- Open Access
GRAB: generalized region assigned to binary
© Sapkota and Boult; licensee Springer. 2013
- Received: 1 December 2012
- Accepted: 21 May 2013
- Published: 21 June 2013
Scale is one of the major challenges in recognition problems. For example, a face captured across large distances is considerably harder to recognize than the same face at small distances. Local binary pattern (LBP) and its variants have been successfully used in face detection, recognition, and many other computer vision applications. While LBP features are shown to be discriminative in face recognition, the pixel level description of LBP features is sensitive to the change in scale of the images. In this work, we extend the utility of a generalized variant of LBP feature descriptor called generalized region assigned to binary (GRAB), previously introduced in an article below, and show that it handles the challenges due to scale. The original LBP operator in another article is defined with respect to the surrounding pixel values while the GRAB operator is defined with respect to overlapping surrounding regions. This gives more general description and flexibility in choosing the right operator depending on the varying imaging conditions such as scale variations. We also propose a way to automatically select the scale of the GRAB operator (size of neighborhood). A pyramid of multi-scale GRAB operators is constructed, and the operator at each scale is applied to an image. Selection of operator’s scale is performed based on the number of stable pixels at different levels of the multi-scale pyramid. The stable pixels are defined to be the pixels in the images for which the GRAB value remains the same even as the GRAB operator scale changes. In addition to the experiments in the former article, we apply basic LBP, Liao et al.’s multi-scale block (MB)-LBP, and GRAB operator on face recognition across multiple scales and demonstrate that GRAB significantly outperforms the basic LBP and is more stable compared to MB-LBP in cases of reduced scale on a subsets of a well-known published database of labeled faces in the wild (LFW). We also perform experiments on the standard LFW database using strict LFW protocol and show the improved performance of GRAB descriptor compared to LBP and Gabor descriptors.
- Support Vector Machine
- Face Recognition
- Face Image
- Local Binary Pattern
- Center Pixel
One of the theoretical challenges in recognition is the extraction of features, which are sufficiently discriminative in addition to being invariant to the variables like illumination, translation, rotation, scale, etc. This work presents a feature descriptor primarily to handle the challenges due to scale in addition to the challenges due to illumination and noise and applies the descriptor for face recognition at low-scale images. Scale is critical in unconstrained face recognition since, in general, subjects may be at different distances from the camera, and the difference between a subject at 4 ft and one at 40 ft is a 10-time change in scale.
In this work, we present a new description based on the original local binary pattern (LBP), which combines micro-structure and global structure, as well as the structure at multiple scales of the face images. We call this operator general region assigned to binary (GRAB) and use this operator to extract features for facial recognition in images of varied scales. The prior extensions to produce the ‘multi-resolution’  LBP simply used a larger neighborhood ‘circle’ but sampled the raw pixels on that circle. While it did consider pixels at greater distances, sampling does not mimic changes in resolution or scale. Our neighborhood operator overcomes this limitation by defining the pixels in terms of varied sizes of overlapping regions.
Classification accuracy of LBP, MB-LBP, and GRAB on images
150 × 130
30 × 26
15 × 13
G3, P1 *
G5, P3 *
Following are the main contributions of our work: 1. Definition of GRAB as a generalized operator for feature description; 2. Method for selection of operator’s scale space; 3. Demonstration of higher accuracy of GRAB descriptor compared to existing methods on low-scale images.
A lot of work has been done in the past in describing meaningful and distinctive features in images that can be used for recognition. Local binary pattern (LBP) is an operator, which was originally used to extract a texture description from imagery and is widely used in face recognition. The operator assigns a label to every pixel of an image by thresholding the 3 × 3 neighborhood of each pixel with the center pixel value, resulting to a binary number [2, 3]. The pixel level features thus obtained are combined in the form of histograms in various ways to generate the global features for the face description. LBP has been one of the best-performing descriptors as it contains the microstructure as well as the macrostructure of the face image. Despite its popularity, there are a number of shortcomings in the LBP approach, including sensitivity to noise, scale changes, and rotation of the image.
One of the extensions of LBP to produce the multi-resolution LBP  uses a larger neighborhood circle but still samples the raw pixels on that circle. While it does consider pixels at greater distances, sampling does not properly model changes in resolution or scale, which results in pixels being combined and not sampled. Consider what happens on a region with a fine binary texture, where sampling chooses one of the two binary colors but changes in scale actually mix the values into new shades/colors. In , this multi-resolution LBP is combined with novel color representations which combine RGB, YCbCr, and YIQ color spaces. The results did improve performance on the FRGC data, but that did not actually contain multiple resolutions so sampling artifacts in color space would impact those experiments.
Studies have introduced the concept of a MB-LBP to provide a more robust operator than LBP . In MB-LBP, the average sum of image intensity is computed in each subregion around a center subregion. These average sums are then compared with the center block. They note that, ‘MB-LBP can be viewed as a certain way of combination using eight ordinal rectangle features’. While MB-LBP does improve recognition by representing a mixture of microstructure and macrostructure of the image pattern, they did not study the impact of scale but rather focused on improving recognition at a fixed scale.
The more recently proposed BRIEF descriptors [6, 7] use binary strings as the feature descriptors instead of using decimal value of binary strings as used in basic LBP and its other variants. The binary strings are defined on the smoothed patches. Binary tests between a pair of pixels are performed for the classification. Similar to our work, they highlight the importance of smoothing before extracting LBP-like features. However, they choose a fixed 9 × 9 window for the experiments. For face recognition, the limited pairs of sample points or test points, with a fixed smoothing window may not be sufficient. Our GRAB features provide sufficient information for face recognition across multiple scales.
LBP features have also been used in the past for face detection. The work in  used LBP features as a facial representation and built a face detection system using SVM as a classifier. Another example of the variant of LBP used for face detection is . It uses multi-block local binary pattern features and the boosting algorithm for face detection .
Due to the peculiarities of the face shape and variability of several aspects of the face, the face recognition problem is different from the other object recognition problems. Some of the previous work used the combination of local as well as global representation of the face descriptors to solve this problem. Multi-resolution histograms of local variation pattern  is one such method which describes face images as the concatenation of the local spatial histogram of local variation patterns computed from multi-resolution Gabor features.
Gabor features are another interesting set of features which are highly applied in face recognition [11, 12]. The Gabor representation of face images incorporates multi-scale feature extraction. The Gabor wavelet representation of an image is the convolution of the image with a family of Gabor wavelets at different scales; for example, Pinto et al. present a V1-like algorithm that considers 96 different Gabor filters. Local features are represented by the coefficient set, or Gabor jet, which orders the convolution results at different orientation and scales for a particular point.
Feature transform (SIFT) is a popular method in object recognition [13, 14]. They extract the features of an image using the key points that are invariant to scale change. To detect such key points, they search the stable features across all possible scales using a scale space and such key points are associated with location, scale, and orientation information. To define the local image features, they sample the local image intensities around the key points at the appropriate scale of the key point. Bicego et al. used SIFT features for authentication in , wherein they used the distance between all pairs of keypoint descriptors in the two images to define the matching score. For face authentication, this type of algorithm was not as successful as it was in other object recognition problems using SIFT-like features. Unfortunately, the planarity assumption underlying the theory of SIFT features and the highly non-planar and self-occluding nature of faces result in weak performance on face recognition tasks. In , SIFT features are combined in a mixed local-global strategy supporting a recognition-from-parts approach to address occlusion.
In this work, we present an operator called GRAB, developed as a generalization of LBP. While we will show the effectiveness of GRAB, like other multi-resolution approaches, there is likelihood that it will suffer the curse of dimensionality. There are techniques for reducing dimensionality. For example, Chan et al.  uses subspace techniques of LDA to help reduce the dimensionality of standard MLBP while maintaining or increasing the accuracy of the added dimensionality. In terms of added accuracy, they argue that, ‘However, by directly applying the similarity measurement to the multi-scale LBP histogram, the performance will be compromised. The reason is that this histogram is of high dimensionality and contains redundant information’. While Chan et al. show impressive results, in this work, we use GRAB and scale-selection algorithm rather than MBLP to avoid sampling issues and will use SVMs for recognition, which remove the redundancy in a different, and generally more effective way. And again, our focus is on addressing recognition under scale changes, not just improving recognition rates.
This definition of GRAB does not use a single uniform definition as in local binary patterns, but it combines, in a more meaningful way, multiple different neighborhood rules. GRAB operator can be implemented as a generalization of ELBP  in the sense that the block averages around the center pixel can be arranged in circular or elliptical fashion. In this work, we consider a fast rectangular integral neighborhood definition.
GRAB as scale invariant operator
GRAB uses windowed operators for the neighborhoods instead of the pixels. In the standard LBP, the comparison is that of a pixel directly with its neighbors. The prior extensions to produce the multi-resolution LBP simply used a larger neighborhood circle but sampled the raw pixels on that circle. While it did consider pixels at greater distances, sampling does not mimic changes in resolution or scale. To address this, our neighborhood operators average the image over a region to define their values. We then define the averaging window and the idea of multi-scale GRAB. While the neighborhoods for averaging could be of any shape, use of rectangular regions allow use of summed area tables , also known as integral images, which allow very efficient computation of averages over rectangle regions.
As an example, eight neighboring regions are labeled as in Figure 3. The regions use N ×N rectangular average, with one-pixel overlap where N is the size of GRAB window operator. For center pixel c, a region of size N ×N is defined, and the average over the region is calculated. This value is assigned to the center pixel c. Similarly, for the neighboring regions of the same size, the average is computed. Now the average value of the central region, which is the value of the center pixel after the transform, is compared with the averages of the neighboring regions, and the threshold is applied to compute the labels of the neighboring pixels. The result is an 8-bit number representing one scale of neighborhoods around the point c. We can then compute a histogram, or partial histogram, of occurrence within the window. For face-based recognition we combine the histogram-based features for the multi-scale facial region description.
This multi-scale representation of GRAB descriptors allows it to account for the changes in spatial resolution in the images since we can store multiple scales at once. This makes facial recognition highly robust to changes in scale and also to changes in image quality.
Selection of GRAB scale
The operators at multiple scales can be automatically selected based on the number of stable pixels in the gallery model and the probe image. Figure 4 shows an example of scale-space pyramid of GRAB operators and the way of selection of scales based on the stable pixels.
As mentioned in section ‘GRAB’, GRAB operator assigns a label to every pixel in the image by thresholding the center pixel with the pixel value of N ×N block average by eight neighbors of N ×N block average. The pattern thus obtained is a binary number and thus every pixel in the image is assigned such a number. Also, using the neighbor as a N ×N block average does not affect the idea of uniform pattern. We can still make use of the uniform pattern which according to [2, 3], is a binary pattern that contains at most two bit-wise transitions from 0 to 1 or vice versa, when the bit pattern is considered circular. For example, the patterns 00000000 (zero transitions), 01110000 (two transitions) and 11001111 (two transitions) are uniform whereas the patterns 11001001 (four transitions) and 01010011 (six transitions) are not. We continued to use uniform pattern in our representation because it accounts for a larger percentage of the image representation in the face recognition technology (FERET) dataset [2, 3], and we are using a subset of this dataset for our experiments. It also has the advantage of dimension reduction while using SVM. To represent the face image, the histogram of such patterns/binary numbers at different levels is used.
For face description using GRAB features, we use the same approach as LBP features because they represent the local and the global description of the face image. Geometrically normalized images, which are all 130-pixel wide and 150-pixel high, are divided into 64 regions (8 rows and 8 columns). GRAB-based histograms are computed in each region and are concatenated to form the global feature vector. To extend this idea to the multi-scale level, we actually compute GRAB histograms at different scales of the GRAB window operator. For example, for GRAB-3-5-7, the binary pattern was computed taking the block average of the 3 × 3, 5 × 5, and 7 × 7 neighbors. We then concatenate the histogram features of each scale to form the global histogram feature vector, which represents the local features and global features, as well as the features at different scales. While we could work in the space of smaller images, scaling down the windows, it is easier to conceptualize and implement, when we scale the different resolution images back to the same size, so all histograms are computed in the same manner and all ‘window sizes’ are in the same space with respect to facial geometry. All scale conversions for the work were done using ImageMagick’s convert function.
We also verified the performance of LBP on the standard FERET partitions as mentioned in , achieving 96% on fafb, 47% on fafc, 57% on Dup1, and 48% on DupII without the weights assigned to the regions. The slight difference in the results could be due to the way the images are normalized.
Performance of the nearest-neighbor classification on FERET240 and LFW610 with weighted regions
Performance comparison of LBP, Gabor, and GRAB on LFW database using strict LFW protocol
0.6625 +/- 0.0064
0.6498 +/- 0.0066
0.7090 +/- 0.0048
Rank 1 recognition rate of GRAB, LBP, and V1-like algorithm
While the underlying models for the matching algorithm differ between our implementation and the standard LBP implementations, the processing of the images to generate a representative feature vector (as described in section ‘Face description using GRAB’) remains the same. Given feature vector representations for both training (gallery) and testing (probe) sets of images, the former set is used to train a multi-class SVM, while the latter set is subsequently tested against the trained model. In particular, we train the multi-class linear SVMs with default parameters(C = 1) implemented via PyML. Concatenated LBP or GRAB histograms form the feature vectors, with each subject’s gallery image being a positive example for the multi-class SVMs. We then test with similar feature vectors obtained from the probe images.
LFW verification set
The labeled faces in the wild database provides the face images collected from the news articles on the web. It provides a protocol for face recognition where the recognition task is defined as a pair-matching problem. The database consists of 3,000 matched pairs and 3,000 non-matched pairs with 10-fold cross-validation. Each validation set consists of 5,400 training pairs, with 2,700 matched and non-matched pairs each and 600 testing pairs, with 300 match and non-match pairs. This is a binary classification problem where given a pair of images, decision is a ‘match’ or a ‘non-match’. We use funneled version of the database , used the match and non-match sets provided by the database and followed ‘Strict LFW’ protocol. The original images are of the size 250 × 250. The face region is almost in the center in each image. We converted the images to gray scale and cropped to the size of 150 × 150 from the center using ImageMagick tool. We cropped the images such that the centers of 250 × 250 size images and 150 × 150 size images remain the same. This is to avoid the background information as much as possible while keeping the face region. We conducted experiments on LBP, Gabor , and GRAB features. The feature vector for an image pair a−b in each set of experiment consists of s q r t|f(a)−f(b)|, where f(a) is the feature vector from image a and f(b) is the feature vector from image b. This experiment was conducted without applying our automatic scale selection algorithm. For both probe and gallery images, we use GRAB operators at 1 × 1, 3 × 3, and 7 × 7 scales and use linear SVMs for recognition.
Rank 1 Recognition rate of GRAB, LBP, and V1-like algorithm
LFW610 and FERET240 subsets
We tested our proposed GRAB operator on subsets of two published datasets. The FERET  set was chosen due to extremely common use, allowing readers to do comparisons with many algorithms. It is, however, relatively constrained in nature: all images used were frontal and under fairly consistent lighting conditions. In order to provide a more robust, and realistic, set of experimental results for unconstrained face problems, the same tests were also run on a subset of LFW . This set is relatively unconstrained and is generally considered one of the most difficult published set for facial analysis.
In our experiments, we use a model-based approach rather than a single-image-based approach. To reduce the potential for an outlier to have potentially disastrous effects on the training of the SVM, while still maintaining a relatively small gallery size and dealing with the limited number of views in the FERET protocol, we used three gallery images per subject.
Thus, the following protocol was designed and used for testing with both datasets: subjects for whom the dataset contained fewer than four images were discarded. For each of the remaining subjects, a set of four images were chosen by an alphabetic sort on the names given in the original dataset. Of these four images, the first three comprised a subject’s gallery; the last was used as a probe image. These subsets have been dubbed FERET240 and LFW610, respectively. For FERET, this ordering means the gallery generally included images from the FA and FB subsets while the probe is from the one of the more difficult sets (DUP1 or DUP2). For LFW, this ordering has no relation to standard sets or collection process. Because we use a multiple-image gallery for building the SVM, it was necessary to deviate from the published protocols for each data set. In addition, our effort is focused on recognition.
Because this protocol deviates so markedly from the published protocol for FERET and LFW, let us briefly mention the performance of Pinto et.al.’s V1 algorithm . When using that algorithm with the above protocols, including the three image gallery training process, the V1-like algorithm achieves 97.5% accuracy (rank one recognition) on FERET240 and 41.3% on LFW610. The first thing to note is that, as one would expect, LFW is more difficult than FERET. The second and more important aspect of this comparison shows how much more difficult our LFW610 protocol is compared to the basic LFW verification protocol where the V1-like algorithms obtains nearly 80% accuracy following the standard LFW protocols.
To evaluate the impact of scale on the algorithms we generate several instances of reduced spatial resolution images. In order to reduce the variables contributing to recognition score differences, enabling us to better focus on the image degradation due to scale, images were first preprocessed using the standard geometric normalization process provided by the CSU face identification evaluation system  using the ground truth eye coordinates available with the databases. This resulted in images of uniform size containing faces oriented approximately the same way. Although the images are preprocessed to have the same pixel dimensions (and thus the same digital resolution), those whose original representation had fewer pixels in either dimension will still have reduced optic resolution due to the interpolation necessary to up-sample the image.
For individual experiments, each dataset was divided into its components gallery and probe subsets. Each image in the probe subset was then downsampled to 10%, 20%, 30%, and 40% of its original size (face dimensions of 13 × 15, 26 × 30, 39 × 45, and 52 × 60 pixels, respectively) thus generating four new sets of probes for our experiments. We computed the four scales, simulating degradation with respect to optic resolution. The image scaling resulted in a decrease in image size (both optic resolution and digital resolution as compared to the original image), which would complicate the data alignment issues. However, the geometric normalization of the preprocessing phase subsequently uses eye location to scale the probes (and the gallery images) to have consistent eye locations and overall face dimensions of a 130-pixel width and a 150-pixel height, regardless of input image size or optical resolution. Since the probe images were considerably smaller than the gallery images, the resulting preprocessed probes have considerably worse optic resolution than the preprocessed gallery images. This procedure was performed for both FERET240 and LFW610.
We conducted experiments using the aforementioned protocols, to compare GRAB and standard LBP on images of various scales. Table 4 summarizes the results obtained with the FERET240 set. We performed similar experiments with the LFW610 dataset, and the results are shown in Table 5. Since FERET is a highly constrained dataset, we get comparatively higher overall performance in FERET240 than in LFW610, which is a highly unconstrained dataset.
We do a similar analysis for the results on LFW610 dataset as well, where the overall problem is much more difficult because of the greater natural variation in the data. The results show a significant improvement in the performance on a reasonably unconstrained dataset.
Impact of selection of scales on GRAB performance on the FERET240 dataset
In this study, we have presented the serious problem in face recognition of size and optic resolution variation due to scale, and we have reviewed various preexisting techniques that have attempted to overcome these obstacles. We have developed the novel GRAB operator and demonstrated its significant performance advantages over LBP in situations of severely decreased scale. While LBP’s performance drops off sharply as resolution decreases, the performance of the GRAB operator remains high despite the radical loss of resolution. We also proposed a way to automatically select the GRAB scale based on the image scale and the number of stable pixels across multiple scales. Due to the nature of GRAB as a generalization of LBP, future work will revolve around evaluation of the many other generalizations, and their ability to address additional issues in unconstrained face recognition.
The authors thank the financial support of ONR MURI N00014-08-1-0638, Army SBIR W15P7T-12-C-A210, ONR STTR N000014-07-M-0421 and SOCOM SBIR H92222-07-P-0020. We also acknowledge earlier related work and help on the paper from Walter Scheirer, Brian Parks, and Tanya Stere.
- Ojala T, Pietikainen M, Maenpaa T: Multiresolution gray-scale and rotation invariant texture classification with local binary patterns. IEEE Trans, Pattern Anal. Machine Intelligence 2002, 24(7):971-987. 10.1109/TPAMI.2002.1017623View ArticleGoogle Scholar
- Ahonen T, Hadid A, Pietikainen M: Face description with local binary patterns: application to face recognition. IEEE Trans. Pattern Anal. Machine Intelligence 2006, 28(12):2037-2041.View ArticleGoogle Scholar
- Zhang W, Shan S, Gao W, Chen X, Zhang H: Local Gabor binary pattern histogram sequence (LGBPHS): a novel non-statistical model for face representation and recognition. Tenth IEEE International Conference on Computer Vision, 2005. (ICCV 2005) Volume 1, 2005:786–791Google Scholar
- Liao S, Zhu X, Lei Z, Zhang L, Li S: Learning Multi-scale Block Local Binary Patterns for Face Recognition. Lecture Notes in Computer Science. Volume 4642. In Advances in Biometrics. Edited by: SW Lee, S Li. Heidelberg: Springer,; 2007:828-837. [http://dx.doi.org/10.1007/978-3-540-74549-5_87]View ArticleGoogle Scholar
- Liu Z, Liu C: Robust face recognition using color information. Lecture Notes in Computer Science, Volume 5558. In Advances in Biometrics. Edited by: M Tistarelli, M Nixon. Heidelberg: Springer,; 2009:122-131. [http://dx.doi.org/10.1007/978-3-642-01793-3_13]View ArticleGoogle Scholar
- Calonder M, Lepetit V, Strecha C, Fua P: BRIEF: binary robust independent elementary features. Lecture Notes in Computer Science. Volume 6314. In Computer Vision Ű ECCV 2010. Edited by: K Daniilidis, P Maragos, N Paragios. Heidelberg: Springer,; 2010:778-792. [http://dx.doi.org/10.1007/978-3-642-15561-1_56]View ArticleGoogle Scholar
- Rublee E, Rabaud V, Konolige K, Bradski G: ORB: an efficient alternative to SIFT or SURF. 2011 IEEE International Conference on Computer Vision (ICCV) 2011, 2564-2571.View ArticleGoogle Scholar
- Hadid A, Pietikainen M, Ahonen T: A discriminative feature space for detecting and recognizing faces. Volume 2. Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004 (CVPR 2004) 2004, II-797–II–804.Google Scholar
- Zhang L, Chu R, Xiang S, Liao S, Li S: Face detection based on multi-block LBP representation. Lecture Notes in Computer Science. Volume 4642. In Advances in Biometrics. Edited by: SW Lee, S Li. Heidelberg: Springer,; 2007:11-18. [http://dx.doi.org/10.1007/978-3-540-74549-5_2]View ArticleGoogle Scholar
- Zhang W, Shan S, Zhang H, Gao W, Chen X: Multi-resolution histograms of local variation patterns (MHLVP) for robust face recognition. Lecture Notes in Computer Science. Volume 3546. In Audio- and Video-Based Biometric Person Authentication. Edited by: T Kanade, A Jain, N Ratha. Heidelberg: Springer,; 2005:937-944. [http://dx.doi.org/10.1007/11527923_98]View ArticleGoogle Scholar
- Shen L, Bai L: A review on Gabor wavelets for face recognition. Pattern Anal. Appl. 2006, 9(2-3):273-292. [http://dx.doi.org/10.1007/s10044-006-0033-y] 10.1007/s10044-006-0033-yMathSciNetView ArticleGoogle Scholar
- Pinto N, DiJ,arlo C, Cox D: How far can you get with a modern face recognition test set using only simple features? IEEE Conference on Computer Vision and Pattern Recognition, 2009 (CVPR 2009). 2009, 2591-2598.View ArticleGoogle Scholar
- Lowe DG: Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vision 2004, 60(2):91-110. [http://dx.doi.org/10.1023/B:VISI.0000029664.99615.94]View ArticleGoogle Scholar
- Lowe D: Object recognition from local scale-invariant features. Volume 2. The Proceedings of the Seventh IEEE International Conference on Computer Vision, 1999 1999, 1150-1157.View ArticleGoogle Scholar
- Bicego M, Lagorio A, Grosso E, Tistarelli M: On the use of SIFT features for face authentication. Conference on Computer Vision and Pattern Recognition Workshop, 2006 (CVPRW ’06) 2006, 35-35.View ArticleGoogle Scholar
- Kisku D, Tistarelli M, Sing J, Gupta P: Face recognition by fusion of local and global matching scores using DS theory: an evaluation with uni-classifier and multi-classifier paradigm. IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, 2009 (CVPR Workshops 2009) 2009, 60-65.View ArticleGoogle Scholar
- Chan J, Kittler CH, Messer K: Multi-scale local binary pattern histograms for face recognition. Lecture Notes in Computer Science. Volume 4642. In Advances in Biometrics. Edited by: SW Lee, S Li. Heidelberg: Springer,; 2007:809-818. [http://dx.doi.org/10.1007/978-3-540-74549-5_85]View ArticleGoogle Scholar
- Liao S, Chung A: Face recognition by using elongated local binary patterns with average maximum distance gradient magnitude. Lecture Notes in Computer Science. Volume 4844. In Asian Conference on Computer Vision Ű ACCV 2007. Edited by: Y Yagi, S Kang, I Kweon, H Zha. Heidelberg: Springer,; 2007:672-679. [http://dx.doi.org/10.1007/978-3-540-76390-1_66]View ArticleGoogle Scholar
- Crow FC: Summed-area tables for texture mapping. In Proceedings of the 11th annual conference on Computer graphics and interactive techniques, SIGGRAPH ’84. New York: ACM,; 1984:207-212. [http://doi.acm.org/10.1145/800031.808600]Google Scholar
- Sapkota A, Parks B, Scheirer W, Boult T: FACE-GRAB: face recognition with general region assigned to binary operator. the 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops (CVPRW) 2010, 82-89.View ArticleGoogle Scholar
- Huang G, Jain V, Learned-Miller E: Unsupervised joint alignment of Complex Images. the IEEE 11th International Conference on Computer Vision, 2007 (ICCV 2007) 2007, 1-8.Google Scholar
- Zhu J, Vai M, Mak P: A new enhanced nearest feature space (ENFS) classifier for Gabor wavelets features-based face recognition. Lecture Notes in Computer Science. Volume 3072. In Biometric Authentication. Edited by: Zhang D, Jain A. Heidelberg: Springer,; 2004:124-130. [http://dx.doi.org/10.1007/978-3-540-25948-0_18]View ArticleGoogle Scholar
- Phillips P, Moon H, Rizvi S, Rauss P: The FERET evaluation methodology for face-recognition algorithms. IEEE Trans. Pattern Anal. Machine Intelligence 2000, 22(10):1090-1104. 10.1109/34.879790View ArticleGoogle Scholar
- Huang M, Ramesh GB, Berg T, Learned-Miller E: Labeled faces in the wild: a database for studying face recognition in unconstrained environments. Tech. Rep. 07-49. (University of Massachusetts, Amherst, 2007)Google Scholar
- Bolme M, Beveridge DS, Teixeira JR, Draper BA: The CSU face identification evaluation system: its purpose, features, and structure. In Proceedings of the 3rd international Conference on Computer vision systems (ICVS’03). Heidelberg: Springer,; 2003:304-313. [http://dl.acm.org/citation.cfm?id=1765473.1765507]Google Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.