Convex Shape Representation with Binary Labels for Image Segmentation:
Models and Fast Algorithms
- URL: http://arxiv.org/abs/2002.09600v1
- Date: Sat, 22 Feb 2020 01:55:20 GMT
- Title: Convex Shape Representation with Binary Labels for Image Segmentation:
Models and Fast Algorithms
- Authors: Shousheng Luo and Xue-Cheng Tai and Yang Wang
- Abstract summary: We present a novel and effective binary representation for convex shapes.
We show the equivalence between the shape convexity and some properties of the associated indicator function.
- Score: 7.847719964338735
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We present a novel and effective binary representation for convex shapes. We
show the equivalence between the shape convexity and some properties of the
associated indicator function. The proposed method has two advantages. Firstly,
the representation is based on a simple inequality constraint on the binary
function rather than the definition of convex shapes, which allows us to obtain
efficient algorithms for various applications with convexity prior. Secondly,
this method is independent of the dimension of the concerned shape. In order to
show the effectiveness of the proposed representation approach, we incorporate
it with a probability based model for object segmentation with convexity prior.
Efficient algorithms are given to solve the proposed models using Lagrange
multiplier methods and linear approximations. Various experiments are given to
show the superiority of the proposed methods.
Related papers
- Dual feature-based and example-based explanation methods [2.024925013349319]
A new approach to the local and global explanation is proposed.
It is based on selecting a convex hull constructed for the finite number of points around an explained instance.
The code of proposed algorithms is available.
arXiv Detail & Related papers (2024-01-29T16:53:04Z) - Linearization Algorithms for Fully Composite Optimization [61.20539085730636]
This paper studies first-order algorithms for solving fully composite optimization problems convex compact sets.
We leverage the structure of the objective by handling differentiable and non-differentiable separately, linearizing only the smooth parts.
arXiv Detail & Related papers (2023-02-24T18:41:48Z) - Sharp Analysis of Sketch-and-Project Methods via a Connection to
Randomized Singular Value Decomposition [14.453949553412821]
We develop a theoretical framework for obtaining sharp guarantees on the convergence rate of sketch-and-project methods.
We show that the convergence rate improves at least linearly with the sketch size, and even faster when the data matrix exhibits certain spectral decays.
Our experiments support the theory and demonstrate that even extremely sparse sketches exhibit the convergence properties predicted by our framework.
arXiv Detail & Related papers (2022-08-20T03:11:13Z) - Object Representations as Fixed Points: Training Iterative Refinement
Algorithms with Implicit Differentiation [88.14365009076907]
Iterative refinement is a useful paradigm for representation learning.
We develop an implicit differentiation approach that improves the stability and tractability of training.
arXiv Detail & Related papers (2022-07-02T10:00:35Z) - Multiple Convex Objects Image Segmentation via Proximal Alternating
Direction Method of Multipliers [2.294014185517203]
The convex shape prior turns out to be a simple quadratic inequality constraint on the binary indicator function associated with each object.
An image segmentation model incorporating convex shape prior into a probability-based method is proposed.
Numerical experiments on natural and medical images demonstrate that the proposed method is superior to some existing methods.
arXiv Detail & Related papers (2022-03-22T00:05:19Z) - Direct Estimation of Appearance Models for Segmentation [0.0]
We describe a novel approach for estimating appearance models directly from an image.
Our approach is based on algebraic expressions that relate local image statistics to the appearance models of spatially coherent regions.
We present experimental results that demonstrate the proposed methods work well in practice and lead to effective image segmentation algorithms.
arXiv Detail & Related papers (2021-02-22T15:50:39Z) - Hybrid Trilinear and Bilinear Programming for Aligning Partially
Overlapping Point Sets [85.71360365315128]
In many applications, we need algorithms which can align partially overlapping point sets are invariant to the corresponding corresponding RPM algorithm.
We first show that the objective is a cubic bound function. We then utilize the convex envelopes of trilinear and bilinear monomial transformations to derive its lower bound.
We next develop a branch-and-bound (BnB) algorithm which only branches over the transformation variables and runs efficiently.
arXiv Detail & Related papers (2021-01-19T04:24:23Z) - Deep Magnification-Flexible Upsampling over 3D Point Clouds [103.09504572409449]
We propose a novel end-to-end learning-based framework to generate dense point clouds.
We first formulate the problem explicitly, which boils down to determining the weights and high-order approximation errors.
Then, we design a lightweight neural network to adaptively learn unified and sorted weights as well as the high-order refinements.
arXiv Detail & Related papers (2020-11-25T14:00:18Z) - Random extrapolation for primal-dual coordinate descent [61.55967255151027]
We introduce a randomly extrapolated primal-dual coordinate descent method that adapts to sparsity of the data matrix and the favorable structures of the objective function.
We show almost sure convergence of the sequence and optimal sublinear convergence rates for the primal-dual gap and objective values, in the general convex-concave case.
arXiv Detail & Related papers (2020-07-13T17:39:35Z) - A level set representation method for N-dimensional convex shape and
applications [2.294014185517203]
We present a new efficient method for convex shape representation, which is regardless of the dimension of the concerned objects.
In this paper, we prove that the convexity of the considered object is equivalent to the convexity of the associated signed distance function.
We apply this new method to two applications: object segmentation with convexity prior and convex hull problem (especially with outliers)
arXiv Detail & Related papers (2020-03-21T07:37:44Z) - MINA: Convex Mixed-Integer Programming for Non-Rigid Shape Alignment [77.38594866794429]
convex mixed-integer programming formulation for non-rigid shape matching.
We propose a novel shape deformation model based on an efficient low-dimensional discrete model.
arXiv Detail & Related papers (2020-02-28T09:54:06Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.