115 research outputs found
A persistent homology-based topological loss function for multi-class CNN segmentation of cardiac MRI
With respect to spatial overlap, CNN-based segmentation of short axis
cardiovascular magnetic resonance (CMR) images has achieved a level of
performance consistent with inter observer variation. However, conventional
training procedures frequently depend on pixel-wise loss functions, limiting
optimisation with respect to extended or global features. As a result, inferred
segmentations can lack spatial coherence, including spurious connected
components or holes. Such results are implausible, violating the anticipated
topology of image segments, which is frequently known a priori. Addressing this
challenge, published work has employed persistent homology, constructing
topological loss functions for the evaluation of image segments against an
explicit prior. Building a richer description of segmentation topology by
considering all possible labels and label pairs, we extend these losses to the
task of multi-class segmentation. These topological priors allow us to resolve
all topological errors in a subset of 150 examples from the ACDC short axis CMR
training data set, without sacrificing overlap performance.Comment: To be presented at the STACOM workshop at MICCAI 202
Persistent Homology with Improved Locality Information for more Effective Delineation
We present a new, more effective way to use Persistent Homology (PH), a
method to compare the topology of two data sets, for training deep networks to
delineate road networks in aerial images and neuronal processes in microscopy
scans. Its essence is in a novel filtration function, derived from a fusion of
two existing techniques: thresholding-based filtration, previously used to
train deep networks to segment medical images, and filtration with height
functions, used before for comparison of 2D and 3D shapes. We experimentally
demonstrate that deep networks trained with our Persistent-Homology-based loss
yield reconstructions of road networks and neuronal processes that preserve the
connectivity of the originals better than existing topological and
non-topological loss functions
Topologically faithful image segmentation via induced matching of persistence barcodes
Image segmentation is a largely researched field where neural networks find
vast applications in many facets of technology. Some of the most popular
approaches to train segmentation networks employ loss functions optimizing
pixel-overlap, an objective that is insufficient for many segmentation tasks.
In recent years, their limitations fueled a growing interest in topology-aware
methods, which aim to recover the correct topology of the segmented structures.
However, so far, none of the existing approaches achieve a spatially correct
matching between the topological features of ground truth and prediction.
In this work, we propose the first topologically and feature-wise accurate
metric and loss function for supervised image segmentation, which we term Betti
matching. We show how induced matchings guarantee the spatially correct
matching between barcodes in a segmentation setting. Furthermore, we propose an
efficient algorithm to compute the Betti matching of images. We show that the
Betti matching error is an interpretable metric to evaluate the topological
correctness of segmentations, which is more sensitive than the well-established
Betti number error. Moreover, the differentiability of the Betti matching loss
enables its use as a loss function. It improves the topological performance of
segmentation networks across six diverse datasets while preserving the
volumetric performance. Our code is available in
https://github.com/nstucki/Betti-matching
Topological Learning for Brain Networks
This paper proposes a novel topological learning framework that can integrate
networks of different sizes and topology through persistent homology. This is
possible through the introduction of a new topological loss function that
enables such challenging task. The use of the proposed loss function bypasses
the intrinsic computational bottleneck associated with matching networks. We
validate the method in extensive statistical simulations with ground truth to
assess the effectiveness of the topological loss in discriminating networks
with different topology. The method is further applied to a twin brain imaging
study in determining if the brain network is genetically heritable. The
challenge is in overlaying the topologically different functional brain
networks obtained from the resting-state functional MRI (fMRI) onto the
template structural brain network obtained through the diffusion MRI (dMRI)
Topological Deep Learning: Going Beyond Graph Data
Topological deep learning is a rapidly growing field that pertains to the
development of deep learning models for data supported on topological domains
such as simplicial complexes, cell complexes, and hypergraphs, which generalize
many domains encountered in scientific computations. In this paper, we present
a unifying deep learning framework built upon a richer data structure that
includes widely adopted topological domains.
Specifically, we first introduce combinatorial complexes, a novel type of
topological domain. Combinatorial complexes can be seen as generalizations of
graphs that maintain certain desirable properties. Similar to hypergraphs,
combinatorial complexes impose no constraints on the set of relations. In
addition, combinatorial complexes permit the construction of hierarchical
higher-order relations, analogous to those found in simplicial and cell
complexes. Thus, combinatorial complexes generalize and combine useful traits
of both hypergraphs and cell complexes, which have emerged as two promising
abstractions that facilitate the generalization of graph neural networks to
topological spaces.
Second, building upon combinatorial complexes and their rich combinatorial
and algebraic structure, we develop a general class of message-passing
combinatorial complex neural networks (CCNNs), focusing primarily on
attention-based CCNNs. We characterize permutation and orientation
equivariances of CCNNs, and discuss pooling and unpooling operations within
CCNNs in detail.
Third, we evaluate the performance of CCNNs on tasks related to mesh shape
analysis and graph learning. Our experiments demonstrate that CCNNs have
competitive performance as compared to state-of-the-art deep learning models
specifically tailored to the same tasks. Our findings demonstrate the
advantages of incorporating higher-order relations into deep learning models in
different applications
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