Curve Descriptor Research Articles

3D Reconstruction with Coronary Artery Based on Curve Descriptor and Projection Geometry-Constrained Vasculature Matching

This paper presents a novel method based on a curve descriptor and projection geometry constrained for vessel matching. First, an LM (Leveberg–Marquardt) algorithm is proposed to optimize the matrix of geometric transformation. Combining with parameter adjusting and the trust region method, the error between 3D reconstructed vessel projection and the actual vessel can be minimized. Then, CBOCD (curvature and brightness order curve descriptor) is proposed to indicate the degree of the self-occlusion of blood vessels during angiography. Next, the error matrix constructed from the error of epipolar matching is used in point pairs matching of the vascular through dynamic programming. Finally, the recorded radius of vessels helps to construct ellipse cross-sections and samples on it to get a point set around the centerline and the point set is converted to mesh for reconstructing the surface of vessels. The validity and applicability of the proposed methods have been verified through experiments that result in the significant improvement of 3D reconstruction accuracy in terms of average back-projection errors. Simultaneously, due to precise point-pair matching, the smoothness of the reconstructed 3D coronary artery is guaranteed.

Accurate Matching Algorithm of Small Celestial Body Surface Texture Curve

Irregular curves are often used as navigation landmark in the landing of celestial probes. Accurate matching of curves is an important premise for visual navigation. For the problem that curve descriptor matching algorithm are difficult to accurately match and curvature matching algorithm can only handle a pair of curves, an accurate curve matching algorithm combining curve descriptor and curvature is proposed. The curves are extracted by Edge Drawing algorithm first; then the descriptors for curves and supporting regions are built, and the rough matching is completed based on Nearest Neighbor Distance Ratio. After, the unsigned curvature integral is calculated and the curvature is sampled at equal integration intervals. The accurate curve matching is realized based on Normalized Cross Correlation. The experimental results demonstrate that, the algorithm can achieve more than 84% accurate matching rate under scale, rotation and illumination transformations.

Visual navigation algorithm for asteroid lander based on irregular curve matching

<p indent="0mm">In order to solve the visual navigation problem of the landing process of the small celestial body lander, this paper proposes an algorithm to estimate the position and attitude of the lander by using point-tangent line on the irregular curve. First, the irregular curve matching in the landing image is completed by constructing the irregular curve descriptor. Second, the constraint relationship between the position attitude and the point-tangent is established. Then, the curve parameterization method is used to solve the higher order equations, and the constraint conditions are used to obtain the unique solution of position attitude parameters and the least squares solution of multiple matching curves. Finally, the influence of noise intensity and the number of matching curves on the navigation accuracy is verified by simulation, and the feasibility of the algorithm is proved.

Feature matching based on curve descriptor and local D-Nets for fish-eye images.

Most feature-matching algorithms based on perspective images, such as scale-invariant feature transform (SIFT), speeded up robust features, or DAISY, construct their feature descriptors from the neighborhood information of feature points. Large nonlinear distortion results in different amounts of neighborhood information at different feature points within the fish-eye images, especially for the case when a feature pixel is at the central region and the corresponding feature pixel is at the periphery. In contrast, descriptor-Nets (D-Nets) is a feature-matching algorithm based on global information. It is more robust, but it is time-consuming. In this paper, we employ the SIFT detector to extract feature pixels, and then we propose a novel feature-matching strategy based on the D-Nets algorithm. We modify the linear descriptors in the traditional D-Nets algorithm and propose a curve descriptor based on the hemispheric model of a fish-eye image. In the traditional D-Nets algorithm, each feature point is described by all other pixels of the entire image, and complicated calculations cause slow matching speed. To solve this problem, we convert the traditional global D-Nets into a novel local D-Nets. In the experiment, we obtain image pairs from real scenery using the binocular fish-eye camera platform. Experimental results show that the proposed local D-Nets method can achieve more than 3 times the initial matching pixels, and the percentage of bad matching is reduced by 40% compared with the best performing method among the comparison methods. In addition, the matching pixel pairs obtained by the proposed method are evenly distributed, either in the center region with small distortion or in the peripheral region with large distortion. Meanwhile, the local D-Nets algorithm is 16 times less than that of the global D-Nets algorithm.

D-MSCD: Mean-Standard Deviation Curve Descriptor Based on Deep Learning

Curve feature description is an important issue in the field of image matching. In the past years, this problem has been studied mainly based on handcrafted methods. To conquer the disadvantages of low discrimination and weak robustness of curve feature description under complex conditions, a Mean-Standard Deviation Curve Descriptor based on Deep learning (D-MSCD) is proposed in this paper. Firstly, a large-scale curve feature dataset with 210,000 labeled curve image patches is constructed for training and testing. After longitudinally compressing the support areas of the curve in each image into the support areas of points, the mean and standard deviation image patches of each curve are obtained, then the curve image patch is uniquely represented. Secondly, a modified L2-Net(DSM) which is a network architecture with dilated convolution is constructed to improve the performance of curve descriptors, and the experimental results on the Brown dataset show the mean FPR95 value is reduced by 17.48%. Finally, the modified L2-Net(DSM) is trained on the large-scale curve feature dataset and the model of D-MSCD is obtained, it achieves the best matching performance in every image change, and the average matching performance on the Oxford dataset is improved by 13.09%. Experimental results demonstrate the proposed D-MSCD has better effectiveness than the traditional handcrafted curve descriptors.

3D human motion analysis framework for shape similarity and retrieval

3D shape similarity from video is a challenging problem lying at the heart of many primary research areas in computer graphics and computer vision applications. In this paper, we address within a new framework the problem of 3D shape representation and shape similarity in human video sequences. Our shape representation is formulated using extremal human curve (EHC) descriptor extracted from the body surface. It allows taking benefits from Riemannian geometry in the open curve shape space and therefore computing statistics on it. It also allows subject pose comparison regardless of geometrical transformations and elastic surface change. Shape similarity is performed by an efficient method which takes advantage of a compact EHC representation in open curve shape space and an elastic distance measure. Thanks to these main assets, several important exploitations of the human action analysis are performed: shape similarity computation, video sequence comparison, video segmentation, video clustering, summarization and motion retrieval.Experiments on both synthetic and real 3D human video sequences show that our approach provides an accurate static and temporal shape similarity for pose retrieval in video, compared with the state-of-the-art approaches. Moreover, local 3D video retrieval is performed using motion segmentation and dynamic time warping (DTW) algorithm in the feature vector space. The obtained results are promising and show the potential of this approach.

Change in Classification Grade by the SRS-Schwab Adult Spinal Deformity Classification Predicts Impact on Health-Related Quality of Life Measures

Multicenter, prospective, consecutive series. To evaluate responsiveness of the Scoliosis Research Society (SRS)-Schwab adult spinal deformity (ASD) classification to changes in health-related quality of life (HRQOL) after treatment for ASD. Ideally, a classification system should describe and be responsive to changes in a disease state. We hypothesized that the SRS-Schwab classification is responsive to changes in HRQOL measures after treatment for ASD. A multicenter, prospective, consecutive series from the International Spine Study Group. ASD, age more than 18, operative or nonoperative treatment, baseline and 1-year radiographs, and HRQOL measures (Oswestry Disability Index [ODI], SRS-22, Short Form [SF]-36). The SRS-Schwab classification includes a curve descriptor and 3 sagittal spinopelvic modifiers (sagittal vertical axis [SVA], pelvic tilt, pelvic incidence/lumbar lordosis [PI-LL] mismatch). Changes in modifiers at 1 year were assessed for impact on HRQOL from pretreatment values based on minimal clinically important differences. Three hundred forty-one patients met criteria (mean age = 54; 85% females; 177 operative and 164 nonoperative). Change in pelvic tilt modifier at 1-year follow-up was associated with changes in ODI and SRS-22 (total and appearance scores) (P ≤ 0.034). Change in SVA modifier at 1 year was associated with changes in ODI, SF-36 physical component score, and SRS-22 (total, activity, and appearance scores) (P ≤ 0.037). Change in PI-LL modifier at 1 year was associated with changes in SF-36 physical component score and SRS-22 (total, activity, and appearance scores) (P ≤ 0.03). Patients with improvement of pelvic tilt, SVA, or PI-LL modifiers were significantly more likely to achieve minimal clinically important difference for ODI, SF-36 physical component score (SVA and PI-LL only), SRS activity, and SRS pain (PI-LL only). The SRS-Schwab classification provides a validated system to evaluate ASD, and the classification components correlate with HRQOL measures. This study demonstrates that the classification modifiers are responsive to changes in disease state and reflect significant changes in patient-reported outcomes. 3.

Novel affine‐invariant curve descriptor for curve matching and occluded object recognition

The authors present a new approach for affine distorted planar curve matching and exploit it for occluded object recognition. There are two main contributions in the study: First, a novel affine‐invariant curve descriptor (AICD) based on a new‐defined affine‐invariant signature and its unsigned sum is proposed to represent the local shape of a curve with high distinctiveness. Second, a part‐to‐part curve matching algorithm is developed by combining AICD with a curve segmentation strategy based on inflexion points, which can be applied to object recognition under affine distortions and partial occlusions. Experimental results demonstrate that the proposed method exhibits effectiveness in occluded object recognition better than the state‐of‐the‐art partial curve matching methods.

Local uniqueness of the circular integral invariant

This article is concerned with the representation of curves by means of integral invariants. In contrast to the classical differential invariants they have the advantage of being less sensitive with respect to noise. The integral invariant most common in use is the circular integral invariant. A major drawback of this curve descriptor, however, is the absence of any uniqueness result for this representation. This article serves as a contribution towards closing this gap by showing that the circular integral invariant is injective in a neighbourhood of the circle. In addition, we provide a stability estimate valid on this neighbourhood. The proof is an application of Riesz--Schauder theory and the implicit function theorem in a Banach space setting.

An extension of the h index that covers the tail and the top of the citation curve and allows ranking researchers with similar h

Citation curves for researchers with the same h index can vary greatly in the heaviness of their top (excess citations to core papers) or the heaviness of their tail (citations to non-core papers), revealing quantitative differences across researchers. Also, promotion to the next higher h depends only on citations received by a small subset of papers, so that researchers with a given h may have citation curves whose top and tail reveal a weaker impact than that of researchers with a lower h. To overcome these problems, we propose a two-sided h index, an extension that computes additional h indices progressively up the top and out the tail of the citation curve. This extension represents a citation curve descriptor one of whose elements is the scalar h. The advantages of the two-sided h index are illustrated through analysis of citation curves for 88 researchers with h indices ranging from 8 to 20. Several schemes are also discussed that use the two-sided h index to define criteria for ranking researchers within and across scalar h indices, according to whether the top of the citation curve, its tail, or both are deemed relevant under the circumstances in which research accomplishments are assessed.

MSLD: A robust descriptor for line matching

Line matching plays an important role in many applications, such as image registration, 3D reconstruction, object recognition and video understanding. However, compared with other features (such as point, region matching), it has made little progress in recent years. In this paper, we investigate the problem of matching line segments automatically only from their neighborhood appearance, without resorting to any other constraints or priori knowledge. A novel line descriptor called mean–standard deviation line descriptor (MSLD) descriptor is proposed for this purpose, which is constructed by the following three steps: (1) For each pixel on the line segment, its pixel support region (PSR) is defined and then the PSR is divided into non-overlapped sub-regions. (2) Line gradient description matrix (GDM) is formed by characterizing each sub-region into a vector. (3) MSLD is built by computing the mean and standard deviation of GDM column vectors. Extensive experiments on real images show that MSLD descriptor is highly distinctive for line matching under rotation, illumination change, image blur, viewpoint change, noise, JPEG compression and partial occlusion. In addition, the concept of MSLD descriptor can also be extended to creating curve descriptor (mean–standard deviation curve descriptor, MSCD), and promising MSCD-based results for both curve and region matching are also demonstrated in this work.

Study of compression efficiency for three-dimensional discrete curves

A study of compression efficiency of 3-D chain codes to represent discrete curves is described. The 3-D Freeman chain code and the five orthogonal change chain directions (5OT) chain code are compared. The 3-D Freeman chain code consists of 26 directions, in 3-D Euclidean space, with no invariance under rotation. The 5OT chain elements represent the orthogonal direction changes of the contiguous straight-line segments of the discrete curve. This chain code only considers relative direction changes, which allows us to have a curve descriptor invariant under rotation, and mirroring curves may be obtained with ease. In the 2-D domain, Freeman chain codes are widely used to represent contour curves. Until now, the authors have had no information of implementing Freeman chain codes to compress 3-D curves. Our contribution is how to implement the Freeeman chain code in 3-D and how to compare it with the recently proposed 5OT code. Finally, to probe our results, we apply the proposed method to three different cases: arbitrary curves, cube-filling Hilbert curves, and lattice knots.

A measure of shape dissimilarity for 3D curves

We present a quantitative approach to the measurement of shape dissimilarity between two 3D (three-dimensional) curves. Any 3D continuous curve can be digitalized and represented as a 3D discrete curve. Thus, a 3D discrete curve is composed of constant orthogonal straightline segments. In order to represent 3D discrete curves, we use the orthogonal direction change chain code. The chain elements represent the orthogonal direction changes of the contiguous straight-line segments of the discrete curve. This chain code only considers relative direction changes, which allows us to have a curve descriptor invariant under translation and rotation. Also, this curve descriptor may be starting point normalized and mirroring curves may be obtained with ease. Thus, using the above-mentioned chain code it is possible to have a unique 3D-curve descriptor. To find out how close in shape two 3D curves are, a measure of shapeof-curve dissimilarity between them is introduced; analogous curves will have a low measure of shape dissimilarity, while different curves will have a high measure of shape dissimilarity. When this measure of shape dissimilarity is normalized, its values vary continuously from 0 to 1. If 1 Author to whom correspondence should be addressed

3D-curve representation by means of a binary chain code

A binary chain code for representing 3D curves is presented. 3D curves are digitalizedand represented as 3D discrete curves. 3D discrete curves are composed of constant straight-line segments using only orthogonal directions. The proposed binary notation is based on the orthogonal direction change chain code. Thus, using the proposed binary chain code it is possible to represent any 3D curve by only two states (“0” and “1”). The proposed binary chain code produces a curve descriptor which is invariant under translation, rotation and may be starting point normalized. Also, we define the complementary chain of a 3D curve which produces the mirror image of the curve.

A formal language approach for a 3D curve representation

A formal language approach for representing three-dimensional (3D) curves is presented. Based on the chain code for representing 3D curves defined in [1], we propose an approach for mapping 3D curves into strings. This mapping allows us to have a unique curve descriptor, which is invariant under translation and rotation. Also, it is possible to use inverse and mirroring operators and the use of formal language techniques for 3D curve generation and analysis. Finally, we present a result of this approach to represent and to generate polygonal sequences convergent to cube-filling Hilbert curves.

RECOGNITION OF 2D STANDALONE AND OCCLUDED OBJECTS USING WAVELET TRANSFORM

A planar curve descriptor which is invariant to translation, size, rotation and starting point in tracing the boundary is developed based on the periodized wavelet transform. Coefficients obtained from the transform are divided into different bands, and feature vectors are extracted for the recognition of two-dimensional closed boundary curves. The weight vectors which include the width of different bands are also derived to differentiate spurious results arising from noisy samples. The technique is further extended for the recognition of occluded objects by incorporating local features into the features vector to form a feature map. Matching the likeliness of a part of the feature map with that of the reference feature maps indicates which class the occluded object belongs to. Experimental results were obtained to show the effectiveness of the proposed technique.

A chain code for representing 3D curves

A chain code for representing three-dimensional (3D) curves is defined. Any 3D continuous curve can be digitalized and represented as a 3D discrete curve. This 3D discrete curve is composed of constant straight-line segments. Thus, the chain elements represent the orthogonal direction changes of the constant straight-line segments of the discrete curve. The proposed chain code only considers relative direction changes, which allows us to have a curve descriptor invariant under translation and rotation. Also, this curve descriptor may be starting point normalized for open and closed curves and invariant under mirroring transformation. In the content of this work the main characteristics of this chain code are presented. This chain code is inspired by the work of Guzmán (MCC Technical Report Number: ACA-254-87, July 13, 1987) for representing 3D Stick Bodies. Finally, we present some results of this chain code to represent and process 3D discrete curves as linear features over the terrain by means of digital elevation model (DEM) data. Also, we use this chain code for representing solids composed of voxels. Thus, each solid represents a DEM which is described by only one chain.

Cartoon Animation and Morphing with Wavelet Curve Descriptor

A new framework for cartoon animation is proposed in this work. By using the wavelet coefficients as the control points, one can manipulate curves so that shape metamorphosis occurs along resolutions as well as spatial locations. We model the motion of a cartoon character with the Lagrangian dynamic equation where the multiscale curve is driven by relevant forces. The spatial and frequency localization property of the multiscale curve model results in a sparse and diagonally dominant representation of the mass and stiffness matrices of the Lagrangian equation and hence the computation can be greatly simplified. To further simplify this model, we consider a model which consists of a decoupled system of ODEs. We then perform an experiment by capturing an image sequence with the locomotion of a walking dog, selecting some key frames, and tracing the positions of limbs between these key frames. The best motion parameters are determined by using the least squares approximation. These extracted parameters are then be used to animate cartoon characters of a similar type of motion. The result shows the proposed curve descriptor with multiscale structure and local control property is promising in cartoon animation applications.

Wavelet descriptor of planar curves: theory and applications

By using the wavelet transform, the authors develop a hierarchical planar curve descriptor that decomposes a curve into components of different scales so that the coarsest scale components carry the global approximation information while the finer scale components contain the local detailed information. They show that the wavelet descriptor has many desirable properties such as multiresolution representation, invariance, uniqueness, stability, and spatial localization. A deformable wavelet descriptor is also proposed by interpreting the wavelet coefficients as random variables. The applications of the wavelet descriptor to character recognition and model-based contour extraction from low SNR images are examined. Numerical experiments are performed to illustrate the performance of the wavelet descriptor.