Piecewise rigid curve deformation via a Finsler steepest descent

This paper introduces a novel steepest descent flow in Banach spaces. This extends previous works on generalized gradient descent, notably the work of Charpiat et al., to the setting of Finsler metrics. Such a generalized gradient allows one to take into account a prior on deformations (e.g., piecewise rigid) in order to favor some specific evolutions. We define a Finsler gradient descent method to minimize a functional defined on a Banach space and we prove a convergence theorem for such a method. In particular, we show that the use of non-Hilbertian norms on Banach spaces is useful to study non-convex optimization problems where the geometry of the space might play a crucial role to avoid poor local minima. We show some applications to the curve matching problem. In particular, we characterize piecewise rigid deformations on the space of curves and we study several models to perform piecewise rigid evolution of curves

Exhaustive Family of Energies Minimizable Exactly by a Graph Cut

International audienceGraph cuts are widely used in many fields of computer vision in order to minimize in small polynomial time complexity certain classes of energies. These specific classes depend on the way chosen to build the graphs representing the problems to solve. We study here all possible ways of building graphs and the associated energies minimized, leading to the exhaustive family of energies minimizable exactly by a graph cut. To do this, we consider the issue of coding pixel labels as states of the graph, i.e. the choice of state interpretations. The family obtained comprises many new classes, in particular energies that do not satisfy the submodularity condition, including energies that are even not permuted-submodular. A generating subfamily is studied in details, in particular we propose a canonical form to represent Markov random fields, which proves useful to recognize energies in this subfamily in linear complexity almost surely, and then to build the associated graph in quasilinear time. A few experiments are performed, to illustrate the new possibilities offered

A Graph-Cut-Based Method for Spatio-Temporal Segmentation of Fire from Satellite Observations

International audienceWe propose a new method based on graph cuts for the segmentation of burned areas in time series of satellite images. The method consists in rewriting a segmentation problem as a (s, t)-min-cut on the spatio-temporal image graph and computing this minimal cut. As burned areas grow in time, we introduce growth constraint in graph cuts by using directed infinite links connecting pixels at the same spatial locations in successive image frames. This method guarantees to find the globally optimal segmentation satisfying the growth constraint in small time complexity. Experimental results on a set of MODIS measurements over the Northern Australia demonstrated that the new approach succeeded in combining both spatial and temporal information for accurate segmentation of burned areas

SE(3)-equivariant Graph Neural Networks for Learning Glassy Liquids Representations

Within the glassy liquids community, the use of Machine Learning (ML) to model particles' static structure in order to predict their future dynamics is currently a hot topic. The actual state of the art consists in Graph Neural Networks (GNNs) (Bapst 2020) which, beside having a great expressive power, are heavy models with numerous parameters and lack interpretability. Inspired by recent advances (Thomas 2018), we build a GNN that learns a robust representation of the glass' static structure by constraining it to preserve the roto-translation (SE(3)) equivariance. We show that this constraint not only significantly improves the predictive power but also allows to reduce the number of parameters while improving the interpretability. Furthermore, we relate our learned equivariant features to well-known invariant expert features, which are easily expressible with a single layer of our network.Comment: 8 pages, 7 figures plus appendi

Spatio-Temporal Video Segmentation with Shape Growth or Shrinkage Constraint

We propose a new method for joint segmentation of monotonously growing or shrinking shapes in a time sequence of noisy images. The task of segmenting the image time series is expressed as an optimization problem using the spatio-temporal graph of pixels, in which we are able to impose the constraint of shape growth or of shrinkage by introducing monodirectional infinite links connecting pixels at the same spatial locations in successive image frames. The globally optimal solution is computed with a graph cut. The performance of the proposed method is validated on three applications: segmentation of melting sea ice floes and of growing burned areas from time series of 2D satellite images, and segmentation of a growing brain tumor from sequences of 3D medical scans. In the latter application, we impose an additional intersequences inclusion constraint by adding directed infinite links between pixels of dependent image structures

Multi-label segmentation of images with partition trees

We propose a new framework for multi-class image segmentation with shape priors using a binary partition tree. In the literature, such trees are used to represent hierarchical partitions of images, and are usually computed in a bottom-up manner based on color similarities, then analyzed to detect objects with a known shape prior. However, not considering shape priors during the construction phase induces mistakes in the later segmentation. This paper proposes a method which uses both color distribution and shape priors to optimize the trees for image segmentation. The method consists in pruning and regrafting tree branches in order to minimize the energy of the best segmentation that can be extracted from the tree. Theoretical guarantees help reducing the search space and make the optimization efficient. Our experiments show that the optimization approach succeeds in incorporating shape information into multi-label segmentation, outperforming the state-of-the-art

Noisy Supervision for Correcting Misaligned Cadaster Maps Without Perfect Ground Truth Data

International audienceIn machine learning the best performance on a certain task is achieved by fully supervised methods when perfect ground truth labels are available. However, labels are often noisy, especially in remote sensing where manually curated public datasets are rare. We study the multi-modal cadaster map alignment problem for which available annotations are mis-aligned polygons, resulting in noisy supervision. We subsequently set up a multiple-rounds training scheme which corrects the ground truth annotations at each round to better train the model at the next round. We show that it is possible to reduce the noise of the dataset by iteratively training a better alignment model to correct the annotation alignment

Hierarchical Representation of Videos with Spatio-Temporal Fibers

International audienceWe propose a new representation of videos, as spatio- temporal fibers. These fibers are clusters of trajectories that are meshed spatially in the image domain. They form a hier- archical partition of the video into regions that are coherent in time and space. They can be seen as dense, spatially- organized, long-term optical flow. Their robustness to noise and ambiguities is ensured by taking into account the relia- bility of each source of information. As fibers allow users to handle easily moving objects in videos, they prove useful for video editing, as demonstrated in a video inpainting example