378 research outputs found
A graph-based mathematical morphology reader
This survey paper aims at providing a "literary" anthology of mathematical
morphology on graphs. It describes in the English language many ideas stemming
from a large number of different papers, hence providing a unified view of an
active and diverse field of research
Hierarchical image simplification and segmentation based on Mumford-Shah-salient level line selection
Hierarchies, such as the tree of shapes, are popular representations for
image simplification and segmentation thanks to their multiscale structures.
Selecting meaningful level lines (boundaries of shapes) yields to simplify
image while preserving intact salient structures. Many image simplification and
segmentation methods are driven by the optimization of an energy functional,
for instance the celebrated Mumford-Shah functional. In this paper, we propose
an efficient approach to hierarchical image simplification and segmentation
based on the minimization of the piecewise-constant Mumford-Shah functional.
This method conforms to the current trend that consists in producing
hierarchical results rather than a unique partition. Contrary to classical
approaches which compute optimal hierarchical segmentations from an input
hierarchy of segmentations, we rely on the tree of shapes, a unique and
well-defined representation equivalent to the image. Simply put, we compute for
each level line of the image an attribute function that characterizes its
persistence under the energy minimization. Then we stack the level lines from
meaningless ones to salient ones through a saliency map based on extinction
values defined on the tree-based shape space. Qualitative illustrations and
quantitative evaluation on Weizmann segmentation evaluation database
demonstrate the state-of-the-art performance of our method.Comment: Pattern Recognition Letters, Elsevier, 201
Scene Parsing with Multiscale Feature Learning, Purity Trees, and Optimal Covers
Scene parsing, or semantic segmentation, consists in labeling each pixel in
an image with the category of the object it belongs to. It is a challenging
task that involves the simultaneous detection, segmentation and recognition of
all the objects in the image.
The scene parsing method proposed here starts by computing a tree of segments
from a graph of pixel dissimilarities. Simultaneously, a set of dense feature
vectors is computed which encodes regions of multiple sizes centered on each
pixel. The feature extractor is a multiscale convolutional network trained from
raw pixels. The feature vectors associated with the segments covered by each
node in the tree are aggregated and fed to a classifier which produces an
estimate of the distribution of object categories contained in the segment. A
subset of tree nodes that cover the image are then selected so as to maximize
the average "purity" of the class distributions, hence maximizing the overall
likelihood that each segment will contain a single object. The convolutional
network feature extractor is trained end-to-end from raw pixels, alleviating
the need for engineered features. After training, the system is parameter free.
The system yields record accuracies on the Stanford Background Dataset (8
classes), the Sift Flow Dataset (33 classes) and the Barcelona Dataset (170
classes) while being an order of magnitude faster than competing approaches,
producing a 320 \times 240 image labeling in less than 1 second.Comment: 9 pages, 4 figures - Published in 29th International Conference on
Machine Learning (ICML 2012), Jun 2012, Edinburgh, United Kingdo
Combinatorial Continuous Maximal Flows
Maximum flow (and minimum cut) algorithms have had a strong impact on
computer vision. In particular, graph cuts algorithms provide a mechanism for
the discrete optimization of an energy functional which has been used in a
variety of applications such as image segmentation, stereo, image stitching and
texture synthesis. Algorithms based on the classical formulation of max-flow
defined on a graph are known to exhibit metrication artefacts in the solution.
Therefore, a recent trend has been to instead employ a spatially continuous
maximum flow (or the dual min-cut problem) in these same applications to
produce solutions with no metrication errors. However, known fast continuous
max-flow algorithms have no stopping criteria or have not been proved to
converge. In this work, we revisit the continuous max-flow problem and show
that the analogous discrete formulation is different from the classical
max-flow problem. We then apply an appropriate combinatorial optimization
technique to this combinatorial continuous max-flow CCMF problem to find a
null-divergence solution that exhibits no metrication artefacts and may be
solved exactly by a fast, efficient algorithm with provable convergence.
Finally, by exhibiting the dual problem of our CCMF formulation, we clarify the
fact, already proved by Nozawa in the continuous setting, that the max-flow and
the total variation problems are not always equivalent.Comment: 26 page
Indoor Semantic Segmentation using depth information
This work addresses multi-class segmentation of indoor scenes with RGB-D
inputs. While this area of research has gained much attention recently, most
works still rely on hand-crafted features. In contrast, we apply a multiscale
convolutional network to learn features directly from the images and the depth
information. We obtain state-of-the-art on the NYU-v2 depth dataset with an
accuracy of 64.5%. We illustrate the labeling of indoor scenes in videos
sequences that could be processed in real-time using appropriate hardware such
as an FPGA.Comment: 8 pages, 3 figure
Watershed of a Continuous Function
Special issue on Mathematical Morphology.International audienceThe notion of watershed, used in morphological segmentation, has only a digital definition. In this paper, we propose to extend this definition to the continuous plane. Using this continuous definition, we present the watershed differences with classical edge detectors. We then exhibit a metric in the plane for which the watershed is a skeleton by influence zones and show the lower semicontinuous behaviour of the associated skeleton. This theoretical approach suggests an algorithm for solving the eikonal equation: ââÆâ = g. Finally, we end with some new watershed algorithms, which present the advantage of allowing the use of markers and/or anchor points, thus opening the way towards grey-tone skeletons
Morse frames
In the context of discrete Morse theory, we introduce Morse frames, which are
maps that associate a set of critical simplexes to all simplexes. The main
example of Morse frames are the Morse references. In particular, these Morse
references allow computing Morse complexes, an important tool for homology. We
highlight the link between Morse references and gradient flows. We also propose
a novel presentation of the Annotation algorithm for persistent cohomology, as
a variant of a Morse frame. Finally, we propose another construction, that
takes advantage of the Morse reference for computing the Betti numbers in mod 2
arithmetic
Courbure discrÚte : théorie et applications
International audienceThe present volume contains the proceedings of the 2013 Meeting on discrete curvature, held at CIRM, Luminy, France. The aim of this meeting was to bring together researchers from various backgrounds, ranging from mathematics to computer science, with a focus on both theory and applications. With 27 invited talks and 8 posters, the conference attracted 70 researchers from all over the world. The challenge of finding a common ground on the topic of discrete curvature was met with success, and these proceedings are a testimony of this wor
New characterizations of minimum spanning trees and of saliency maps based on quasi-flat zones
We study three representations of hierarchies of partitions: dendrograms
(direct representations), saliency maps, and minimum spanning trees. We provide
a new bijection between saliency maps and hierarchies based on quasi-flat zones
as used in image processing and characterize saliency maps and minimum spanning
trees as solutions to constrained minimization problems where the constraint is
quasi-flat zones preservation. In practice, these results form a toolkit for
new hierarchical methods where one can choose the most convenient
representation. They also invite us to process non-image data with
morphological hierarchies
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