Automatic blood vessel extraction from 3D medical images is crucial for
vascular disease diagnoses. Existing methods based on convolutional neural
networks (CNNs) may suffer from discontinuities of extracted vessels when
segmenting such thin tubular structures from 3D images. We argue that
preserving the continuity of extracted vessels requires to take into account
the global geometry. However, 3D convolutions are computationally inefficient,
which prohibits the 3D CNNs from sufficiently large receptive fields to capture
the global cues in the entire image. In this work, we propose a hybrid
representation learning approach to address this challenge. The main idea is to
use CNNs to learn local appearances of vessels in image crops while using
another point-cloud network to learn the global geometry of vessels in the
entire image. In inference, the proposed approach extracts local segments of
vessels using CNNs, classifies each segment based on global geometry using the
point-cloud network, and finally connects all the segments that belong to the
same vessel using the shortest-path algorithm. This combination results in an
efficient, fully-automatic and template-free approach to centerline extraction
from 3D images. We validate the proposed approach on CTA datasets and
demonstrate its superior performance compared to both traditional and CNN-based
baselines.

提出了一种基于深度学习的自动血管提取方法，旨在解决 3D 卷积神经网络在处理 3D 医学图像时 “断排” 问题，该方法采用局部外观的卷积神经网络和全局几何的点云网络相结合，通过最短路径算法将提取的局部部分相连，实现了从 3D 医学图像中高效、自动地提取血管轮廓线的效果。

自动三维血管中心线提取的混合表示学习

Learning Hybrid Representations for Automatic 3D Vessel Centerline  Extraction

We examine the theoretical properties of enforcing priors provided by
generative deep neural networks via empirical risk minimization. In particular
we consider two models, one in which the task is to invert a generative neural
network given access to its last layer and another in which the task is to
invert a generative neural network given only compressive linear observations
of its last layer. We establish that in both cases, in suitable regimes of
network layer sizes and a randomness assumption on the network weights, that
the non-convex objective function given by empirical risk minimization does not
have any spurious stationary points. That is, we establish that with high
probability, at any point away from small neighborhoods around two scalar
multiples of the desired solution, there is a descent direction. Hence, there
are no local minima, saddle points, or other stationary points outside these
neighborhoods. These results constitute the first theoretical guarantees which
establish the favorable global geometry of these non-convex optimization
problems, and they bridge the gap between the empirical success of enforcing
deep generative priors and a rigorous understanding of non-linear inverse
problems.

本文探讨了通过经验风险最小化强制使用生成深度神经网络提供的先验的理论属性，特别是两个模型：一个是在仅访问其最后一层的情况下反演生成神经网络的任务，另一个是在仅对其最后一层进行信息压缩的情况下反演生成神经网络的任务。我们建立了在网络层大小和网络权重的随机性假设的适当区域内，在两种情况下，经验风险最小化所给出的非凸目标函数没有任何虚假稳定点的结论。这些结果是这些非凸优化问题最优全局几何的第一批理论保证，它们弥合了加强深度生成先验的经验成功和对非线性反演问题的严格理解之间的差距。

通过经验风险实施深度生成先验的全球保证

Global Guarantees for Enforcing Deep Generative Priors by Empirical Risk

This paper considers the minimization of a general objective function $f(X)$
over the set of rectangular $n\times m$ matrices that have rank at most $r$. To
reduce the computational burden, we factorize the variable $X$ into a product
of two smaller matrices and optimize over these two matrices instead of $X$.
Despite the resulting nonconvexity, recent studies in matrix completion and
sensing have shown that the factored problem has no spurious local minima and
obeys the so-called strict saddle property (the function has a directional
negative curvature at all critical points but local minima). We analyze the
global geometry for a general and yet well-conditioned objective function
$f(X)$ whose restricted strong convexity and restricted strong smoothness
constants are comparable. In particular, we show that the reformulated
objective function has no spurious local minima and obeys the strict saddle
property. These geometric properties imply that a number of iterative
optimization algorithms (such as gradient descent) can provably solve the
factored problem with global convergence.

本文研究将矩阵分解后进行优化以减少计算量，并分析了具有全局收敛特性的目标函数