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Soil particle shape analysis was conducted on two calcareous sands from Dissa and Matmata in Tunisia and one silica sand from Jumunjin in Korea using an image analysis method. This technique uses complex Fourier shape descriptors and image analysis of sand grains SEM photographs to provide accurate quantification of particle morphology and texture. The Fourier descriptors, denoted “Signature Descriptors”, provide measures of Elongation, Triangularity, Squareness, and Asymmetry and identify the overall shape of soil particles. A summary of higher-order descriptors provides textural information linked up to local roughness and texture characteristics. After analyzing the Fourier descriptors, elongation was found to be the major characteristics of the three sands, mainly for the Dissa and Matmata carbonate sands. In addition, the elongation signature descriptors for the Dissa and Matmata sands have very high values compared to those of Ras Alkhair (Saudi Arabia) and Dog’s bay (Ireland) sands. Therefore, the Dissa and Matmata carbonate sands have higher angles of friction and higher critical state angle of friction than Ras Alkhair and Dog’s bay sands. Furthermore, the Dissa and Matmata carbonate sands show higher roughness than Jumunjin’s silica sand.

Fourier descriptors are classical global shape descriptors with high matching speed but low accuracy. To obtain higher accuracy, a novel framework for forming Fourier descriptors is proposed and named as MSFDGF (multiscale Fourier descriptor using group feature). MSFDGF achieves multiscale description by generating coarser contours. Then, a group of complementary features are extracted on the generated coarser contours. Finally, Fourier transform is performed on the features. MSFDGF-SH is a new global descriptor using the MSFDGF framework and shape histograms. Experiments are conducted on four databases, which are MPEG-7 CE-1 Part B, Swedish Plant Leaf, Kimia 99 and Expanded Articulated Database, to evaluate the performance of MSFDGF-SH. The experimental results show that MSFDGF-SH is an effective and efficient global shape descriptor. This new descriptor has a high accuracy of 87.76%, which exceeds the Shape Tree on the MPEG-7 CE-1 Part B dataset. This is the first Fourier descriptor that surpasses the Shape Tree method in terms of both accuracy and speed on this dataset.

Shape information plays an important role in the human visual system, and how to represent the shape accurately is a very challenging issue in shape recognition. In recent years, many shape description approaches have been proposed. However, most of the existing methods are still facing challenges on accuracy and computational efficiency. Fourier descriptor is regarded as a promising shape description method because it has a solid theoretical foundation and at the same time possesses the strength of appealing invariance properties and high computational efficiency. We introduce a novel multiscale Fourier descriptor based on triangular features which is used to identify shapes. The local and global characteristics of a shape are effectively captured by the proposed shape descriptor. Meanwhile, the proposed shape descriptor has good properties, such as the invariant of the geometric transformation and the starting point of an object. We tested this descriptor on four popular benchmarking datasets, including MPEG-7, Swedish leaf, ETH-80, and Flavia leaf. The results confirm that our method is better than comparable-complexity approaches based on Fourier descriptors and does not perform unfavorably with respect to more complex, state-of-the-art, shape descriptors. In particular, our method is far superior to the complex shape description methods in terms of retrieval efficiency and computational complexity.

Shape retrieval is an interesting and challenging issue in computer vision and robot vision. The recent works employing Fourier-based multi-scale descriptors achieve some success in shape retrieval, especially make real-time application possible by improving the efficiency. However, these methods are commonly adopting really complex shape descriptors to present the shape information which is not intuitive enough. In our work, we propose a new Fourier-based method with novel multi-scale descriptor which is a combination of contour feature and regional feature. This novel descriptor has two main characteristics: First, utilize six different invariant signatures which are based on plane orthogonal vectors; Second, leverage multiple scale structures to describe local and global information of shapes. Except the easiness in understanding, this descriptor approach also produces a more distinct topology of shapes than other approaches which means the property of stability on variations, linear or nonlinear. The method is tested on some popular databases that provides a promising retrieval rate(87.46% and 99.27%) with constant time complexity optimization. The results confirm that our method is more capable of representing the topology of shapes than most other methods based on Fourier descriptor.

Coupled serial mechanism is a class of mechanisms that couple the relative rotation of successive links utilizing gears or cable-pulley systems. They can be used to generate complex end-effector trajectories or motions with a single actuator. With the employment of Fourier descriptors, a novel approach to integrate type synthesis and dimensional synthesis of such mechanisms is proposed in this paper. Through the Fourier analysis of two arbitrary trajectories from the given motion, the simplest trajectory that contains the least number of harmonic components is identified. Then, characteristic information of those harmonics such as their numbers, amplitudes and initial phases are used to determine the topology and dimensions of the corresponding coupled serial mechanism, thus effectively solving the motion synthesis problem of this type of mechanisms. Finally, three examples are given to demonstrate the validity of the proposed method.

In image retrieval, the shape feature is one of the key features of image content description. At present, most of the widely used Fourier descriptors in shape descriptors are invariant in translation, rotation and scale expansion. But Fourier descriptors are susceptible to the location of the starting point. In this paper, an improved image retrieval method based on Fourier descriptors is proposed. First, the image is preprocessed and the edge of the image is extracted. Secondly, the starting point of the contour is determined by the minimum inertia axis. Then Fourier transform is used to get eigenvectors. Finally, the correlation coefficient is used to calculate the similarity. Experiments show that the Fourier Descriptor Image Retrieval Method based on the minimum inertia axis is more efficient than other methods in Swedish Leaf database.

A shape descriptor is an effective tool for describing the shape feature of an object in remote sensing images. Researchers have put forward a lot of excellent descriptors. The discriminability of some descriptors is very strong in the experiments, but usually their computational cost is large, which makes them unsuitable to be used in practical applications. This paper proposes a new descriptor-FMSCCD (Fourier descriptor based on multiscale centroid contour distance)&mdash, which is a frequency domain descriptor based on the CCD (centroid contour distance) method, multiscale description, and Fourier transform. The principle of FMSCCD is simple, and the computational cost is very low. What is commendable is that its discriminability is still strong, and its compatibility with other features is also great. Experiments on three databases demonstrate its strong discriminability and operational efficiency.

International audience; With increasing number of Unmanned Aerial Vehicles (UAVs) -also known as drones- in our lives, safety and privacy concerns have arose. Especially, strategic locations such as governmental buildings, nuclear power stations etc. are under direct threat of these publicly available and easily accessible gadgets. Various methods are proposed as counter-measure, such as acoustics based detection, RF signal interception, micro-doppler RADAR etc. Computer vision based approach for detecting these threats seems as a viable solution due to various advantages. We envision an autonomous drone detection and tracking system for the protection of strategic locations. In this work, 2-dimensional scale, rotation and translation invariant Generic Fourier Descriptor (GFD) features (which are analyzed with a neural network) are used for classifying aerial targets as a drone or bird. For the training of this system, a large dataset composed of birds and drones is gathered from open sources. We have achieved up to 85.3% overall correct classification rate.

Aiming at the innovation of the contours of automobile side, this paper presents an innovative design method of vehicle side profile based on Fourier descriptor. The design flow of this design method is: pre-processing, coordinate extraction, standardization, discrete Fourier transform, simplified Fourier descriptor, exchange descriptor innovation, inverse Fourier transform to get the outline of innovative design. Innovative concepts of the innovative methods of gene exchange among species and the innovative methods of gene exchange among different species are presented, and the contours of the innovative design are obtained separately. A three-dimensional model of a car is obtained by referring to the profile curve which is obtained by exchanging xenogeneic genes. The feasibility of the method proposed in this paper is verified by various aspects.

Fourier descriptors are an interesting method for modeling 2D shapes that are described as closed contours. Unlike polylines or splines, which are explicit and local descriptions of the contour, Fourier descriptors are global shape representations, that is, each component stands for a particular characteristic of the entire shape. If one component is changed, the whole shape will change. The advantage is that it is possible to capture coarse shape properties with only a few numeric values, and the level of detail can be increased (or decreased) by adding (or removing) descriptor elements. In the following, we describe what is called “cartesian” (or “elliptical”) Fourier descriptors, how they can be used to model the shape of closed 2D contours and how they can be adapted to compare shapes in a translation-, scale-, and rotation-invariant fashion.

Shape descriptors have demonstrated encouraging potential for retrieving images based on image content, and a number of them have been reported in the literature. Nevertheless, most of the reported descriptors are still face accuracy and computational challenges. Fourier descriptors are considered to be promising descriptors as they are based on a sound theoretical foundation and also have the advantages of computational efficiency and attractive invariance properties. This paper proposes a new curvature-based Fourier descriptor (CBFD) for shape retrieval. The proposed descriptor takes an unconventional view of the curvature-scale-space representation of a shape contour as it treats it as a 2-D binary image (hence referred to as curvature-scale image, or CSI). The invariant descriptor is derived from the 2-D Fourier transform of the curvature-scale image. This method allows the descriptor to capture the detailed dynamics of the shape curvature and enhance the efficiency of the shape-matching process. Experiments using the widely known MPEG-7 databases in conjunction with a created noisy database have been conducted in order to compare the performance of the proposed descriptor with six commonly used shape-retrieval descriptors: curvature-scale-space descriptor (CSSD), angular radial transform descriptors (ARTD), Zernike moment descriptors (ZMD), radial Tchebichef moment descriptors (RTMD), generic Fourier descriptor (GFD), and the 1-D Fourier descriptor (1-FD). The performance of the proposed descriptor has surpassed that of many of these notable descriptors.

The optical, electrical, magnetic, and catalytic properties of colloidal nanocrystals are intimately tied to their form, in particular their physical size and shape. Synthetic techniques have been developed to produce metallic and semiconducting nanomaterials with well-controlled forms; however, characterization tools for describing shape have remained limited to small samples and lack the quantitative rigor necessary for a universal classification scheme. Here complex Fourier descriptors are shown to be a quantitative and high-throughput approach for classifying the shape of colloidal nanocrystals. Large, monodisperse, and polydisperse ensembles of CdSe nanocrystals are characterized with respect to shape and categorized as circles, triangles, squares, rods, and pentagonal or hexagonal platelets. These results suggest that classification of shape by Fourier descriptor analysis may in the near future be a powerful tool for continuous monitoring of synthesis, purification, or packaging/integration processe...

In object class recognition, the state-of-the-art works shows using combination varies local features may produce a good performance in recognition. These local features may have a different performance on one category to other category which it depends on the richness of local features. Due to that limitation, the shape features of objects are taken into consideration to be combined with local features. In this paper, we use Fourier Descriptor (FD), Elliptical Fourier Descriptors (EFD) and Moment Invariant (MI) as a global shape feature and Scale Invariant Feature Transform (SIFT) as local features. For learning technique, boosting is used in improving the recognition objects. This approach identifies the correct and misclassified dataset iteratively. Experimental results indicate that the recognition model outperform improved the accuracy of classification by up to 10% that is comparable to or better than that of state-of-the-art approaches.

Hand is a highly variable organ and hand features are easily affected by environmental factors. Considering the characteristics of hand gesture, a novel hand gesture recognition algorithm based on hybrid moments is presented. First, According to the color cue, the hand shape is available to extract from the complicated background, then the contour moment invariant and Fourier Descriptor are extracted and fused into a hybrid feature, finally the hybrid feature are put into the BP network to identity. The experimental results show that the method has better robustness and higher recognition rate.

Purpose To describe a method for unified description, statistical modeling, and comparison of voice range profile (VRP) contours, even from diverse sources. Method A morphologic modeling technique, which is based on Fourier descriptors (FDs), is applied to the VRP contour. The technique, which essentially involves resampling of the curve of the contour, is assessed and also is compared to density-based VRP averaging methods that use the overlap count. Results VRP contours can be usefully described and compared using FDs. The method also permits the visualization of the local covariation along the contour average. For example, the FD-based analysis shows that the population variance for ensembles of VRP contours is usually smallest at the upper left part of the VRP. To illustrate the method’s advantages and possible further application, graphs are given that compare the averaged contours from different authors and recording devices—for normal, trained, and untrained male and female voices as well as for child voices. Conclusions The proposed technique allows any VRP shape to be brought to the same uniform base. On this uniform base, VRP contours or contour elements coming from a variety of sources may be placed within the same graph for comparison and for statistical analysis.

Numeral recognition remains one of the most important problems in pattern recognition. To the best of our knowledge, little work has been done in Devnagari script compared with those for non Indian scripts like Latin, Chinese and Japanese. In this paper we propose an effective method for recognition of isolated Marathi handwritten numerals written in Devnagari script. Fourier Descriptors that describe the shape of Marathi handwritten numerals are used as feature. 64 dimensional Fourier Descriptors represents the shape of numerals, invariant to rotation, scale and translation. Three different classifiers, namely, nearest neighborhood (NN), K-nearest neighborhood (KNN) and Support Vector Machine (SVM) are used independently in order to recognize test numeral. These classifiers are trained with 64 dimensional Fourier Descriptors (FD) of training samples. The proposed system is experimented with a database of 13000 samples of Marathi handwritten numerals using fivefold cross validation method for result computation. An overall recognition rate of 97.05%, 97.04%and 97.85% are obtained for NN, KNN and SVM respectively.

Abstrct. There is a theoretical and experimental evidence that Fourier analysis is a powerful tool for tackling image processing problems. Its usefulness has been proven through its successful application in several fields. This paper describes the application of a new Fourier descriptor for outlining geographical profiles to be used in reconstruction and recognition.

Swiftlets are birds contained within the four genera Aerodramus, Hydrochous, Schoutedenapus and Collocalia. To date, the bird nest grading is based on weight, shape and size. Current inspection and grading for raw, edible bird nest were performed visually by expert panels. This conventional method is relying more on human judgments and often biased. A novel hybrid method from Fourier Descriptor (FD) method and Farthest Fourier Point Signature (FFPS) was developed using Charge Coupled Device (CCD) image data to grade bird nest by its shape and size. From the result, the hybrid method was able to differentiate different shape such as super AAA, super and corner grade depending on the Swiftlet species and geographical origin. The Wilks' lambda analysis was invoked to transform and compress the data set comprising of a large number of interconnected variables to a reduced set of varieties. Overall, the vision system was able to correctly classify 92.6 % of the super AAA, super and Corner shaped grades using the combined FD and FFPS features.

Shape-based image recognition is a key technology in computer vision, and Fourier descriptor (FD) is one important way to describe such images. FD uses the Fourier Transform of the contour coordinate as eigenvector to describe the image contour property. However, it can only show the contour property, but may fail to distinguish images with the same contour but different content. And the length of FD varies with the size of the image. In this paper, a modified Fourier descriptor (MFD) is proposed, which is invariant with translation, rotation, and scaling of the image. It takes both the contour property and the content into consideration. A 2D shape-based image can be represented by a one-dimensional discrete array with constant length, which makes it convenient to recognize different images. To prove the efficiency of the proposed algorithm, we have applied it to shape recognition experiments and got reasonable results.

Shape is an essential visual feature of an image and it is widely used to describe image content in image classification and retrieval. In this paper, two new Fourier-based approaches for contour-based shape description are presented. These approaches present Fourier descriptors in multiple scales, which improves the shape classification and retrieval accuracy. The proposed methods outperform ordinary Fourier descriptors in the retrieval of complicated shapes without increasing computational cost.

Shape is one of the primary low-level image features exploited in the newly emerged content-based image retrieval (CBIR). Many shape methods exist. Among these shape methods, Fourier descriptor (FD) is one of the most widely used shape descriptors due to its simple computation, clarity and coarse to fine description capability. FD has been applied to a variety of applications, including image retrieval application. Generally, FD can be acquired in a number of ways, however, FD acquired from different ways can have different retrieval performance. In this paper, we study shape retrieval using FD. Specifically, we study different ways of acquiring FD, the number of FD features needed for general shape description and the retrieval performance of different FD. A Java client–server retrieval framework has been developed to facilitate the study. The retrieval performance of the different FD is tested using a standard shape database and a commonly used performance measurement.

Two subsystems of living systems were studied as quasi-periodic synchronized processes x 1(t) and x 2(t). The signals were monitored during time interval T, which was determined according to the goals of the tests and the origin of processes. The phase portrait of the system was formed in the framework of references x 1(t) – x 2(t) within the time interval T. The portrait outlook was plotted. Fourier descriptors of the outlook were calculated. The system was classified in the space of Fourier descriptors.

Shape is an important image feature-it is one of the primary low level image features exploited in content-based image retrieval (CBIR). There are generally two types of shape descriptors in the literature: contour-based and region-based. In MPEG-7, the curvature scale space descriptor (CSSD) and Zernike moment descriptor (ZMD) have been adopted as the contour-based shape descriptor and region-based shape descriptor, respectively. In this paper, the two shape descriptors are evaluated against other shape descriptors, and the two shape descriptors are also evaluated against each other. Standard methodology is used in the evaluation. Specifically, we use standard databases, large data sets and query sets, commonly used performance measurement and guided principles. A Java-based client-server retrieval framework has been implemented to facilitate the evaluation. Results show that Fourier descriptor (FD) outperforms CSSD, and that CSSD can be replaced by either FD or ZMD.

Shape description is one of the key parts of image content description for image retrieval. Most of the existing shape descriptors are usually either application dependent or non-robust, making them undesirable for generic shape description. In this paper, a generic Fourier descriptor (GFD) is proposed to overcome the drawbacks of existing shape representation techniques. The proposed shape descriptor is derived by applying two-dimensional Fourier transform on a polar-raster sampled shape image. The acquired shape descriptor is application independent and robust. Experimental results show that the proposed GFD outperforms common contour-based and region-based shape descriptors.

Fourier descriptor (FD) values computed from spectrophotometric measurements were used to compute a purity index. The Fourier Descriptors calculated for a set of absorbencies are independent of concentration and is sensitive to the presence of interferents. Such condition was proven by calculating the FD for pure and degraded benyzylpenicillin. Absorbance data were measured and recorded for twelve different benzenoid compounds. The calculated FD values for these compounds showed significant discrimination between them. Also the reproducibility of FDs was tested by measurement over several successive days and the relative standard deviation obtained was less than 2 %.

The General Shape Analysis (GSA) is a problem of finding the most similar basic shape to the test one. It is close to traditional recognition or retrieval of shapes. Main difference is that GSA does not aim at the identification of an exact object shape but at the indication of one or few most similar to it general templates --- simple shape figures, e.g. rectangle, circle or triangle. By comparing more complicated shapes with simple ones it is possible to determine the most general information about a particular object. In order to perform the comparison using the template matching approach it is necessary to define methods for the representation and similarity estimation of shapes. In this paper the attention is paid to two-dimensional Fourier Descriptor applied for the representation of a shape and two matching methods, namely Euclidean distance and correlation. The effectiveness of the shape descriptor is estimated as a convergence between the experimental results and results provided by humans through the inquiry forms concerning the same GSA task. Performed experiments allowed us to determine the influence of the matching method on the final effectiveness of the approach applying Fourier Descriptors. Selection of the absolute spectrum subpart size is also discussed.

International audience; In the context of plant leaf roughness analysis for precision spraying, this study explores the capability and the performance of some combinations of pattern recognition and computer vision techniques to extract the roughness feature. The techniques merge feature extraction, linear and nonlinear dimensionality reduction techniques, and several kinds of methods of classification. The performance of the methods is evaluated and compared in terms of the error of classification. The results for the characterization of leaf roughness by generalized Fourier descriptors for feature extraction, kernel-based methods such as support vector machines for classification and kernel discriminant analysis for dimensionality reduction were encouraging. These results pave the way to a better understanding of the adhesion mechanisms of droplets on leaves that will help to reduce and improve the application of phytosanitary products and lead to possible modifications of sprayer configurations

Fourier descriptors (FDs) have been used successfully to characterize the boundary of objects in images. It is demonstrated that FDs are appropriate for characterizing objects in speech spectrograms consisting of 40 sounds representing 10 speaker-dependent words containing the English semivowels /w y l r/. With 10 FDs, a 97.5% recognition rate is attained. Different sounds are misclassified by wide- and narrow-band methods, suggesting that multiscaling and FD changes (differences) may be appropriate features. With a FD difference approach, recognition rates equaled or exceeded those obtained with a conventional linear predictive coding (LPC) classifier as well as those obtained with wide- and narrow-band FD methods alone.

Since contours often contain many different sized structures they need to be described at multiple scales. Rather than describe a contour at all scales it is more efficient to identify the most significant scales that best represent the structures present. These natural scales are determined by examining the Fourier descriptors of the contour and searching for significant bands. These correspond to bandwidths required to extract features at qualitatively significant resolution. Examples are given of using the determined scales in both low pass and high pass filters to eliminate fine and coarse detail.

The droplet shape in the process of droplet dropping can embodies the fundamental intrinsic properties of droplet, which can be used to identify the characteristics of liquid types. A new method is proposed by using Moment characters- Fourier descriptor to analysis the information of droplet dropping image. Data of the droplet profile changing is collected through the CCD camera. Moment characters sequence is calculated to represent the shape. The sequence is given Fourier counterchanges and normalized. The feature descriptor carries the liquid image features and unique information of liquid.

In many industrial applications, Fourier descriptors are commonly used when the description of the object shape is an important characteristic of the image. However, these descriptors are limited to single objects. We propose a general Fourier-based approach, called statistical Fourier descriptor (SFD), which computes shape statistics in grey level images. The SFD is computationally efficient and can be used for defect image classification. In a first example, we deployed the SFD to the inspection of welding seams with promising results.

Shape representation provides fundamental features formany applications in computer vision and it is known to be important cues for human vision. This paper presents an experimental study on recognition of mice behavior. We investigate the performance of the four shape recognition methods, namely Chain-Code, Curvature, Fourier descriptors and Zernike moments. These methods are applied to a real database that consists of four mice behaviors. Our experiments show that Zernike moments and Fourier descriptors provide the best results. To evaluate the noise tolerance, we corrupt each contour with different levels of noise. In this scenario, Fourier descriptor shows invariance to high levels of noise.

Fourier descriptors based upon the waveform induced by a pattern's projection overcome a number of classic difficulties with Fourier-descriptor methodology. Not only are the descriptors invariant with respect to scale, translation, and rotation (as is usually the case), they are also continuous in the Hausdorff metric and robust with respect to both point noise and occlusion; insensitivity with respect to minimum occlusions is perhaps their most significant advantage. Continuity in the Hausdorff metric allows prediction of the effect on the descriptors when morphologically filtering a pattern. The effect of occlusion is also predictable.

By generating Fourier descriptors based upon the waveform induced by a pattern's geometric projection, a number of classic difficulties with the Fourier-descriptor methodology are mitigated. Not only are the descriptors invariant with respect to scale, translation, and rotation (as is usually the case), they are also continuous in the Hausdorff metric and robust with respect to both point noise and occlusion. An additional advantage is that they can be computed relative to a thresholded image without first finding an edge, thereby avoiding the difficulties typically present in thinning and orientation determination. The present paper discusses the method of projection-generated Fourier descriptors, as well as a study of the sensitivity to point noise. A companion paper will present the morphological properties and the effect of pattern occlusion.

Image normalization is useful for image recognition by the matching method. Recently, a normalization algorithm was developed to normalize images under the distortion of translation, rotation, scaling and skew. However, the method fails when the image is rotationally symmetric. A method is introduced called the modified Fourier descriptor to normalize rotationally symmetric shapes. This method is simple and fast, and can be combined with the preceding normalization algorithm to make it more general and realizable.

A sort of software for peanut shape identification based on artificial neural network was developed. Images of peanut which is advantageous for carries on the characteristic extraction were acquired by means of red component extraction, filter, image division, edge examination, and so on. The method to describe the shape of irregular peanut was studied, in which the Fourier transform and Fourier inverse transform were applied. It was concluded that the first thirteen harmonics of the Fourier descriptor were enough to represent the primary shape of peanut, The method achieved an accuracy of 90% for oblong peanuts, 93.3% for simple peanuts, 96.7% for trilateral peanuts, 100% for elliptic peanuts and 93.3% for circular peanuts.

A pattern recognition system is described for recognizing shipbuilding parts using artificial neural networks and Fourier descriptors. The system uses shape contour information that is invariant of size, translation, and rotation. Fourier descriptors provide information, and the neural networks make decisions about the shapes. A brief review of the current state of the art is included, and results from testing show that the system distinguished between various shapes and proved to be a valid approach.

The most widely used method for comparing mode shapes from finite elements and experimental measurements is the Modal Assurance Criterion (MAC), which returns a single numerical value and carries no explicit information on shape features. New techniques, based on image processing (IP) and pattern recognition (PR) are described in this paper. The Zernike moment descriptor (ZMD), Fourier descriptor (FD), and wavelet descriptor (WD), presented in this article, are the most popular shape descriptors having properties that include efficiency of expression, robustness to noise, invariance to geometric transformation and rotation, separation of local and global shape features and computational efficiency. The comparison of mode shapes is readily achieved by assembling the shape features of each mode shape into multi-dimensional shape feature vectors (SFVs) and determining the distances separating them. © 2009 IOP Publishing Ltd.

A Fortify method of moving object detection is proposed in this paper. Based on color and edge geometric features, the new method can automatically organize a supervised area. First, by the color features in a real supervised scene, the method extracts several regions of interest (ROI) with noise, then matches them with geometric shape by Fourier descriptors in the database and sequentially achieves an automatic-organizing supervised area. Experimental results show that this method has low operation cost, high efficiency, strong anti-jamming, high accuracy and robustness.

The method of Fourier descriptors is extended to produce a set of normalized coefficients which are invariant under any affine transformation (translation, rotation, scaling, and shearing). The method is based on a parameterized boundary description which is transformed to the Fourier domain and normalized there to eliminate dependencies on the affine transformation and on the starting point. Invariance to affine transforms allows considerable robustness when applied to images of objects which rotate in all three dimensions, as is demonstrated by processing silhouettes of aircraft maneuvering in three-space. >

Eel otolith shapes can be separated into distinct groups which can be assigned to certain age groups. The shape is described exactly through Fourier series using the maximum-projection-area. Clusters formed by the magnitudes of Fourier descriptors agreed with age groups of three year intervals by 66% (kappa = · 522, p

Human movement analysis has recently gained growing interest for computer vision researchers. In this paper, a simple but efficient algorithm using Fourier descriptor to represent spatial-temporal silhouette for human movement analysis is proposed. For each image sequence, motion detection and segmentation methods are used to segment and extract the moving silhouettes of people. Then, Fourier descriptor(FD)is used to describe the moving silhouettes. HMMs and Haudorff distance are applied to the time-varying distance signals described by FD for the activity classification and gait recognition. Experimental results have demonstrated that the proposed algorithm greatly improve the recognition rates.

This paper presents a novel normalization for the Fourier descriptor, named as spatial normalization Fourier descriptor, which presents a new method to normalization the Fourier descriptor. Especially in the finding start point there is innovation comparing with former algorithm. This invent greatly improve the performance of the Fourier descriptor, and provides high robust and invariant. The same time its foundation in theory is obvious and that make it easy to be understood and fulfilled. It will greatly impulse the pattern recognition of shape, and in the so many applications for the Fourier descriptor it is highlighted. Lastly the experiment verifies it and it outperform the traditional Fourier descriptor.

A novel shape description method, statistical chord-length features (SCLF), is proposed for shape retrieval. SCLF first describes the contour of a 2D shape using k/2 one-dimensional chord-length functions derived from partitioning the contour into k arcs of the same length, where k is the parameter of SCLF. The means and variances of all the chord-length functions are then calculated and a k dimensional feature vector is generated as a shape descriptor. Two experiments are conducted and the results show that SCLF achieves higher retrieval performance than traditional description methods such as geometric moment invariants and Fourier descriptors.

This paper describes a rose variety recognition project and proposes the modified Fourier descriptor. Based on the modified descriptor, a new measurement, angle measurement, is proposed for image shape analysis. We use it for rose flower shape analysis and the experimental results show that this measurement is quite efficient for image shape analysis.

The shape and the condition of stem are important features in classification of Huanghua pears. As the commonly used thinning and erosion-dilation algorithm in judging the presence of the stem is too slow, a new fast algorithm was put forward. Compared with other part of the pear, the stem is obviously thin and long, with the help of various sized templates, the judgment of whether the stem is present was easily made, meanwhile the stem head and the intersection point of stem bottom and pear were labeled. Furthermore, after the slopes of the tangential line of stem head and tangential line of stem bottom were found, the included angle of these two lines was calculated. It was found that the included angle of the broken stem was obviously different from that of the good stem. After the analysis of 53 pictures of pears, the accuracy to judge whether the stem is present is 100% and whether the stem is good reaches 93%. Also, the algorithm is of robustness and can be made invariant to translation and rotation Meanwhile, the method to describe the shape of irregular fruits was studied. Fourier transformation and inverse Fourier transformation pair were adopted to describe the shape of Huanghua pears, and the algorithm for shape identification, which was based on artificial neural network, was developed. The first sixteen harmonic components of the Fourier descriptor were enough to represent the primary shape of pear, and the identification accuracy could reach 90% by applying the Fourier descriptor in combination with artificial neural network.

The authors propose a viewpoint-invariant Fourier descriptor which has all the properties inherent in classical Fourier descriptors, providing starting point invariance. Experiments have shown that the new shape representation has better performance in terms of discrimination power and computation speed.

Shape recognition of three-dimensional rigid objects when viewed by a two-dimensional imaging system is discussed. Fourier descriptor features are used that are invariant to scale, translation, and rotation about the viewing axis. A differential library storage method is developed which allows compact storage of the many shapes generated by viewing an object from different aspect angles. Experimental results are presented using aircraft and normalized Fourier descriptors which show the effectiveness of the differential library storage. An automatic shape learning system is also demonstrated.

SUMMARY A general method for shape characterization of two-dimensional (2-D) microscopical particles is presented. The proposed procedure based on Fourier analysis techniques can be regarded as a generalization and further development of methods described in the literature. The geometry of the particles is characterized by a set of shape functions which is invariant under translation, rotation and dilation. Shape descriptors generated from the Fourier coefficients are used for shape evaluation. Similarity between particles has been evaluated using an appropriately defined distance measure. The method is demonstrated by an application using a collection of 2-D objects.