2,699 research outputs found
Writing Reusable Digital Geometry Algorithms in a Generic Image Processing Framework
Digital Geometry software should reflect the generality of the underlying
mathe- matics: mapping the latter to the former requires genericity. By
designing generic solutions, one can effectively reuse digital geometry data
structures and algorithms. We propose an image processing framework focused on
the Generic Programming paradigm in which an algorithm on the paper can be
turned into a single code, written once and usable with various input types.
This approach enables users to design and implement new methods at a lower
cost, try cross-domain experiments and help generalize resultsComment: Workshop on Applications of Discrete Geometry and Mathematical
Morphology, Istanb : France (2010
A Parallel Thinning Algorithm for Grayscale Images
International audienceGrayscale skeletonization offers an interesting alternative to traditional skeletonization following a binarization. It is well known that parallel algorithms for skeletonization outperform sequential ones in terms of quality of results, yet no general and well defined framework has been proposed until now for parallel grayscale thinning. We introduce in this paper a parallel thinning algorithm for grayscale images, and prove its topological soundness based on properties of the critical kernels framework. The algorithm and its proof, given here in the 2D case, are also valid in 3D. Some applications are sketched in conclusion
Homological Region Adjacency Tree for a 3D Binary Digital Image via HSF Model
Given a 3D binary digital image I, we define and compute
an edge-weighted tree, called Homological Region Tree (or Hom-Tree,
for short). It coincides, as unweighted graph, with the classical Region
Adjacency Tree of black 6-connected components (CCs) and white 26-
connected components of I. In addition, we define the weight of an edge
(R, S) as the number of tunnels that the CCs R and S “share”. The
Hom-Tree structure is still an isotopic invariant of I. Thus, it provides
information about how the different homology groups interact between
them, while preserving the duality of black and white CCs.
An experimentation with a set of synthetic images showing different
shapes and different complexity of connected component nesting is performed
for numerically validating the method.Ministerio de EconomĂa y Competitividad MTM2016-81030-
Extracting 3D parametric curves from 2D images of Helical objects
Helical objects occur in medicine, biology, cosmetics, nanotechnology, and engineering. Extracting a 3D parametric curve from a 2D image of a helical object has many practical applications, in particular being able to extract metrics such as tortuosity, frequency, and pitch. We present a method that is able to straighten the image object and derive a robust 3D helical curve from peaks in the object boundary. The algorithm has a small number of stable parameters that require little tuning, and the curve is validated against both synthetic and real-world data. The results show that the extracted 3D curve comes within close Hausdorff distance to the ground truth, and has near identical tortuosity for helical objects with a circular profile. Parameter insensitivity and robustness against high levels of image noise are demonstrated thoroughly and quantitatively
Automatic correction of Ma and Sonka's thinning algorithm using P-simple points
International audienceMa and Sonka proposed a fully parallel 3D thinning algorithm which does not always preserve topology. We propose an algorithm based on P-simple points which automatically corrects Ma and Sonka's Algorithm. As far as we know, our algorithm is the only fully parallel curve thinning algorithm which preserves topology
A skeletonization algorithm for gradient-based optimization
The skeleton of a digital image is a compact representation of its topology,
geometry, and scale. It has utility in many computer vision applications, such
as image description, segmentation, and registration. However, skeletonization
has only seen limited use in contemporary deep learning solutions. Most
existing skeletonization algorithms are not differentiable, making it
impossible to integrate them with gradient-based optimization. Compatible
algorithms based on morphological operations and neural networks have been
proposed, but their results often deviate from the geometry and topology of the
true medial axis. This work introduces the first three-dimensional
skeletonization algorithm that is both compatible with gradient-based
optimization and preserves an object's topology. Our method is exclusively
based on matrix additions and multiplications, convolutional operations, basic
non-linear functions, and sampling from a uniform probability distribution,
allowing it to be easily implemented in any major deep learning library. In
benchmarking experiments, we prove the advantages of our skeletonization
algorithm compared to non-differentiable, morphological, and
neural-network-based baselines. Finally, we demonstrate the utility of our
algorithm by integrating it with two medical image processing applications that
use gradient-based optimization: deep-learning-based blood vessel segmentation,
and multimodal registration of the mandible in computed tomography and magnetic
resonance images.Comment: Accepted at ICCV 202
The Ellipsoid Factor for quantification of rods, plates and intermediate forms in 3D geometries
The Ellipsoid Factor (EF) is a method for the local determination of the rod- or plate-like nature of porous or spongy continua. EF at a point within a 3D structure is defined as the difference in axis ratios of the greatest ellipsoid which fits inside the structure and which contains the point of interest, and ranges from -1 for strongly oblate (discus-shaped) ellipsoids, to +1 for strongly prolate (javelin-shaped) ellipsoids. For an ellipsoid with axes a ≤ b ≤ c, EF = a/b – b/c. Here, EF is demonstrated in a Java plugin, Ellipsoid Factor for ImageJ, distributed in the BoneJ plugin collection. Ellipsoid Factor utilises an ellipsoid optimisation algorithm which assumes that maximal ellipsoids are centred on the medial axis, then dilates, rotates and translates slightly each ellipsoid until it cannot increase in volume any further. Ellipsoid Factor successfully identifies rods, plates and intermediate structures within trabecular bone, and summarises the distribution of geometries with an overall EF mean and standard deviation, EF histogram and Flinn diagram displaying a/b versus b/c. Ellipsoid Factor is released to the community for testing, use, and improvement
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