An approach to 3-D object recognition using Legendre moment invariants

A comprehensive treaty on the theory and applications of moment functions in image analysis. Moment functions are widely-used in various realms of computer vision and image processing. Numerous algorithms and techniques have been developed using image moments, in the areas of pattern recognition, object identification, three-dimensional object pose estimation, robot sensing, image coding and reconstruction. This is a compilation of the theoretical aspects related to different types of moment functions, and their applications in the above areas. The book is organized in two parts. The first part discusses the fundamental concepts behind important moments such as geometric moments, complex moments, Legendre moments, Zernike moments, and moment tensors. Most of the commonly-used properties of moment functions and the mathematical framework for the derivation of basic theorems and results are discussed. This includes the derivation of moment invariants, implementation aspects of moments, transport properties, and fast methods for computing the moment functions for both binary and gray-level images. The second part presents the key application areas of moments, such as pattern recognition, object identification, image-based pose estimation, edge detection, clustering, segmentation, coding and reconstruction. Important algorithms in each of these areas are discussed. A list of bibliographic references on image moments is also included.

Rotation and translation invariants of Gaussian–Hermite moments

One of the main contributions of this paper is to show that contrary to the common belief Tchebichef moments are more sensitive to noise added to the image than Zernike moments. We show this by imposing different types and levels of noise on various images and measuring the error due to the added noise alone after image reconstruction. To calculate the error due to added noise alone, the image reconstruction error is subtracted from the total error, which initially includes both reconstruction and added noise errors. Another contribution of this paper is to present some analysis and compare the reconstruction capability of Tchebichef moments to that of Zernike and Legendre moments in noise free environments independent of the image used. We show this by spectrally analyzing the performance of Tchebichef, Legendre, and Zernike moments using single frequency images. Here the total reconstruction error of an arbitrary image is equal to the integration of the spectral errors, whose transfer functions are calculated using single frequency images, for all frequencies.

Simple and fast computation of moments

Objective To compare the reproducibility and reliability of facial soft tissue landmarks using a direct and an indirect placement methods in facial three-dimensional (3D) soft tissue assessment.Methods 3D coordinates of 37 soft tissue landmarks were obtained respectively in 35 normal healthy volunteers from 3D optical capture system and Materialise's interactive medical image control system (Mimics).Landmarks were affixed on the cutaneous surface (direct method) and marked on the 3D reconstructed craniofacial model (indirect method).Intra-class correlation coefficients (ICCs) and paired t-tests were used to compare the reliability and reproducibility of facial landmarks between two placement methods.Results For the direct placement method,86.5 ％ landmarks had an ICC higher than 0.75.For the indirect placement method,75.7％ landmarks had an ICC higher than 0.75.The inter-observer variability using the direct placement method was (1.259±0.566) mm,which was significantly smaller (P＜0.05) than (1.420±0.638) mm obtained by the indirect placement method.Conclusions Compared with indirect method,direct method has higher reliability and reproducibility in evaluating facial soft tissue. Key words: Computed tomography; Cephalometrics; Optical capture technology

Efficient Legendre moment computation for grey level images

Explicit invariance of Cartesian Zernike moments

This paper proposes an approach combining the set of Krawtchouk moments and HMMs (Hidden Markov Models) for unconstrained offline handwritten Chinese character recognition. The Krawtchouk moments can be effectively used as pattern features in analysis of two-dimensional images. Since the basis set is orthogonal in the discrete domain of the image coordinate space, the implementation of Krawtchouk moments doesn't involve any numerical approximation or coordinate transformation. This property makes Krawtchouk moments superior to conventional, more continuous moments such as Legendre moments and Zernike moments. In the field of character recognition, HMMs architecture has been used widely because of its strong adaptability to written distortion and variability. In this paper, Krawtchouk moments and HMMs are combined to recognize unconstrained offline handwritten Chinese amount in words. Experiments show that the average recognition of Krawtchouk is higher than Zernike and Legendre moments within the HMM framework.

Analysis of direct and indirect quantification methods of CO2 fixation via microalgae cultivation in photobioreactors: A critical review

Aforestation activities, silvicultural prescription, forest management decisions and land use planning are based on site information to develop appropriate actions for implementation. Forest site classification has been one of the major problems of Turkish forestry for long time. Both direct and indirect methods can be used to determine forest site productivity. Indirect methods are usually reserved for practical applications as they are relatively simple, yet provide less accurate site estimation. However, direct method is highly time-demanding, expensive and hard to conduct, necessitating the use of information technologies such as Geographic Information Systems (GIS) and Remote Sensing (RS). This study, first of all, generated a forest site map using both direct and indirect methods based on ground measurements in 567.2 ha sample area. Then, supervised classification was conducted on Landsat 7 ETM image using forest site map generated from direct method as ground measurements to generate site map. The classification resulted in moist site of 262.5 ha, very moist site of 122.5 ha and highly moist site of 191.2 ha in direct method; sites I-II cover 38.9 ha, III 289.6 ha, IV-V 143.5 ha and treeless-degraded areas of 104.2 ha in indirect method; moist site of 203.5 ha, very moist site of 232.1 ha and highly moist site of 140.6 ha in remote sensing method. However, 104.2 ha treeless and degraded areas were not determined by indirect method, yet by the other methods. Secondly, forest site map for the whole area (5,980.8 ha) was generated based on the site map generated by the direct method for sampled area. The Landsat 7 ETM image was classified based on the forest site map of sample area. The site index (SI) map for the whole area was generated using conventional inventory measurements. The classification resulted in sites I-II cover 134.1 ha, III 1,643.6 ha, IV-V 1,396.5 ha, treeless-degraded areas of 1,097.3 ha and settlement-agriculture areas of 1,709.3 ha in indirect method; moist site of 1,674.3 ha, very moist site of 853.6 ha, highly moist site of 1,729.6 ha and settlement-agriculture areas 1,723.3 ha in remote sensing method. Again the treeless- degraded areas of 1,097.3 ha were not determined by indirect method but by remote sensing method.

Introduction A number of methods of therapy of stuttering have been developed, which can be grouped as direct, indirect and compound methods. Direct methods are aimed at the very speech act and lead to improving speech fluency. Indirect methods are supposed to influence the person and his/her organism. Compound methods are a combination of direct and indirect methods in the form of a therapeutic program. Aim The aim of the overview was to analyze 17 articles that presented studies over the efficiency of direct, indirect and compound therapies of stuttering, as published in PubMed database between 2008 and 2015. Discussion As far as direct methods of stuttering are concerned, devices like SpeechEasy, DAF and FAF (i.e. the one which alter the patient's perception of his/her own speech), as well as a metronome turn out to be really efficient. Indirect methods which use biofeedback, tactile and visual transmission of feedback as well as hypnotherapy combined with diaphragm exercise are equally effective. Laser acupuncture and cognitive therapy seem to improve the positive results achieved by means of other methods. Among the compound methods, Lidcombe Program in its different variants proves to be highly efficient among children, whereas Camperdown Program works well among teenagers and adults. One may have certain hopes with regard to an innovative program referred to as Acceptance and Commitment Therapy. Conclusions Studies on efficiency of therapies of stuttering are scattered, do not cover the whole structure of the disorder and are focused on the symptom i.e. on assessing the severity of speech disfluency. Considering the research done so far, one cannot conclude that some methods are better than others since neither of them were compared in an experimental way.

Affixing markers on the face in vivo with an optical surface imaging system and placing landmarks on a computed tomographic reconstructive facial model represent two helpful approaches prevailing in three-dimensional cephalometric analysis of facial aesthetics. In this study, the authors determine the suitability of these methods for soft-tissue evaluation along with the reproducibility and reliability of landmark placement. Thirty-seven soft-tissue landmarks were investigated in 35 normal healthy volunteers who underwent cephalometric analysis by direct and indirect placement methods. Two operators performed the analysis twice for each method at a 1-week interval. Landmark positions were measured on the three-dimensional coordinates, and data were standardized and converted into landmark placement errors for the estimation, by two-way random intraclass correlation coefficients. Using the direct method, 86.5 percent of the landmarks had a higher intraclass correlation coefficient than 0.75, and 67.6 percent were higher than 0.90. The authors found that 75.7 percent were higher than 0.75 and 43.2 percent were higher than 0.90 with the indirect method. Both methods showed good reliability in identifying midline-related structures, although the correlations of markers surrounding eyelashes and lips were better using the direct method. The direct method had a significantly smaller landmark placement error and better reproducibility than that identified indirectly (p<0.05). When evaluating well-defined contours and the natural texture of the face, the direct placement method shows better accuracy than the indirect method. The three-dimensional evaluation emphasizes the eye, lip, and some structures more laterally, therefore providing comprehensive analysis for clinical diagnosis. Diagnostic, II.

The Direct and Indirect Methods of Ionospheric TEC Predictions and Their Comparison

Forest site classification has long been a problem for managers of Turkish forests. Forest management decisions and land use planning involving afforestation activities and silvicultural prescriptions are based on sound site information to formulate appropriate actions on the ground. In Turkey, two methods of forest site productivity are used; direct and indirect method. Indirect methods are usually reserved for practical applications as they are relatively simple, yet provide less accurate estimation of the real productivity. In this study direct, indirect and remote sensing (RS) methods were used to distinguish and map forest sites of Karanlikdere Forest District in Gumushane, Turkey. One hundred and twenty-two sample plots were established with 300 m × 300 m grids in summer of 2003. In each sample plot, soil samples and the classical timber inventory measurements were taken. According to direct method, water-air economy method is preferred due to a water deficiency in the study area. Four different forest site classes; very dry, dry, moderate fresh and fresh were determined and mapped with geographic information system (GIS). In indirect method, the guiding curve was used to generate anamorphic site indexes (SI) of three classes; good (SI = I and II), medium (SI = III) and poor (SI = IV and V). Furthermore, forest sites were estimated with Landsat 7 ETM (2000) data using supervised classification with a 0.843 kappa statistic value and 88% accuracy assessments. Some important differences between the methods were discovered. The indirect method indicate that site indices I and II are 298.5 ha, III 254.3 ha and IV and V 347.7 ha. In contrast, direct method related to very dry site of 107.7 ha, dry site of 484.6 ha, moderate fresh site of 304.7 ha and fresh site of 246.3 ha. Satellite image indicate that very dry site covers 291.2 ha, dry site 239.2 ha, moderate fresh site 287.4 and fresh site 325.5 ha. Approximately 242.8 ha area (open and degraded areas) were not determined by indirect method but were captured with RS method. The statistical analyses (ANOVA) showed no statistically significant (F = 0.720, p = 0.543) relationship between indirect method and direct method-RS method indicating clearly that indirect method is not an adequate measurement of forest site productivity. Forest sites, particularly in open and degraded areas should be determined with direct method.

The definition of pseudo-Zernike moments has a form of projection of the image intensity function onto the pseudo-Zernike polynomials, and they are defined using a polar coordinate representation of the image space. Hence, they are commonly used in recognition tasks requiring rotation invariance. However, this coordinate representation does not easily yield a scale invariant function because it is difficult to extract a common scale factor from the radial polynomials. As a result, vision applications generally resort to image normalisation method or using a combination of scale invariants of geometric orradial moments to achieve the corresponding invariants of pseudo-Zernike moments. In this paper, we present a mathematical framework to derive a new set of scale invariants of pseudo-Zernike moments based on pseudo-Zernike polynomials. They are algebraically obtained by eliminating the scale factor contained in the scaled pseudo-Zernike moments. They remain unchanged under equal-shape expansion, contraction and reflection of theoriginal image. They can be directly computed from any scaled image without prior knowledge of the normalisation parameters, or assistance of geometric or radial moments. Their performance is experimentally verified using a set of Chinese and Latin characters. In addition, a comparison of computational speed between the proposed descriptors and the present methods is also presented.