Exploiting color for graph-based 3D point cloud denoising

A point cloud is a representation of a 3D scene as a discrete collection of geometry plus other attributes such as color, normal, transparency associated with each point. The traditional acquisition process of a 3D point cloud, e.g. using depth information acquired directly by active sensors or indirectly from multi-viewpoint images, suffers from a significant amount of noise. Hence, the problem of point cloud denoising has recently received a lot of attention. However, most existing techniques attempt to denoise only the geometry of each point, based on the geometry information of the neighboring points; there are very few works at all considering the problem of denoising the color attributes of a point cloud. In this paper, we move beyond the state of the art and we propose a novel technique employing graph-based optimization, taking advantage of the correlation between geometry and color, and using it as a powerful tool for several different tasks, i.e. color denoising, geometry denoising, and combined geometry and color denoising. The proposed method is based on the notion that the correct location of a point also depends on the color attribute and not only the geometry of the neighboring points, and the correct color also depends on the geometry of the neighbors. The proposed method constructs a suitable k-NN graph from geometry and color and applies graph-based convex optimization to obtain the denoised point cloud. Extensive simulation results on both real-world and synthetic point clouds show that the proposed denoising technique outperforms state-of-the-art methods using both subjective and objective quality metrics.     

Adaptive surface extraction from anisotropic volumetric data: contouring on generalized octrees

In this article, we present an algorithm to extract adaptive surfaces from anisotropic volumetric data. For example, this kind of data can be obtained from a set of segmented images from the sampling of an implicit function, or it can be built by using depth images produced by time-of-flight cameras. However, for many applications as geometry modeling, rendering, or finite elements, it is better to use an explicit surface representation. This surface must fit to the geometrical and topological features of the object in order to obtain a good approximation and to avoid topological artifacts. Our algorithm is able to extract adaptive surfaces that accurately approximate the geometry of the original object while minimizing aliasing effects. In addition, our solution is suitable to handle the anisotropy of volumetric representations. In comparison with relevant methods in the state of the art, ours offers a good compromise between mesh quality and precision in the geometrical approximation.     

Region tracking on level-sets methods

Since the work by Osher and Sethian on level-sets algorithms for numerical shape evolutions, this technique has been used for a large number of applications in numerous fields. In medical imaging, this numerical technique has been successfully used, for example, in segmentation and cortex unfolding algorithms. The migration from a Lagrangian implementation to a Eulerian one via implicit representations or level-sets brought some of the main advantages of the technique, i.e., topology independence and stability. This migration means also that the evolution is parametrization free. Therefore, we do not know exactly how each part of the shape is deforming and the point-wise correspondence is lost. In this note we present a technique to numerically track regions on surfaces that are being deformed using the level-sets method. The basic idea is to represent the region of interest as the intersection of two implicit surfaces and then track its deformation from the deformation of these surfaces. This technique then solves one of the main shortcomings of the very useful level-sets approach. Applications include lesion localization in medical images, region tracking in functional MRI (fMRI) visualization, and geometric surface mapping.     

Reconciling Distance Functions and Level Sets

This paper is concerned with the simulation of the partial differential equation driven evolution of a closed surface by means of an implicit representation. In most applications, the natural choice for the implicit representation is the signed distance function to the closed surface. Osher and Sethian have proposed to evolve the distance function with a Hamilton–Jacobi equation. Unfortunately the solution to this equation is not a distance function. As a consequence, the practical application of the level set method is plagued with such questions as When do we have to reinitialize the distance function? How do we reinitialize the distance function?, which reveal a disagreement between the theory and its implementation. This paper proposes an alternative to the use of Hamilton–Jacobi equations which eliminates this contradiction: in our method the implicit representation always remains a distance function by construction, and the implementation does not differ from the theory anymore. This is achieved through the introduction of a new equation. Besides its theoretical advantages, the proposed method also has several practical advantages which we demonstrate in three applications: (i) the segmentation of the human cortex surfaces from MRI images using two coupled surfaces (X. Zeng, et al., in Proceedings of the International Conference on Computer Vision and Pattern Recognition, June 1998), (ii) the construction of a hierarchy of Euclidean skeletons of a 3D surface, (iii) the reconstruction of the surface of 3D objects through stereo (O. Faugeras and R. Keriven, Lecture Notes in Computer Science, Vol. 1252, pp. 272–283).     

Optimal shape design of microwave device using FDTD and designsensitivity analysis

In this paper, a novel optimal shape design method is proposed using the finite-difference time-domain (FDTD) method and the design sensitivity analysis to obtain broad-band characteristics of microwave devices. In shape design problem, the nodes that describe the shape of geometry to be optimized are taken as design variables. The design sensitivity is evaluated using the adjoint variable equation that is obtained from a terminal-value problem. The adjoint equation can be solved by the FDTD technique with the backward time scheme. With this method, a Ka-band unilateral fin line is tested to show validity     

同伦方法在图像稀疏去噪中的应用

本文在深入研究稀疏表示和字典学习理论的基础上,建立了图像去噪模型并提出一种新的图像去噪算法。该算法采用同伦方法学习字典,充分利用了同伦方法收敛速度快以及对信号的恢复准确度高的特点。之后利用 OMP 算法求出带噪图像在该字典下的稀疏表示系数,并结合稀疏去噪模型实现对图像的去噪。实验结果显示本文算法在不同的噪声环境下具有较好的去噪效果,同时在与 K-SVD 算法关于收敛速度比较的实验中,实验结果充分显示了使用同伦算法学习字典在收敛速度上的优势。      

Boundary detection in medical images using edge following algorithm based on intensity gradient and texture gradient features

Finding the correct boundary in noisy images is still a difficult task. This paper introduces a new edge following technique for boundary detection in noisy images. Utilization of the proposed technique is exhibited via its application to various types of medical images. Our proposed technique can detect the boundaries of objects in noisy images using the information from the intensity gradient via the vector image model and the texture gradient via the edge map. The performance and robustness of the technique have been tested to segment objects in synthetic noisy images and medical images including prostates in ultrasound images, left ventricles in cardiac magnetic resonance (MR) images, aortas in cardiovascular MR images, and knee joints in computerized tomography images. We compare the proposed segmentation technique with the active contour models (ACM), geodesic active contour models, active contours without edges, gradient vector flow snake models, and ACMs based on vector field convolution, by using the skilled doctors' opinions as the ground truths. The results show that our technique performs very well and yields better performance than the classical contour models. The proposed method is robust and applicable on various kinds of noisy images without prior knowledge of noise properties.     

Image Guided Personalization of Reaction-Diffusion Type Tumor Growth Models Using Modified Anisotropic Eikonal Equations

Reaction-diffusion based tumor growth models have been widely used in the literature for modeling the growth of brain gliomas. Lately, recent models have started integrating medical images in their formulation. Including different tissue types, geometry of the brain and the directions of white matter fiber tracts improved the spatial accuracy of reaction-diffusion models. The adaptation of the general model to the specific patient cases on the other hand has not been studied thoroughly yet. In this paper, we address this adaptation. We propose a parameter estimation method for reaction-diffusion tumor growth models using time series of medical images. This method estimates the patient specific parameters of the model using the images of the patient taken at successive time instances. The proposed method formulates the evolution of the tumor delineation visible in the images based on the reaction-diffusion dynamics; therefore, it remains consistent with the information available. We perform thorough analysis of the method using synthetic tumors and show important couplings between parameters of the reaction-diffusion model. We show that several parameters can be uniquely identified in the case of fixing one parameter, namely the proliferation rate of tumor cells. Moreover, regardless of the value the proliferation rate is fixed to, the speed of growth of the tumor can be estimated in terms of the model parameters with accuracy. We also show that using the model-based speed, we can simulate the evolution of the tumor for the specific patient case. Finally, we apply our method to two real cases and show promising preliminary results.      

Direct reconstruction method for wavelet transform extremarepresentation

In contrast to the iterative reconstruction algorithm of projections onto convex sets a noniterative method that completely solves the problem of reconstructing from the wavelet transform extrema representation is presented for the first time. The solution obtained by the proposed method is mathematically consistent and is indistinguishable from the true solution, i.e. both give the same representation. The proposed method consists of first finding a least-squares solution in the space spanned by the wavelet sampling bases. An orthogonal component that is to be added to the least-squares solution to form a consistent solution is then found by solving a set of linear inequalities specified by the a priori information in the representation using the linear programming technique. Numerical results presented show that the reconstructions are of good quality     

Wavelet-based Interpolation Scheme for Resolution Enhancement of Medical Images

A novel interpolation method for resolution enhancement is proposed in this paper. This method estimates wavelet coefficients in the high frequency subbands from a low resolution image using our proposed filters. An inverse wavelet transform is then performed for synthesis of a higher resolution image. Experimental results show that our proposed method outperforms other commonly used schemes objectively and subjectively. In addition, the processing time required in an algorithm-implemented Digital Signal Processor (DSP) is satisfied. By using the DSP hardware platform, off-line interpolation processing becomes easier and more feasible. The interpolated image has merits of high contrast and remarkable sharpness which essentially meet the requirements for interpolation of medical images. Our method can provide better quality of interpolated medical images compared to other methods to assist physicians in making diagnoses.     

Fusing integrated visual vocabularies-based bag of visual words and weighted colour moments on spatial pyramid layout for natural scene image classification

The bag of visual words (BOW) model is an efficient image representation technique for image categorization and annotation tasks. Building good visual vocabularies, from automatically extracted image feature vectors, produces discriminative visual words, which can improve the accuracy of image categorization tasks. Most approaches that use the BOW model in categorizing images ignore useful information that can be obtained from image classes to build visual vocabularies. Moreover, most BOW models use intensity features extracted from local regions and disregard colour information, which is an important characteristic of any natural scene image. In this paper, we show that integrating visual vocabularies generated from each image category improves the BOW image representation and improves accuracy in natural scene image classification. We use a keypoint density-based weighting method to combine the BOW representation with image colour information on a spatial pyramid layout. In addition, we show that visual vocabularies generated from training images of one scene image dataset can plausibly represent another scene image dataset on the same domain. This helps in reducing time and effort needed to build new visual vocabularies. The proposed approach is evaluated over three well-known scene classification datasets with 6, 8 and 15 scene categories, respectively, using 10-fold cross-validation. The experimental results, using support vector machines with histogram intersection kernel, show that the proposed approach outperforms baseline methods such as Gist features, rgbSIFT features and different configurations of the BOW model.     

多形态稀疏性正则化的图像超分辨率算法

 如何设计更加高效并能保持图像几何和纹理结构的多幅图像超分辨模型和算法是目前该领域有待解决的难点问题.针对图像的几何、纹理结构形态,分别建立符合类内强稀疏而类间强不相干的几何结构和纹理分量稀疏表示子成份字典,形成图像的多形态稀疏表示模型,进而提出一种新的基于多形态稀疏性正则化的多帧图像超分辨凸变分模型,模型中的正则项刻画了理想图像在多成份字典下的稀疏性先验约束,保真项度量其在退化模型下与观测信号的一致性,采用交替迭代法对该多变量优化问题进行数值求解,每一子问题采用前向后向的算法分裂法进行快速求解.针对可见光与红外图像序列进行了数值仿真,实验结果验证了本文模型与数值算法的有效性.     

Salient region detection through sparse reconstruction and graph-based ranking

In this paper, we propose a salient region detection algorithm from the point of view of unique and compact representation of individual image. In first step, the original image is segmented into super-pixels. In second step, the sparse representation measure and uniqueness of the features are computed. Then both are ranked on the basis of the background and foreground seeds respectively. Thirdly, a location prior map is used to enhance the foci of attention. We apply the Bayes procedure to integrate computed results to produce smooth and precise saliency map. We compare our proposed algorithm against the state-of-the-art saliency detection methods using four of the largest widely available standard data-bases, experimental results specify that the proposed algorithm outperforms. We also show that how the saliency map of the proposed method is used to discover outline of object, furthermore using this outline our method produce the saliency cut of the desired object.     

Compactly supported radial basis functions based collocation method for level-set evolution in image segmentation.

The partial differential equation driving level-set evolution in segmentation is usually solved using finite differences schemes. In this paper, we propose an alternative scheme based on radial basis functions (RBFs) collocation. This approach provides a continuous representation of both the implicit function and its zero level set. We show that compactly supported RBFs (CSRBFs) are particularly well suited to collocation in the framework of segmentation. In addition, CSRBFs allow us to reduce the computation cost using a kd-tree-based strategy for neighborhood representation. Moreover, we show that the usual reinitialization step of the level set may be avoided by simply constraining the l1-norm of the CSRBF parameters. As a consequence, the final solution is topologically more flexible, and may develop new contours (i.e., new zero-level components), which are difficult to obtain using reinitialization. The behavior of this approach is evaluated from numerical simulations and from medical data of various kinds, such as 3-D CT bone images and echocardiographic ultrasound images.     

A direct measurement technique for small geometry MOS transistor capacitances

Accurate representation of MOS transistor capacitances is important for accurate circuit simulation. Due to the difficulties of direct measurement with meters, MOS intrinsic capacitances have not been studied extensively. Although several "on-chip" methods have been developed, the need for measurement circuits fabricated alongside the devices of interest seems to be impractical for statistical data generation. In addition, the characterization of both current-voltage (I-V) and capacitance-voltage (CV) relationships is not as convenient by using the "on-chip" configurations. Consequently, the direct measurement technique is more desirable than the "on-chip" methods. A direct measurement technique for the intrinsic gate capacitances in a small geometry MOS transistor has been developed and is presented in this letter. By using this method, n-channel transistors withW_{eff}/L_{eff}of, 11/11, 11/2.2, and 11/1.65 µm have been measured. The difference between the long- and short-channel devices can be clearly observed in the measured curves. The results show that the small MOSFET intrinsic capacitances can be accurately determined using off the self meters, and the use of "on-chip" circuitry is unnecessary.     

Single-Pass K-SVD for Efficient Dictionary Learning

Sparse representation has been widely used in machine learning, signal processing and communications. K-SVD, which generalizes k-means clustering, is one of the most famous algorithms for sparse representation and dictionary learning. K-SVD is an iterative method that alternates between encoding the data sparsely by using the current dictionary and updating the dictionary based on the sparsely represented data. In this paper, we introduce a single-pass K-SVD method. In this method, the previous input data are first summarized as a condensed representation of weighted samples. Then, we developed a weighted K-SVD algorithm to learn a dictionary from the union of this representation and the newly input data. Experimental results show that our approach can approximate K-SVD’s performance well by consuming considerably less storage resource.     

An Efficient Numerical Model for Planar Spiral Inductor On-Chip

In this paper, a very useful numerical technique has been developed for analyzing the transient characteristics of a planar-spiral inductor on-chip. A locally conformal technique and an alternating-direction implicit scheme are applied to the finite-difference time-domain method. A formulation for solving three dimensional Maxwell’s equations is proposed. Using the proposed method, various parameters of the planar-spiral inductors have been analyzed and an equivalent circuit, which includes frequency-independent circuit elements, has been introduced. Highly computational efficiency is implemented. Numerical results show excellent agreement with the measured data over a wide frequency range.     

The boundary element method in the forward and inverse problem of electrical impedance tomography

In this paper, a new formulation of the reconstruction problem of electrical impedance tomography (EIT) is proposed. Instead of reconstructing a complete two-dimensional picture, a parameter representation of the gross anatomy is formulated, of which the optimal parameters are determined by minimizing a cost function. The two great advantages of this method are that the number of unknown parameters of the inverse problem is drastically reduced and that quantitative information of interest (e.g., lung volume) is estimated directly from the data, without image segmentation steps. The forward problem of EIT is to compute the potentials at the voltage measuring electrodes, for a given set of current injection electrodes and a given conductivity geometry. In this paper, it is proposed to use an improved boundary element method (BEM) technique to solve the forward problem, in which flat boundary elements are replaced by polygonal ones. From a comparison with the analytical solution of the concentric circle model, it appears that the use of polygonal elements greatly improves the accuracy of the BEM, without increasing the computation time. In this formulation, the inverse problem is a nonlinear parameter estimation problem with a limited number of parameters. Variants of Powell's and the simplex method are used to minimize the cost function. The applicability of this solution of the EIT problem was tested in a series of simulation studies. In these studies, EIT data were simulated using a standard conductor geometry and it was attempted to find back this geometry from random starting values. In the inverse algorithm, different current injection and voltage measurement schemes and different cost functions were compared. In a simulation study, it was demonstrated that a systematic error in the assumed lung conductivity results in a proportional error in the lung cross sectional area. It appears that our parametric formulation of the inverse problem leads to a stable minimization problem, with a high reliability, provided that the signal-to-noise ratio is about ten or higher.     

A variational method for geometric regularization of vascular segmentation in medical images

In this paper, a level-set-based geometric regularization method is proposed which has the ability to estimate the local orientation of the evolving front and utilize it as shape induced information for anisotropic propagation. We show that preserving anisotropic fronts can improve elongations of the extracted structures, while minimizing the risk of leakage. To that end, for an evolving front using its shape-offset level-set representation, a novel energy functional is defined. It is shown that constrained optimization of this functional results in an anisotropic expansion flow which is usefull for vessel segmentation. We have validated our method using synthetic data sets, 2-D retinal angiogram images and magnetic resonance angiography volumetric data sets. A comparison has been made with two state-of-the-art vessel segmentation methods. Quantitative results, as well as qualitative comparisons of segmentations, indicate that our regularization method is a promising tool to improve the efficiency of both techniques.