Scale Space Technique Research Articles

STUDY OF CORRELATIONS IN THE RELIEF OF COMPLEX SURFACES USING THE EXAMPLE OF AMORPHOUS HYDROGENATED SILICON

Abstract. The results of a study of correlations in the surface relief of amorphous hydrogenated silicon using the methods of average mutual information andtwo-dimensional detrended fluctuation analysis by identifying its structural components using the scale-space technique are presented. The experimental samples were model and real surfaces of amorphous hydrogenated silicon. The model surface was formed bysuperimposing the surfaces "Stochastic fractal", "Particles" and "Gaussian noise". The values of the scaling index were obtained from the dependences of the fluctuation function on the scale, as well as the values of the average mutual information and themaximum mutual information were calculated. A comparative analysis of the correlation dependencies of the model and the real surfaces of amorphous hydrogenated silicon has shown that the model surface "Particles" is closest to the surface structure of theexperimental sample in terms of its characteristics. It was found that particles with dimensions of 65±10 nm are present in the surface structure of the experimental sample.

Tri-level handwritten text segmentation techniques for Gujarati language

Objectives: To improve the efficiency of tri-level segmentation tasks for handwritten Gujarati text. Methods: Using hybrid methods for tri-level segmentation, we have used line, word and character segmentation from the image. This study presents a segmentation paradigm that works with touching characters, slop of the line written on the page, character overlapping, etc. It evaluated on the dataset of 500+ images created by us on different writing sentences by different people. We have used the Horizontal projection technique for line segmentation, Scale-space technique for word segmentation and the Vertical projection technique for character segmentation. Findings: The experimental results show that the proposed method is more efficient for handwritten Gujarati text with diacritics. We have obtained the accuracy for character level segmentation is 82%, word-level is 90% and for the line-level segmentation is 87%. Novelty: We have designed a methodology to segment Gujarati handwritten text with diacritics at all three levels including characters, words and lines. Applications: We have proposed tri-level segmentation which is pre-processing task that can be used in any character recognition systems i.e. OCR. Keywords: Deep learning; trilevel segmentation; handwritten Gujarati text

A restoration–segmentation algorithm based on flexible Arnoldi–Tikhonov method and Curvelet denoising

In this paper, we illustrate a two-stage algorithm consisting of restoration and segmentation to reach binary segmentation from the noisy and blurry image. The results of our method can be applied in main fields of the image processing such as object extraction. In the first stage, we have a linear discrete ill-posed problem with a noise-contaminated right-hand side, arising from the image restoration. We consider problems in which the coefficient matrix is the sum of Kronecker products of matrices and present a global flexible Arnoldi–Tikhonov method coupled with the generalized cross-validation for the computation of the regularization parameter at each iteration. The proposed algorithm is based on the global Arnoldi method that allows using a more flexible solution subspace. In the second stage, we segment the restored image in order to reach a binary image in which the target object is emphasized. In our segmentation method, we use Gaussian scale-space technique to compute discrete gradients of the restored image for pre-segmenting. Also, in order to denoise, we use a tight frame of Curvelet transforms and thresholding which is based on the principle obtained by minimizing Stein’s unbiased risk estimate. This algorithm has an iterative part based on the iterative part of TFA (Cai et al. in SIAM J Imaging 6(1):464–486, 2013), but we use eigenvectors of Hessian matrix of image for improving this part. Theoretical properties of the method of both stages and numerical experiments are presented.

A Morphological Classification Method of ECG ST-Segment Based on Curvature Scale Space

Aomalous changes in the ST segment, including ST level deviation and ST shape change, are the major parameters in clinical electrocardiogram (ECG) diagnosis of myocardial ischemia. Automatic detection of ST segment morphology can provide a more accurate evidence for clinical diagnosis of myocardial ischemia. In this paper, we proposed a method for classifying the shape of the ST-segment based on the curvature scale space (CSS) technique. First, we established a reference ST set and preprocessed the ECG signal by using the CSS technique. Then, the corner points in the ST-segment were detected at a high scale of the CSS and tracked through multiple lower scales, in order to improve its localization. Finally, the current beat of ST morphology can be distinguished by the corner points. We applied the developed algorithm to the ECG recordings in European ST-T database and QT database to validate the accuracy of the algorithm. The experimental results showed that the average detection accuracy of our algorithm was 91.60%. We could conclude that the proposed method is able to provide a new way for the automatic detection of myocardial ischemia.

Similar gait action recognition using an inertial sensor

This paper tackles a challenging problem of inertial sensor-based recognition for similar gait action classes (such as walking on flat ground, up/down stairs, and up/down a slope). We solve three drawbacks of existing methods in the case of gait actions: the action signal segmentation, the sensor orientation inconsistency, and the recognition of similar action classes. First, to robustly segment the walking action under drastic changes in various factors such as speed, intensity, style, and sensor orientation of different participants, we rely on the likelihood of heel strike computed employing a scale-space technique. Second, to solve the problem of 3D sensor orientation inconsistency when matching the signals captured at different sensor orientations, we correct the sensor׳s tilt before applying an orientation-compensative matching algorithm to solve the remaining angle. Third, to accurately classify similar actions, we incorporate the interclass relationship in the feature vector for recognition. In experiments, the proposed algorithms were positively validated with 460 participants (the largest number in the research field), and five similar gait action classes (namely walking on flat ground, up/down stairs, and up/down a slope) captured by three inertial sensors at different positions (center, left, and right) and orientations on the participant׳s waist.

Shape analysis using fractal dimension: A curvature based approach

The present work shows a novel fractal dimension method for shape analysis. The proposed technique extracts descriptors from a shape by applying a multi-scale approach to the calculus of the fractal dimension. The fractal dimension is estimated by applying the curvature scale-space technique to the original shape. By applying a multi-scale transform to the calculus, we obtain a set of descriptors which is capable of describing the shape under investigation with high precision. We validate the computed descriptors in a classification process. The results demonstrate that the novel technique provides highly reliable descriptors, confirming the efficiency of the proposed method.

On the Convergence of Planar Curves Under Smoothing

Curve smoothing has two important applications in computer vision and image processing: 1) the curvature scale-space (CSS) technique for shape analysis, and 2) the Gaussian filter for noise suppression. In this paper, we study how planar curves converge as they are smoothed with increasing scales. First, two types of convergence behavior are clarified. The coined term shrinkage refers to the reduction of arc-length of a smoothed planar curve, which describes the convergence of the curve latitudinally; and another coined term collapse refers to the movement of each point to its limiting position, which describes the convergence of the curve longitudinally. A systematic study on the shrinkage and collapse of three categories of curve models is then presented. The corner models helps to reveal how the local structures of planar curves collapse and what the smoothed curves may converge to. The sawtooth models allows us to gain insights regarding how noise is suppressed from noisy planar curves by the Gaussian filter. Our investigation on the closed curves shows that each curve collapses to a point at its center of mass. However, different curves may yield different limiting shapes at the infinity scale. Finally, based upon the derived results the performance of the CSS technique in corner detection and shape representation is analyzed, and a fast implementation method of the Gaussian filter for noise suppression is proposed.

Robust Image Corner Detection Using Curvature Product in Direct Curvature Scale Space

In this paper we propose an image corner detector based on the direct curvature scale space (DCSS) technique, referred to as the curvature product DCSS (CP-DCSS) corner detector. After the contours of interested objects are extracted from a real-world image, their curvature functions are respectively convolved with the Gaussian function as its standard deviation gradually increases. By measuring the product of the curvature values computed at several given scales, true corners on the contours can be easily detected since false or insignificant corners have been effectively suppressed. A point is declared as a corner when the absolute value of the curvature product exceeds a given threshold and is a local maximum at the mentioned point. CP-DCSS combines the advantages of two recently proposed corner detectors, namely, the DCSS corner detector and the multi-scale curvature product (MSCP) corner detector. Compared to DCSS, CP-DCSS omits a parsing process of the DCSS map, and hence it has a simpler structure. Compared to MSCP, CP-DCSS works equally well, however, at less computational cost.

Curvature product corner detection in direct curvature scale space

An efficient corner detector based on the direct curvature scale space (DCSS) technique, referred to as the curvature product direct curvature scale space (CP-DCSS) corner detector, is introduced and studied. The contours of interested objects are extracted from a real-world image, and then their curvature functions are respectively convolved with the Gaussian function, whose standard deviation gradually increases and is treated as a scale parameter of corner detection. By measuring the product of the curvature values computed at several given scales, true corners on the contours can be easily detected since false or insignificant corners have been effectively suppressed. A point is declared as a corner when the absolute value of the curvature product exceeds a given threshold and is a local maximum at the mentioned point. CP-DCSS combines the advantages of two recently proposed corner detectors, namely, the DCSS corner detector and the multi-scale curvature product (MSCP) corner detector. Compared to DCSS, CP-DCSS omits a parsing process of the DCSS map, and hence it has a simpler structure. Compared to MSCP, CP-DCSS works equally well, however, at less computational cost.

Scale-Space Behavior of Planar-Curve Corners

The curvature scale-space (CSS) technique is suitable for extracting curvature features from objects with noisy boundaries. To detect corner points in a multiscale framework, Rattarangsi and Chin investigated the scale-space behavior of planar-curve corners. Unfortunately, their investigation was based on an incorrect assumption, viz., that planar curves have no shrinkage under evolution. In the present paper, this mistake is corrected. First, it is demonstrated that a planar curve may shrink nonuniformly as it evolves across increasing scales. Then, by taking into account the shrinkage effect of evolved curves, the CSS trajectory maps of various corner models are investigated and their properties are summarized. The scale-space trajectory of a corner may either persist, vanish, merge with a neighboring trajectory, or split into several trajectories. The scale-space trajectories of adjacent corners may attract each other when the corners have the same concavity, or repel each other when the corners have opposite concavities. Finally, we present a standard curvature measure for computing the CSS maps of digital curves, with which it is shown that planar-curve corners have consistent scale-space behavior in the digital case as in the continuous case.

Direct Curvature Scale Space: Theory and Corner Detection

The Curvature Scale Space (CSS) technique is considered to be a modern tool in image processing and computer vision. Direct Curvature Scale Space (DCSS) is defined as the CSS that results from convolving the curvature of a planar curve with a Gaussian kernel directly. In this paper we present a theoretical analysis of DCSS in detecting corners on planar curves. The scale space behavior of isolated single and double corner models is investigated and a number of model properties are specified which enable us to transform a DCSS image into a tree organization and, so that corners can be detected in a multiscale sense. To overcome the sensitivity of DCSS to noise, a hybrid strategy to apply CSS and DCSS is suggested.

Local feature extraction and matching partial objects

A primary shortcoming of existing techniques for hree-dimensional (3D) model matching is the reliance on global information of the model’s structure. Models are matched in their entirety, depending on overall topology and geometry information. A currently open challenge is how to perform partial matching. Partial matching is important for finding similarities across part models with different global shape properties and for the segmentation and matching of data acquired from 3D scanners. This paper presents a Scale–Space feature extraction technique based on recursive decomposition of polyhedral surfaces into surface patches. The experimental results presented in this paper suggest that this technique can potentially be used to perform matching based on local model structure. In our previous work, Scale–Space decomposition has been used successfully to extract features from mechanical artifacts. Scale–Space techniques can be parameterized to generate decompositions that correspond to manufacturing, assembly or surface features relevant to mechanical design. One application of these technique is to support matching and content-based retrieval of solid models. This paper shows how a Scale–Space technique can extract features that are invariant with respect to the global structure of the model as well as small perturbations that 3D laser scanning process introduce. In order to accomplish this, we introduce a new distance function defined on triangles instead of points. We believe this technique offers a new way to control the feature decomposition process, which results in the extraction of features that are more meaningful from an engineering viewpoint. The new technique is computationally practical for use in indexing large models. Examples are provided that demonstrate effective feature extraction on 3D laser scanned models. In addition, a simple sub-graph isomorphism algorithm was used to show that the feature adjacency graphs, obtained through feature extraction, are meaningful descriptors of 3D CAD objects. All of the data used in the experiments for this work is freely available at: http://www.designrepository.org/datasets/.

Automatic fitting of digitised contours at multiple scales through the curvature scale space technique

The curvature scale space (CSS) technique has been used in conjunction with Hermite curves for automatic fitting of digitised contours at multiple scales. CSS is a powerful contour shape descriptor which has been selected for MPEG-7 standardisation. Hermite curves were used since each Hermite curve is defined by two endpoints and the tangent vectors at those points. No points external to the input contour are required for Hermite curves. Hermite endpoints are defined as consecutive curvature zero-crossing points extracted at multiple scales using the CSS method. Hermite tangent vectors can also be determined using the CSS technique. Approximation error and compression ratio are computed at each scale. The graph of compression ratio as a function of approximation error is smoothed to remove noise. The bending point of that function is defined as the largest maximum of its second derivative. This point can be considered as the boundary between the mostly vertical and the mostly horizontal segments of the graph. It can be used for automatic selection of an optimal scale. Finally, the original contour reconstruction technique has been extended to improve the quality of fit. This has been achieved by adjusting the lengths of tangent vectors for each spline segment independently.

A visual display device for significant features in complicated signals

For many applications the significant features found in a data set depend on the level of resolution for which the data are considered. An excellent example of this is in climatology where the features found on scales of tens and hundreds of years, respectively, may be very different. A natural way to study such data sets is through the scale-space approach. In this paper a new scale-space method, which finds significant features in signals, is proposed. The new method, posterior smoothing, is formulated in a Bayesian framework and utilizes sampling from the posterior density. We compare the new methodology to a successful, existing scale-space technique entitled SiZer (Significant Zero crossings of derivatives). For smooth signals SiZer and the new method have similar performance. In signals containing complicated structures, posterior smoothing is preferable. This is demonstrated by applying the methods to simulated and real data sets. In particular, we show that posterior smoothing has better performance in applications taken from climatology, medical imaging, and fish industry.

Silhouette-based occluded object recognition through curvature scale space

A complete and practical system for occluded object recognition has been developed which is very robust with respect to noise and local deformations of shape (due to weak perspective distortion, segmentation errors and non-rigid material) as well as scale, position and orientation changes of the objects. The system has been tested on a wide variety of free-form 3D objects. An industrial application is envisaged where a fixed camera and a light-box are utilized to obtain images. Within the constraints of the system, every rigid 3D object can be modeled by a limited number of classes of 2D contours corresponding to the object's resting positions on the light-box. The contours in each class are related to each other by a 2D similarity transformation. The Curvature Scale Space technique [26, 28] is then used to obtain a novel multi-scale segmentation of the image and the model contours. Object indexing [16, 32, 36] is used to narrow down the search space. An efficient local matching algorithm is utilized to select the best matching models.