3,333 research outputs found
Delineation of line patterns in images using B-COSFIRE filters
Delineation of line patterns in images is a basic step required in various
applications such as blood vessel detection in medical images, segmentation of
rivers or roads in aerial images, detection of cracks in walls or pavements,
etc. In this paper we present trainable B-COSFIRE filters, which are a model of
some neurons in area V1 of the primary visual cortex, and apply it to the
delineation of line patterns in different kinds of images. B-COSFIRE filters
are trainable as their selectivity is determined in an automatic configuration
process given a prototype pattern of interest. They are configurable to detect
any preferred line structure (e.g. segments, corners, cross-overs, etc.), so
usable for automatic data representation learning. We carried out experiments
on two data sets, namely a line-network data set from INRIA and a data set of
retinal fundus images named IOSTAR. The results that we achieved confirm the
robustness of the proposed approach and its effectiveness in the delineation of
line structures in different kinds of images.Comment: International Work Conference on Bioinspired Intelligence, July
10-13, 201
Detection of curved lines with B-COSFIRE filters: A case study on crack delineation
The detection of curvilinear structures is an important step for various
computer vision applications, ranging from medical image analysis for
segmentation of blood vessels, to remote sensing for the identification of
roads and rivers, and to biometrics and robotics, among others. %The visual
system of the brain has remarkable abilities to detect curvilinear structures
in noisy images. This is a nontrivial task especially for the detection of thin
or incomplete curvilinear structures surrounded with noise. We propose a
general purpose curvilinear structure detector that uses the brain-inspired
trainable B-COSFIRE filters. It consists of four main steps, namely nonlinear
filtering with B-COSFIRE, thinning with non-maximum suppression, hysteresis
thresholding and morphological closing. We demonstrate its effectiveness on a
data set of noisy images with cracked pavements, where we achieve
state-of-the-art results (F-measure=0.865). The proposed method can be employed
in any computer vision methodology that requires the delineation of curvilinear
and elongated structures.Comment: Accepted at Computer Analysis of Images and Patterns (CAIP) 201
Left-invariant evolutions of wavelet transforms on the Similitude Group
Enhancement of multiple-scale elongated structures in noisy image data is
relevant for many biomedical applications but commonly used PDE-based
enhancement techniques often fail at crossings in an image. To get an overview
of how an image is composed of local multiple-scale elongated structures we
construct a multiple scale orientation score, which is a continuous wavelet
transform on the similitude group, SIM(2). Our unitary transform maps the space
of images onto a reproducing kernel space defined on SIM(2), allowing us to
robustly relate Euclidean (and scaling) invariant operators on images to
left-invariant operators on the corresponding continuous wavelet transform.
Rather than often used wavelet (soft-)thresholding techniques, we employ the
group structure in the wavelet domain to arrive at left-invariant evolutions
and flows (diffusion), for contextual crossing preserving enhancement of
multiple scale elongated structures in noisy images. We present experiments
that display benefits of our work compared to recent PDE techniques acting
directly on the images and to our previous work on left-invariant diffusions on
orientation scores defined on Euclidean motion group.Comment: 40 page
Nilpotent Approximations of Sub-Riemannian Distances for Fast Perceptual Grouping of Blood Vessels in 2D and 3D
We propose an efficient approach for the grouping of local orientations
(points on vessels) via nilpotent approximations of sub-Riemannian distances in
the 2D and 3D roto-translation groups and . In our distance
approximations we consider homogeneous norms on nilpotent groups that locally
approximate , and which are obtained via the exponential and logarithmic
map on . In a qualitative validation we show that the norms provide
accurate approximations of the true sub-Riemannian distances, and we discuss
their relations to the fundamental solution of the sub-Laplacian on .
The quantitative experiments further confirm the accuracy of the
approximations. Quantitative results are obtained by evaluating perceptual
grouping performance of retinal blood vessels in 2D images and curves in
challenging 3D synthetic volumes. The results show that 1) sub-Riemannian
geometry is essential in achieving top performance and 2) that grouping via the
fast analytic approximations performs almost equally, or better, than
data-adaptive fast marching approaches on and .Comment: 18 pages, 9 figures, 3 tables, in review at JMI
A PDE Approach to Data-driven Sub-Riemannian Geodesics in SE(2)
We present a new flexible wavefront propagation algorithm for the boundary
value problem for sub-Riemannian (SR) geodesics in the roto-translation group
with a metric tensor depending on a smooth
external cost , , computed from
image data. The method consists of a first step where a SR-distance map is
computed as a viscosity solution of a Hamilton-Jacobi-Bellman (HJB) system
derived via Pontryagin's Maximum Principle (PMP). Subsequent backward
integration, again relying on PMP, gives the SR-geodesics. For
we show that our method produces the global minimizers. Comparison with exact
solutions shows a remarkable accuracy of the SR-spheres and the SR-geodesics.
We present numerical computations of Maxwell points and cusp points, which we
again verify for the uniform cost case . Regarding image
analysis applications, tracking of elongated structures in retinal and
synthetic images show that our line tracking generically deals with crossings.
We show the benefits of including the sub-Riemannian geometry.Comment: Extended version of SSVM 2015 conference article "Data-driven
Sub-Riemannian Geodesics in SE(2)
Numerical Approaches for Linear Left-invariant Diffusions on SE(2), their Comparison to Exact Solutions, and their Applications in Retinal Imaging
Left-invariant PDE-evolutions on the roto-translation group (and
their resolvent equations) have been widely studied in the fields of cortical
modeling and image analysis. They include hypo-elliptic diffusion (for contour
enhancement) proposed by Citti & Sarti, and Petitot, and they include the
direction process (for contour completion) proposed by Mumford. This paper
presents a thorough study and comparison of the many numerical approaches,
which, remarkably, is missing in the literature. Existing numerical approaches
can be classified into 3 categories: Finite difference methods, Fourier based
methods (equivalent to -Fourier methods), and stochastic methods (Monte
Carlo simulations). There are also 3 types of exact solutions to the
PDE-evolutions that were derived explicitly (in the spatial Fourier domain) in
previous works by Duits and van Almsick in 2005. Here we provide an overview of
these 3 types of exact solutions and explain how they relate to each of the 3
numerical approaches. We compute relative errors of all numerical approaches to
the exact solutions, and the Fourier based methods show us the best performance
with smallest relative errors. We also provide an improvement of Mathematica
algorithms for evaluating Mathieu-functions, crucial in implementations of the
exact solutions. Furthermore, we include an asymptotical analysis of the
singularities within the kernels and we propose a probabilistic extension of
underlying stochastic processes that overcomes the singular behavior in the
origin of time-integrated kernels. Finally, we show retinal imaging
applications of combining left-invariant PDE-evolutions with invertible
orientation scores.Comment: A final and corrected version of the manuscript is Published in
Numerical Mathematics: Theory, Methods and Applications (NM-TMA), vol. (9),
p.1-50, 201
Extraction of Airways with Probabilistic State-space Models and Bayesian Smoothing
Segmenting tree structures is common in several image processing
applications. In medical image analysis, reliable segmentations of airways,
vessels, neurons and other tree structures can enable important clinical
applications. We present a framework for tracking tree structures comprising of
elongated branches using probabilistic state-space models and Bayesian
smoothing. Unlike most existing methods that proceed with sequential tracking
of branches, we present an exploratory method, that is less sensitive to local
anomalies in the data due to acquisition noise and/or interfering structures.
The evolution of individual branches is modelled using a process model and the
observed data is incorporated into the update step of the Bayesian smoother
using a measurement model that is based on a multi-scale blob detector.
Bayesian smoothing is performed using the RTS (Rauch-Tung-Striebel) smoother,
which provides Gaussian density estimates of branch states at each tracking
step. We select likely branch seed points automatically based on the response
of the blob detection and track from all such seed points using the RTS
smoother. We use covariance of the marginal posterior density estimated for
each branch to discriminate false positive and true positive branches. The
method is evaluated on 3D chest CT scans to track airways. We show that the
presented method results in additional branches compared to a baseline method
based on region growing on probability images.Comment: 10 pages. Pre-print of the paper accepted at Workshop on Graphs in
Biomedical Image Analysis. MICCAI 2017. Quebec Cit
- …