Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA level set representation method for N-dimensional convex shape and applications
82
0
0.0
(
0
)
Added by
Lingfeng Li
Publication date
2020
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
In this work, we present a new efficient method for convex shape representation, which is regardless of the dimension of the concerned objects, using level-set approaches. Convexity prior is very useful for object completion in computer vision. It is a very challenging task to design an efficient method for high dimensional convex objects representation. In this paper, we prove that the convexity of the considered object is equivalent to the convexity of the associated signed distance function. Then, the second order condition of convex functions is used to characterize the shape convexity equivalently. We apply this new method to two applications: object segmentation with convexity prior and convex hull problem (especially with outliers). For both applications, the involved problems can be written as a general optimization problem with three constraints. Efficient algorithm based on alternating direction method of multipliers is presented for the optimization problem. Numerical experiments are conducted to verify the effectiveness and efficiency of the proposed representation method and algorithm.
rate research
Read More
Stochastic convex optimization problems with expectation constraints (SOECs) are encountered in statistics and machine learning, business, and engineering. In data-rich environments, the SOEC objective and constraints contain expectations defined with respect to large datasets. Therefore, efficient algorithms for solving such SOECs need to limit the fraction of data points that they use, which we refer to as algorithmic data complexity. Recent stochastic first order methods exhibit low data complexity when handling SOECs but guarantee near-feasibility and near-optimality only at convergence. These methods may thus return highly infeasible solutions when heuristically terminated, as is often the case, due to theoretical convergence criteria being highly conservative. This issue limits the use of first order methods in several applications where the SOEC constraints encode implementation requirements. We design a stochastic feasible level set method (SFLS) for SOECs that has low data complexity and emphasizes feasibility before convergence. Specifically, our level-set method solves a root-finding problem by calling a novel first order oracle that computes a stochastic upper bound on the level-set function by extending mirror descent and online validation techniques. We establish that SFLS maintains a high-probability feasible solution at each root-finding iteration and exhibits favorable iteration complexity compared to state-of-the-art deterministic feasible level set and stochastic subgradient methods. Numerical experiments on three diverse applications validate the low data complexity of SFLS relative to the former approach and highlight how SFLS finds feasible solutions with small optimality gaps significantly faster than the latter method.
We analyze the set ${cal A}_N^Q$ of mixed unitary channels represented in the Weyl basis and accessible by a Lindblad semigroup acting on an $N$-level quantum system. General necessary and sufficient conditions for a mixed Weyl quantum channel of an arbitrary dimension to be accessible by a semigroup are established. The set ${cal A}_N^Q$ is shown to be log--convex and star-shaped with respect to the completely depolarizing channel. A decoherence supermap acting in the space of Lindblad operators transforms them into the space of Kolmogorov generators of classical semigroups. We show that for mixed Weyl channels the hyper-decoherence commutes with the dynamics, so that decohering a quantum accessible channel we obtain a bistochastic matrix form the set ${cal A}_N^C$ of classical maps accessible by a semigroup. Focusing on $3$-level systems we investigate the geometry of the sets of quantum accessible maps, its classical counterpart and the support of their spectra. We demonstrate that the set ${cal A}_3^Q$ is not included in the set ${cal U}^Q_3$ of quantum unistochastic channels, although an analogous relation holds for $N=2$. The set of transition matrices obtained by hyper-decoherence of unistochastic channels of order $Nge 3$ is shown to be larger than the set of unistochastic matrices of this order, and yields a motivation to introduce the larger sets of $k$-unistochastic matrices.
We aim to detect pancreatic ductal adenocarcinoma (PDAC) in abdominal CT scans, which sheds light on early diagnosis of pancreatic cancer. This is a 3D volume classification task with little training data. We propose a two-stage framework, which first segments the pancreas into a binary mask, then compresses the mask into a shape vector and performs abnormality classification. Shape representation and classification are performed in a joint manner, both to exploit the knowledge that PDAC often changes the shape of the pancreas and to prevent over-fitting. Experiments are performed on 300 normal scans and 136 PDAC cases. We achieve a specificity of 90.2% (false alarm occurs on less than 1/10 normal cases) at a sensitivity of 80.2% (less than 1/5 PDAC cases are not detected), which show promise for clinical applications.
We present a novel compact point cloud representation that is inherently invariant to scale, coordinate change and point permutation. The key idea is to parametrize a distance field around an individual shape into a unique, canonical, and compact vector in an unsupervised manner. We firstly project a distance field to a $4$D canonical space using singular value decomposition. We then train a neural network for each instance to non-linearly embed its distance field into network parameters. We employ a bias-free Extreme Learning Machine (ELM) with ReLU activation units, which has scale-factor commutative property between layers. We demonstrate the descriptiveness of the instance-wise, shape-embedded network parameters by using them to classify shapes in $3$D datasets. Our learning-based representation requires minimal augmentation and simple neural networks, where previous approaches demand numerous representations to handle coordinate change and point permutation.
Garment representation, animation and editing is a challenging topic in the area of computer vision and graphics. Existing methods cannot perform smooth and reasonable garment transition under different shape styles and topologies. In this work, we introduce a novel method, termed as DeepCloth, to establish a unified garment representation framework enabling free and smooth garment style transition. Our key idea is to represent garment geometry by a UV-position map with mask, which potentially allows the description of various garments with different shapes and topologies. Furthermore, we learn a continuous feature space mapped from the above UV space, enabling garment shape editing and transition by controlling the garment features. Finally, we demonstrate applications of garment animation, reconstruction and editing based on our neural garment representation and encoding method. To conclude, with the proposed DeepCloth, we move a step forward on establishing a more flexible and general 3D garment digitization framework. Experiments demonstrate that our method can achieve the state-of-the-art garment modeling results compared with the previous methods.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
