The widespread use of mobile devices for all kinds of transactions makes necessary reliable and real-time identity authentication, leading to the adoption of face recognition (FR) via the cameras embedded in such devices. Progress of deep Convolutional Neural Networks (CNNs) has provided substantial advances in FR. Nonetheless, the size of state-of-the-art architectures is unsuitable for mobile deployment, since they often encompass hundreds of megabytes and millions of parameters. We address this by studying methods for deep network compression applied to FR. In particular, we apply network pruning based on Taylor scores, where less important filters are removed iteratively. The method is tested on three networks based on the small SqueezeNet (1.24M parameters) and the popular MobileNetv2 (3.5M) and ResNet50 (23.5M) architectures. These have been selected to showcase the method on CNNs with different complexities and sizes. We observe that a substantial percentage of filters can be removed with minimal performance loss. Also, filters with the highest amount of output channels tend to be removed first, suggesting that high-dimensional spaces within popular CNNs are over-dimensioned. The models of this paper are available at https://github.com/HalmstadUniversityBiometrics/CNN-pruning-for-face-recognition . • We summarize works in CNN network pruning applied to face recognition. • We apply a Taylor score-based network pruning method to three CNNs of different sizes. • We analyse impact on performance, parameters, embeddings, layers, and activations.

This paper presents the summary of the Efficient Face Recognition Competition (EFaR) held at the 2023 International Joint Conference on Biometrics (IJCB 2023). The competition received 17 submissions from 6 different teams. To drive further development of efficient face recognition models, the submitted solutions are ranked based on a weighted score of the achieved verification accuracies on a diverse set of benchmarks, as well as the deployability given by the number of floating-point operations and model size. The evaluation of submissions is extended to bias, cross-quality, and large-scale recognition benchmarks. Overall, the paper gives an overview of the achieved performance values of the submitted solutions as well as a diverse set of baselines. The submitted solutions use small, efficient network architectures to reduce the computational cost, some solutions apply model quantization. An outlook on possible techniques that are underrepresented in current solutions is given as well.

Workplace injuries are common in today’s society due to a lack of adequately worn safety equipment. A system that only admits appropriately equipped personnel can be created to improve working conditions. The goal is thus to develop a system that will improve workers’ safety using a camera that will detect the usage of Personal Protective Equipment (PPE). To this end, we collected and labeled appropriate data from several public sources, which have been used to train and evaluate several models based on the popular YOLOv4 object detector. Our focus, driven by a collaborating industrial partner, is to implement our system into an entry control point where workers must present themselves to obtain access to a restricted area. Combined with facial identity recognition, the system would ensure that only authorized people wearing appropriate equipment are granted access. A novelty of this work is that we increase the number of classes to five objects (hardhat, safety vest, safety gloves, safety glasses, and hearing protection), whereas most existing works only focus on one or two classes, usually hardhats or vests. The AI model developed provides good detection accuracy at a distance of 3 and 5 meters in the collaborative environment where we aim at operating (mAP of 99/89%, respectively). The small size of some objects or the potential occlusion by body parts have been identified as potential factors that are detrimental to accuracy, which we have counteracted via data augmentation and cropping of the body before applying PPE detection. © 2023 by SCITEPRESS-Science and Technology Publications, Lda.

We describe a technical solution implemented at Halmstad University to automatise assessment and reporting of results of paper-based quiz exams. Paper quizzes are affordable and within reach of campus education in classrooms. Offering and taking them is accepted as they cause fewer issues with reliability and democratic access, e.g. a large number of students can take them without a trusted mobile device, internet, or battery. By contrast, correction of the quiz is a considerable obstacle. We suggest mitigating the issue by a novel image processing technique using harmonic spirals that aligns answer sheets in sub-pixel accuracy to read student identity and answers and to email results within minutes, all fully automatically. Using the described method, we carry out regular weekly examinations in two master courses at the mentioned centre without a significant workload increase. The employed solution also enables us to assign a unique identifier to each quiz (e.g. week 1, week 2…) while allowing us to have an individualised quiz for each student.

Beautification and augmented reality filters are very popular in applications that use selfie images. However, they can distort or modify biometric features, severely affecting the ability to recognise the individuals’ identity or even detect the face. Accordingly, we address the effect of such filters on the accuracy of automated face detection and recognition. The social media image filters studied modify the image contrast, illumination, or occlude parts of the face. We observe that the effect of some of these filters is harmful to face detection and identity recognition, especially if they obfuscate the eye or (to a lesser extent) the nose. To counteract such effect, we develop a method to reverse the applied manipulation with a modified version of the U-NET segmentation network. This method is observed to contribute to better face detection and recognition accuracy. From a recognition perspective, we employ distance measures and trained machine learning algorithms applied to features extracted using several CNN backbones. We also evaluate if incorporating filtered images into the training set of machine learning approaches is beneficial. Our results show good recognition when filters do not occlude important landmarks, especially the eyes. The combined effect of the proposed approaches also allows mitigating the impact produced by filters that occlude parts of the face.

Application of ocular biometrics in mobile and at a distance environments still has several open challenges, with the lack quality and resolution being an evident issue that can severely affects performance. In this paper, we evaluate two trained image reconstruction algorithms in the context of smart-phone biometrics. They are based on the use of coupled dictionaries to learn the mapping relations between low and high resolution images. In addition, reconstruction is made in local overlapped image patches, where up-scaling functions are modelled separately for each patch, allowing to better preserve local details. The experimental setup is complemented with a database of 560 images captured with two different smart-phones, and two iris comparators employed for verification experiments. We show that the trained approaches are substantially superior to bilinear or bicubic interpolations at very low resolutions (images of 13×13 pixels). Under such challenging conditions, an EER of ~7% can be achieved using individual comparators, which is further pushed down to 4-6% after the fusion of the two systems.

This work presents the 2ndCross-Spectrum Iris/Periocular Recognition Competition (Cross-Eyed2017). The main goal of the competition is to promote and evaluate advances in cross-spectrum iris and periocular recognition. This second edition registered an increase in the participation numbers ranging from academia to industry: five teams submitted twelve methods for the periocular task and five for the iris task. The benchmark dataset is an enlarged version of the dual-spectrum database containing both iris and periocular images synchronously captured from a distance and within a realistic indoor environment. The evaluation was performed on an undisclosed test-set. Methodology, tested algorithms, and obtained results are reported in this paper identifying the remaining challenges in path forward.

In this paper, we present a new approach for periocular recognition based on the Symmetry Assessment by Feature Expansion (SAFE) descriptor, which encodes the presence of various symmetric curve families around image key points. We use the sclera center as single key point for feature extraction, highlighting the object-like identity properties that concentrates to this unique point of the eye. As it is demonstrated, such discriminative properties can be encoded with a reduced set of symmetric curves. Experiments are done with a database of periocular images captured with a digital camera. We test our system against reference periocular features, achieving top performance with a considerably smaller feature vector (given by the use of a single key point). All the systems tested also show a nearly steady correlation between acquisition distance and performance, and they are also able to cope well when enrolment and test images are not captured at the same distance. Fusion experiments among the available systems are also provided.

Fingerprint alteration is a type of presentation attack in which the attacker strives to avoid identification, e.g. at border control or in forensic investigations. As a countermeasure, fingerprint alteration detection aims to automatically discover the occurrence of such attacks by classifying fingerprint images as `normal' or `altered'. In this paper, we propose four new features for improving the performance of fingerprint alteration detection modules. We evaluate the usefulness of these features on a benchmark and compare them to four existing features from the literature.

We evaluate the most useful regions for periocular recognition. For this purpose, we employ our periocular algorithm based on retinotopic sampling grids and Gabor analysis of the spectrum. We use both NIR and visible iris images. The best regions are selected via Sequential Forward Floating Selection (SFFS). The iris neighborhood (including sclera and eyelashes) is found as the best region with NIR data, while the surrounding skin texture (which is over-illuminated in NIR images) is the most discriminative region in visible range. To the best of our knowledge, only one work in the literature has evaluated the influence of different regions in the performance of periocular recognition algorithms. Our results are in the same line, despite the use of completely different matchers. We also evaluate an iris texture matcher, providing fusion results with our periocular system as well.

Classical iris biometric systems assume ideal environmental conditions and cooperative users for image acquisition. When conditions are less ideal or users are uncooperative or unaware of their biometrics being taken the image acquisition quality suffers. This makes it harder for iris localization and segmentation algorithms to properly segment the acquired image into iris and non-iris parts. Segmentation is a critical part in iris recognition systems, since errors in this initial stage are propagated to subsequent processing stages. Therefore, the performance of iris segmentation algorithms is paramount to the performance of the overall system. In order to properly evaluate and develop iris segmentation algorithm, especially under difficult conditions like off angle and significant occlusions or bad lighting, it is beneficial to directly assess the segmentation algorithm. Currently, when evaluating the performance of iris segmentation algorithms this is mostly done by utilizing the recognition rate, and consequently the overall performance of the biometric system. In order to streamline the development and assessment of iris segmentation algorithms with the dependence on the whole biometric system we have generated a iris segmentation ground truth database. We will show a method for evaluating iris segmentation performance base on this ground truth database and give examples of how to identify problematic cases in order to further analyse the segmentation algorithms.

Comparing a latent fingerprint minutiae set against a ten print fingerprint minutiae set using an automated fingerprint identification system is a challenging problem. This is mainly because latent fingerprints obtained from crime scenes are mostly partial fingerprints, and most automated systems expect approximately the same number of minutiae between query and the reference fingerprint under comparison for good performance. In this work, we propose a methodology to reduce the minutiae set of ten print with respect to that of query latent minutiae set by registering the orientation field of latent fingerprint with the ten print orientation field. By reducing the search space of minutiae from the ten print, we can improve the performance of automated identification systems for latent fingerprints. We report the performance of our registration algorithm on the NIST-SD27 database as well as the improvement in the Rank Identification accuracy of a standard minutiae-based automated system.

Amharic is the official language of Ethiopia and uses Ethiopic script for writing. In this paper, we present writer-independent HMM-based Amharic word recognition for offline handwritten text. The underlying units of the recognition system are a set of primitive strokes whose combinations form handwritten Ethiopic characters. For each character, possibly occurring sequences of primitive strokes and their spatial relationships, collectively termed as primitive structural features, are stored as feature list. Hidden Markov models for Amharic words are trained with such sequences of structural features of characters constituting words. The recognition phase does not require segmentation of characters but only requires text line detection and extraction of structural features in each text line. Text lines and primitive structural features are extracted by making use of direction field tensor. The performance of the recognition system is tested by a database of unconstrained handwritten documents collected from various sources.

This paper describes an offline handwriting recognition system for Amharic words based on lexicon. The system computes direction fields of scanned handwritten documents, from which pseudo-characters are segmented. The pseudo-characters are organized based on their proximity and direction to form text lines. Words are then segmented by analyzing the relative gap between subsequent pseudo-characters in text lines. For each segmented word image, the structural characteristics of pseudo-characters are syntactically analyzed to predict a set of plausible characters forming the word. The most likelihood word is finally selected among candidates by matching against the lexicon. The system is tested by a database of unconstrained handwritten Amharic documents collected from various sources. The lexicon is prepared from words appearing in the collected database.

Video databases and their corresponding evaluation protocols are used to compare classifiers, such as face detection and tracking. In this paper, a six level evaluation protocol for the Damascened XM2VTS (DXM2VTS) database is presented to measure face detection and tracking performance. Additionally, a novel database containing thousands of videos is created by combining video from the XM2VTS database with a set of newly recorded standardized real-life video used as background and with several realistic degradations, such as motion blur, noise, etc. Moreover, two publicly available and published face detection algorithms are tested on the six suggested difficulty levels of the protocol. Their performance on video in terms of false acceptance, false rejection, correct detection, and repeatability, are reported and conclusions are drawn.

Signal-quality awareness has been found to increase recognition rates and to support decisions in multisensor environments significantly. Nevertheless, automatic quality assessment is still an open issue. Here, we study the orientation tensor of fingerprint images to quantify signal impairments, such as noise, lack of structure, blur, with the help of symmetry descriptors. A strongly reduced reference is especially favorable in biometrics, but less information is not sufficient for the approach. This is also supported by numerous experiments involving a simpler quality estimator, a trained method (NFIQ), as well as the human perception of fingerprint quality on several public databases. Furthermore, quality measurements are extensively reused to adapt fusion parameters in a monomodal multialgorithm fingerprint recognition environment. In this study, several trained and nontrained score-level fusion schemes are investigated. A Bayes-based strategy for incorporating experts' past performances and current quality conditions, a novel cascaded scheme for computational efficiency, besides simple fusion rules, is presented. The quantitative results favor quality awareness under all aspects, boosting recognition rates and fusing differently skilled experts efficiently as well as effectively (by training).

Accurate fingerprint recognition presupposes robust feature extraction which is often hampered by noisy input data. We suggest common techniques for both enhancement and minutiae extraction, employing symmetry features. For enhancement, a Laplacian-like image pyramid is used to decompose the original fingerprint into sub-bands corresponding to different spatial scales. In a further step, contextual smoothing is performed on these pyramid levels, where the corresponding filtering directions stem from the frequency-adapted structure tensor (linear symmetry features). For minutiae extraction, parabolic symmetry is added to the local fingerprint model which allows to accurately detect the position and direction of a minutia simultaneously. Our experiments support the view that using the suggested parabolic symmetry features, the extraction of which does not require explicit thinning or other morphological operations, constitute a robust alternative to conventional minutiae extraction. All necessary image processing is done in the spatial domain using 1-D filters only, avoiding block artifacts that reduce the biometric information. We present comparisons to other studies on enhancement in matching tasks employing the open source matcher from NIST, FIS2. Furthermore, we compare the proposed minutiae extraction method with the corresponding method from the NIST package, mindtct. A top five commercial matcher from FVC2006 is used in enhancement quantification as well. The matching error is lowered significantly when plugging in the suggested methods. The FVC2004 fingerprint database, notable for its exceptionally low-quality fingerprints, is used for all experiments.

In real life, documents contain several font types, styles, and sizes. However, many character recognition systems show good results for specific type of documents and fail to produce satisfactory results for others. Over the past decades, various pattern recognition techniques have been applied with the aim to develop recognition systems insensitive to variations in the characteristics of documents. In this paper, we present a robust recognition system for Ethiopic script using a hybrid of classifiers. The complex structures of Ethiopic characters are structurally and syntactically analyzed, and represented as a pattern of simpler graphical units called primitives. The pattern is used for classification of characters using similarity-based matching and neural network classifier. The classification result is further refined by using template matching. A pair of directional filters is used for creating templates and extracting structural features. The recognition system is tested by real life documents and experimental results are reported.

Serto is the cursive alphabet of Syriac-Aramaic, which is used by the largest corpus of documents in libraries in Aramaic. A lingua franca, and often a source language, Aramaic has influenced major Judaic, Christian and Islamic thoughts as well as the development of science. The script is cursive, e.g. Arabic, and consequently it has a hand-writing appearance compared to Latin. Serto, and Aramaic in practice, has not an automatic character recognition system, OCR Most library documents are reproductions using printed characters. The readers would strongly benefit from having an OCR, as these reproductions are predominantly books, printed in the pre-computer era. We propose a segmentation-free OCR using linear symmetry features with an individual threshold for the tensors of the characters, and an ordered search sequence. It yields ~ 90 % correctly identified characters in the average. As a first recognition scheme for Serto, it represents a base-line OCR for Syriac-Aramaic.

This paper presents the scheme and evaluation of a robust audio-visual digit-and-speaker-recognition system using lip motion and speech biometrics. Moreover, a liveness verification barrier based on a person's lip movement is added to the system to guard against advanced spoofing attempts such as replayed videos. The acoustic and visual features are integrated at the feature level and evaluated first by a support vector machine for digit and speaker identification and, then, by a Gaussian mixture model for speaker verification. Based on ap300 different personal identities, this paper represents, to our knowledge, the first extensive study investigating the added value of lip motion features for speaker and speech-recognition applications. Digit recognition and person-identification and verification experiments are conducted on the publicly available XM2VTS database showing favorable results (speaker verification is 98 percent, speaker identification is 100 percent, and digit identification is 83 percent to 100 percent).

One of the open issues in fingerprint verification is the lack of robustness against image-quality degradation. Poor-quality images result in spurious and missing features, thus degrading the performance of the overall system. Therefore, it is important for a fingerprint recognition system to estimate the quality and validity of the captured fingerprint images. In this work, we review existing approaches for fingerprint image-quality estimation, including the rationale behind the published measures and visual examples showing their behavior under different quality conditions. We have also tested a selection of fingerprint image-quality estimation algorithms. For the experiments, we employ the BioSec multimodal baseline corpus, which includes 19 200 fingerprint images from 200 individuals acquired in two sessions with three different sensors. The behavior of the selected quality measures is compared, showing high correlation between them in most cases. The effect of low-quality samples in the verification performance is also studied for a widely available minutiae-based fingerprint matching system.

The 12 regular papers and three correspondences in this special issue focus on human detection and recognition. The papers represent gait, face (3-D, 2-D, video), iris, palmprint, cardiac sounds, and vulnerability of biometrics and protection against the spoof attacks.

A robust face detection technique along with mouth localization, processing every frame in real time (video rate), is presented. Moreover, it is exploited for motion analysis onsite to verify "liveness" as well as to achieve lip reading of digits. A methodological novelty is the suggested quantized angle features ("quangles") being designed for illumination invariance without the need for preprocessing (e.g., histogram equalization). This is achieved by using both the gradient direction and the double angle direction (the structure tensor angle), and by ignoring the magnitude of the gradient. Boosting techniques are applied in a quantized feature space. A major benefit is reduced processing time (i.e., that the training of effective cascaded classifiers is feasible in very short time, less than 1 h for data sets of order 104). Scale invariance is implemented through the use of an image scale pyramid. We propose "liveness" verification barriers as applications for which a significant amount of computation is avoided when estimating motion. Novel strategies to avert advanced spoofing attempts (e.g., replayed videos which include person utterances) are demonstrated. We present favorable results on face detection for the YALE face test set and competitive results for the CMU-MIT frontal face test set as well as on "liveness" verification barriers.

We suggest a set of complex differential operators that can be used to produce and filter dense orientation (tensor) fields for feature extraction, matching, and pattern recognition. We present results on the invariance properties of these operators, that we call symmetry derivatives. These show that, in contrast to ordinary derivatives, all orders of symmetry derivatives of Gaussians yield a remarkable invariance: They are obtained by replacing the original differential polynomial with the same polynomial, but using ordinary coordinates x and y corresponding to partial derivatives. Moreover, the symmetry derivatives of Gaussians are closed under the convolution operator and they are invariant to the Fourier transform. The equivalent of the structure tensor, representing and extracting orientations of curve patterns, had previously been shown to hold in harmonic coordinates in a nearly identical manner. As a result, positions, orientations, and certainties of intricate patterns, e.g., spirals, crosses, parabolic shapes, can be modeled by use of symmetry derivatives of Gaussians with greater analytical precision as well as computational efficiency. Since Gaussians and their derivatives are utilized extensively in image processing, the revealed properties have practical consequences for local orientation based feature extraction. The usefulness of these results is demonstrated by two applications: 1) tracking cross markers in long image sequences from vehicle crash tests and 2) alignment of noisy fingerprints.

Presents results of the face verification contest that was organized in conjunction with International Conference on Pattern Recognition 2000. Participants had to use identical data sets from a large, publicly available multimodal database XM2VTSDB. Training and evaluation was carried out according to an a priori known protocol. Verification results of all tested algorithms have been collected and made public on the XM2VTSDB website, facilitating large scale experiments on classifier combination and fusion. Tested methods included, among others, representatives of the most common approaches to face verification -elastic graph matching, Fisher's linear discriminant and support vector machines.

Elastic graph matching has been proposed as a practical implementation of dynamic link matching, which is a neural network with dynamically evolving links between a reference model and an input image. Each node of the graph contains features that characterize the neighborhood of its location in the image. The elastic graph matching usually consists of two consecutive steps, namely a matching with a rigid grid, followed by a deformation of the grid, which is actually the elastic part. The deformation step is introduced in order to allow for some deformation, rotation, and scaling of the object to be matched. This method is applied here to the authentication of human faces where candidates claim an identity that is to be checked. The matching error as originally suggested is not powerful enough to provide satisfying results in this case. We introduce an automatic weighting of the nodes according to their significance. We also explore the significance of the elastic deformation for an application of face-based person authentication. We compare performance results obtained with and without the second matching step. Results show that the deformation step slightly increases the performance, but has lower influence than the weighting of the nodes. The best results are obtained with the combination of both aspects. The results provided by the proposed method compare favorably with two methods that require a prior geometric face normalization, namely the synergetic and eigenface approaches.

This paper investigates the application of statistical pattern recognition methods in the framework of the dynamic link matching approach. This method describes objects by means of local frequency information on nodes of a sparse grid. Matching of an input image with a reference is achieved by displacement and deformation of the grid. This method is applied here to the authentication of human faces in a cooperative scenario where candidates claim an identity that is to be checked. The matching error is not powerful enough to provide satisfying results in this case. We introduce an automatic weighting of the nodes according to their significance. Results show that for regular grids, this weighting leads to a significant improvement of the performance.

A conjugate harmonic function pair is a suitable curvi-linear coordinate pair with which image iso-gray curves can be described. In this representation, images or parts of images which are symmetric with respect to such a function pair, have iso-gray curves which are lines or parallel line patterns. Detecting these lines, or generalized linear symmetry fitting as it will be called, corresponds to finding invariants of Lie groups of transformations. The associated Lie infinitesimal operators help constructing detection algorithms which are simple. The procedure, which is shown to be an extension of the generalized Hough transform, performs detection by voting and accumulating evidence for the searched pattern. Experimental results illustrating the theory are presented.

Radio-frequency (RF) ultrasonic data carry complete information about the object to be analyzed. Conventional analysis methods consist of exploiting only one-dimensional envelope information of the RF data, phase information being often neglected. A method is presented that is based on exploiting two-dimensional spatial phase information of RF data through the use of Gabor and Mexican hat filters. The method is illustrated with the aid of examples on physical RF data. The obtained results demonstrate the interest of spatial phase for the detection of objects in RF ultrasonic images.

Unstable fixation due to involuntary eye movements, poor visual acuity or oculomotor disorder is one of the biggest difficulties in applying noninvasive diagnostic techniques to the human eye in a clinical setting. To address this limitation, the authors have implemented a motion estimation algorithm applicable to fundus image sequences which is based on an affine model of eye movement. A hierarchical coding scheme accommodating various spatial resolutions was used in view of minimizing the processing time and adapting the algorithm to various types of eye movements that may be encountered in patients suffering from different eye diseases. The results suggest that the technique can successfully monitor patient fixation and could be used to disable other measurements or procedures during those time intervals when fixation is not maintained within predetermined limits.

For content based image retrieval using shape descriptors, most approaches so far extract shape information from a segmentation of the image. Shape features derived based on a specific segmentation are not suitable for images containing complex structures. Further, static segmentation based approaches are useful only for a small set of queries. In this paper we discuss the limitations of such boundary based shape features, and propose an alternative shape characterization technique based on orientation radiograms. A working image retrieval system based on this approach is described and sample results are presented for a full-image query.

A layered motion estimation scheme using fuzzy clustering is introduced in this paper. Once motion estimation is performed a modified objective criterion is applied to discard non significant classes.

Keywords: LTS1 Reference LTS-CONF-1995-018 Record created on 2006-06-14, modified on 2016-08-08

Design of 3-D filters for image sequences is addressed. A family of filter banks which is capable of mimicking low level human motion perception i.e. being sensitive to low spatial frequencies moving fast and high spatial frequencies moving slowly, is proposed. The sensitivity is modelled quantitatively as existence of many filters with small band widths in a range of measurements. The speed, orientation, and spatial frequency tunings as well as the corresponding sensitivities are controllable in an explicit fashion. Implementation results are discussed.

Complex moments of the Gabor power spectrum yield estimates of the N-folded symmetry of the local image content at different frequency scales, that is, they allow to detect linear, rectangular, hexagonal/triangular, and so on, structures with very fine to very coarse resolutions. Results from experiments on the unsupervised segmentation of real textures indicate their importance for image processing applications. Real geometric moments computed in Gabor space also provide for very powerful texture features, but lack the clear geometrical interpretation of complex moments.>

An approach to image feature extraction is proposed. Complex moments of the Gabor power spectrum are used to detect linear, rectangular, hexagonal/triangular, and other structures with very fine to very coarse resolutions. When the method is applied to texture segmentation, good results are obtained.>

Proposes to reduce the dimensionality of feature vectors by using the principles of Karhunen-Loeve transform, (KL) applied to the feature images locally and globally. The reduction is achieved by choosing the resulting basis vectors which are closest to those of the classical KL transform. An efficient implementation technique using pyramids is proposed. Experimental results are presented.>

The problem of detection of orientation in finite dimensional Euclidean spaces is solved in the least squares sense. The theory is developed for the case when such orientation computations are necessary at all local neighborhoods of the n-dimensional Euclidean space. Detection of orientation is shown to correspond to fitting an axis or a plane to the Fourier transform of an n-dimensional structure. The solution of this problem is related to the solution of a well-known matrix eigenvalue problem. The computations can be performed in the spatial domain without actually doing a Fourier transformation. Along with the orientation estimate, a certainty measure, based on the error of the fit, is proposed. Two applications in image analysis are considered: texture segmentation and optical flow. The theory is verified by experiments which confirm accurate orientation estimates and reliable certainty measures in the presence of noise. The comparative results indicate that the theory produces algorithms computing robust texture features as well as optical flow.>

An efficient, new method for computing texture features based on dominant local orientation is introduced. The features are computed as the Laplacian pyramid is built up. At each level of the Laplacian pyramid, the linear symmetry feature is computed. This feature is anisotropic and estimates the optimal local orientation in the Least Square Error (LSE) sense. This corresponds to the orientation interpolation obtained from the filter responses of a polar gabor decomposition of the local image. The linear symmetry feature consists of two components, the local orientation estimate and its confidence measure based on the error. Since the latter is a measure of evidence for existence of a definite direction, the linear symmetry feature computed as proposed, has the property of orientation selectivity within each frequency channel. The algorithm is based on convolutions with simple separable filters and pixel-wise non-linear arithmetic operations. These properties allow highly parallel implementation, for example on a pyramid machine, yielding real time applications. Experiments based on test images of natural textures are presented.

A method for modeling symmetries of the neighborhoods in gray-value images is derived. It is based on the form of the iso-gray-value curves. For every neighborhood a complex number is obtained through a convolution of a complex-valued image with a complex-valued filter. The magnitude of the complex number is the degree of symmetry with respect to the a priori chosen harmonic function pair. The degree of symmetry has a clear definition which is based on the error in the Fourier domain. The argument of the complex number is the angle representing the relative dominance of one of the pair of harmonic functions compared to the other.>