefficients at a particular subband produced by various type of wavelet transforms may be achieved by adaptively varying two parameters of the generalized Gaussian density (GGD) [29], [30], [7], =-=[31]-=-, which is defined as (12) where is the Gamma function, i.e., , . Here models the width of the PDF peak (standard deviation), while is inversely proportional to the decreasing rate of the peak. Someti... |

165 | Texture Classification by Wavelet Packet Signatures
- Laine, Fan
- 1993
(Show Context)
Citation Context ...yout. In this work, we focus on the use of texture information for image retrieval. Some of the most popular texture extraction methods for retrieval are based on filtering or wavelet-like approaches =-=[2]��-=-�[8]. Essentially, these methods measure energy (possibly weighted) at the output of filter banks as extracted features for texture discrimination. The basic assumption of these approaches is that the... |

118 |
Color Indexing,” Int
- Swain, Ballard
- 1991
(Show Context)
Citation Context ...ying assumptions. Statistical modeling has been used in CBIR systems before. Perhaps the most well-known examples are the use of histograms to capture the distribution of image features such as color =-=[16]-=-. Wouwer et al. [7] employed generalized Gaussian density functions to represent texture images in the wavelet domain. The model parameters are estimated using a method of moment matching, and the sim... |

117 | Periodicity, directionality and randomness: Wold features for image modeling and retrieval
- Liu, Picard
- 1996
(Show Context)
Citation Context ...by visually examining the images of retrieval results. However, this can only be based on a subjective perceptual similarity since there exists no “correct” ordering that is agreed upon by all peo=-=ple [36]. Fi-=-g. 10 shows some examples of retrieval results to demonstrate the capability of our method. In Fig. 10(a), the query image is “leaves.” The system almost perfectly retrieves all images of the same... |

113 | Transform Features for Texture Classification and Discrimination in Large Image Databases - Smith, Chang - 1994 |

98 | Texture characterization via joint statistics of wavelet coefficient magnitudes
- Simoncelli, Portilla
- 1998
(Show Context)
Citation Context ...rate texture models can be obtained via a fusion of marginal distributions using minimax entropy principles [25] or by taking into account the joint statistics of wavelet coefficients across subbands =-=[28]-=-. However, considering complexity as a major constraint in the image retrieval application, in this work we simply characterize texture images via marginal distributions of their wavelet subband coeff... |

89 | Query by image example: The CANDID approach - Kelly, Cannon, et al. - 1995 |

75 | Multimedia analysis and retrieval system (MARS) project - Huang, Methotra, et al. - 1997 |

72 |
G.L.: Towards a texture naming system: Identifying relevant dimensions of texture. Visualization
- Rao, Lohse
- 1993
(Show Context)
Citation Context ...hand, the ultimate goal is to define similarity functions that match with human perception, but how humans judge the similarity between images is a topic of ongoing research. Perceptual studies [12], =-=[13]-=- identified texture dimensions by conducting experiments that asked observers to group textures according to perceived similarity. The detected perceptual criteria and rules for similarity judgment fr... |

66 | Matching and retrieval based on the vocabulary and grammar of color patterns
- Mojsilovic, Kovacevic, et al.
(Show Context)
Citation Context ... textures according to perceived similarity. The detected perceptual criteria and rules for similarity judgment from this type of subjective experiments can be used in building image retrieval system =-=[14]-=-. On the othersDO AND VETTERLI: WAVELET-BASED TEXTURE RETRIEVAL 147 hand, many current retrieval systems take a simple approach by using typically norm-based distances (e.g., Euclidean distance) on th... |

56 |
Fast approximation of Kullback-Leibler distance for dependence trees andHidden Markov models
- Do
- 2003
(Show Context)
Citation Context ... effectively here for modeling the coefficients from the wavelet transforms and wavelet frames and can applied to other similar filtering schemes such as wavelet packets and Gabor transforms. In [38]�=-=��[40]-=-, we employed the statistical framework tosDO AND VETTERLI: WAVELET-BASED TEXTURE RETRIEVAL 157 more complex texture models that aggregate wavelet descriptors across scales and orientations using hidd... |

54 |
Local linear transforms for texture measurements
- Unser
- 1986
(Show Context)
Citation Context ...better results might be obtained by taking into account the distribution (e.g., covariances) of the feature vector itself from each predefined class and then employing the optimal Bayesian classifier =-=[37]-=-. Of course, this requires an additional training step which one cannot usually afford in the general retrieval problem. The proposed statistical framework can be applied to other and more general ret... |

54 | Texture recognition using a non parametric multi-scale statistical model - Bonet, Viola - 1998 |

53 | Wavelet-based signal processing using Hidden Markov models - Crouse, Nowak, et al. - 1998 |

42 | Rotation invariant texture characterization and retrieval using steerable wavelet-domain hidden markov models - Do, Vetterli - 2002 |

41 |
Estimation of shape parameter for generalized Gaussian distributions in subband decompositions of video
- Sharifi, Leon-Garcia
- 1995
(Show Context)
Citation Context ...nal density of coefficients at a particular subband produced by various type of wavelet transforms may be achieved by adaptively varying two parameters of the generalized Gaussian density (GGD) [29], =-=[30]-=-, [7], [31], which is defined as (12) where is the Gamma function, i.e., , . Here models the width of the PDF peak (standard deviation), while is inversely proportional to the decreasing rate of the p... |

38 |
Statistical texture characterization from discrete wavelet representations
- Wouwer, Scheunders, et al.
- 1999
(Show Context)
Citation Context ...atistical modeling has been used in CBIR systems before. Perhaps the most well-known examples are the use of histograms to capture the distribution of image features such as color [16]. Wouwer et al. =-=[7]-=- employed generalized Gaussian density functions to represent texture images in the wavelet domain. The model parameters are estimated using a method of moment matching, and the similarity function is... |

36 |
Theories of visual texture perception
- Bergen, Adelson
- 1991
(Show Context)
Citation Context ...esearch on human texture perception which suggests that two homogeneous textures are often difficult to discriminate if they produce similar marginal distributions of responses from a bank of filters =-=[26]-=-. In fact, Heeger and Bergen [27] successfully synthesized many natural looking 2 This is an abuse of terminology since strictly speaking v norm is not an energy function. Sometimes it is chosen due t... |

34 |
Parameteric Generalized Gaussian density estimation
- Varanasi, Aazhang
- 1989
(Show Context)
Citation Context ...aussian and Laplacian PDFs as special cases, using and , respectively. Within a CBIR statistical framework, the desired estimator in our case is the maximum-likelihood (ML) estimator. Furthermore, in =-=[32]-=- evaluation of accuracy of estimates for both large and small samples for GGD models among classic statistical methods shows that the ML estimator is significantly superiors150 IEEE TRANSACTIONS ON IM... |

19 | A unifying view of image similarity
- Vasconcelos, Lippman
- 2000
(Show Context)
Citation Context ...mated using a method of moment matching, and the similarity function is again defined as weighted Euclidean distances on extracted model parameters. Independently of our work, Vasconcelos and Lippman =-=[17]-=- recently took a similar approach where they introduced a probabilistic formulation of the CBIR problem as a common ground for several currently used similarity functions. As an important case of CBIR... |

16 |
ªTexture Recognition Using a Nonparametric Multiscale Statistical Model,º
- Bonet, Viola
- 1998
(Show Context)
Citation Context ...h image models can incorporate the knowledge from perceptual studies to closely match human judgment. We point out that the Kullback–Leibler distance has been used in comparing images (e.g., in [21]=-=, [22]-=-) but, to our knowledge, its use has not yet been sufficiently justified in the context of the image retrieval problem by jointly considering the two related tasks FE and SM. To combine the KLDs from ... |

14 |
Invariant image retrieval using wavelet maxima moment
- Do
- 1998
(Show Context)
Citation Context ...ent transforms [2]–[8]. Furthermore, since wavelets are used in major future image compression standards [11] and are also shown to be prominent in searching for images based on color and shape [23]=-=, [24]-=-, a wavelet-based texture retrieval system can be used effectively in conjunction with a compression system and retrieval systems using other image features (see Fig. 2). Using the assumption that the... |

12 | Embedded mixture modeling for efficient probabilistic content-based indexing and retrieval - Vasconcelos, Lippman - 1998 |

11 | Color indexing," Int - Swain, Ballard - 1991 |

4 |
An Introduction to Signal Estimation and Detection
- Poor
- 1994
(Show Context)
Citation Context ... , and then we choose the next best one among the remain hypotheses, and keep doing so for times. Under the common assumption that all prior probabilities of the hypotheses are equal, it can be shown =-=[18]-=- that, for each recursive step the optimum rule (with the minimum probability of error criterion) is to choose the hypothesis with the highest likelihood among the possible ones. Thus for CBIR, it is ... |

4 | Rotation invariant texture retrieval using steerable wavelet-domain hidden Markov models
- Do, Lozano, et al.
- 2000
(Show Context)
Citation Context ... used effectively here for modeling the coefficients from the wavelet transforms and wavelet frames and can applied to other similar filtering schemes such as wavelet packets and Gabor transforms. In =-=[38]��-=-�[40], we employed the statistical framework tosDO AND VETTERLI: WAVELET-BASED TEXTURE RETRIEVAL 157 more complex texture models that aggregate wavelet descriptors across scales and orientations using... |

3 | Husoy, "Filtering for texture classification: a comparative study - Randen, H - 1999 |

2 |
Multiscale branch and bound algorithm image database
- Chen, Bouman, et al.
- 1997
(Show Context)
Citation Context ...s. Such image models can incorporate the knowledge from perceptual studies to closely match human judgment. We point out that the Kullback–Leibler distance has been used in comparing images (e.g., i=-=n [21]-=-, [22]) but, to our knowledge, its use has not yet been sufficiently justified in the context of the image retrieval problem by jointly considering the two related tasks FE and SM. To combine the KLDs... |