-
M. Hanselmann, U. Köthe, B.Y. Renard, M. Kirchner, R.M.A. Heeren, F.A. Hamprecht:
- Multivariate Watershed Segmentation of Compositional Data,
in: S. Brlek, C. Reutenauer, X. Provençal (Eds.): Discrete Geometry for Computer Imagery, Proc. DGCI 2009, Lecture Notes in Computer Science 5810, pp. 180-192, Berlin: Springer, 2009. (note: this article is © Springer-Verlag)
Abstract | PDF
Watershed segmentation of spectral images is typically achieved
by first transforming the high-dimensional input data into a scalar
boundary indicator map which is used to derive the watersheds. We propose
to combine a Random Forest classifier with the watershed transform
and introduce three novel methods to obtain scalar boundary indicator
maps from class probability maps. We further introduce the multivariate
watershed as a generalization of the classic watershed approach.
-
H. Meine, P. Stelldinger, U. Köthe:
- Pixel Approximation Errors in Common Watershed Algorithms,
in: S. Brlek, C. Reutenauer, X. Provençal (Eds.): Discrete Geometry for Computer Imagery, Proc. DGCI 2009, Lecture Notes in Computer Science 5810, pp. 193-202, Berlin: Springer, 2009. (note: this article is © Springer-Verlag)
Abstract | PDF
The exact, subpixel watershed algorithm delivers very accurate
watershed boundaries based on a spline interpolation, but is slow
and only works in 2D. On the other hand, there are very fast pixel watershed
algorithms, but they produce errors not only in certain exotic
cases, but also in real-world images and even in the most simple scenarios.
In this work, we examine closely the source of these errors and
propose a new algorithm that is fast, approximates the exact watersheds
(with pixel resolution), and can be extended to 3D.
-
C. Bähnisch, P. Stelldinger, U. Köthe:
- Fast and Accurate 3D Edge Detection for Surface Reconstruction,
in: J. Denzler, G. Notni, H. Süße (Eds.): Pattern Recognition, Proc. DAGM 2009, Lecture Notes in Computer Science 5748 , pp. 111-120, Berlin: Springer, 2009. (note: this article is © Springer-Verlag)
Abstract | PDF
Although edge detection is a well investigated topic, 3D edge
detectors mostly lack either accuracy or speed. We will show, how to
build a highly accurate subvoxel edge detector, which is fast enough for
practical applications. In contrast to other approaches we use a spline
interpolation in order to have an efficient approximation of the theoretically
ideal sinc interpolator. We give theoretical bounds for the accuracy
and show experimentally that our approach reaches these bounds while
the often-used subpixel-accurate parabola fit leads to much higher edge
displacements.
-
B. Andres, U. Köthe, A. Bonea, B. Nadler, F.A. Hamprecht:
- Quantitative Assessment of Image Segmentation Quality by Random Walk Relaxation Times,
in: J. Denzler, G. Notni, H. Süße (Eds.): Pattern Recognition, Proc. DAGM 2009, Lecture Notes in Computer Science 5748 , pp. 502-511, Berlin: Springer, 2009. (note: this article is © Springer-Verlag)
Abstract | PDF
The purpose of image segmentation is to partition the pixel
grid of an image into connected components termed segments such that
(i) each segment is homogenous and (ii) for any pair of adjacent segments,
their union is not homogenous. (If it were homogenous the segments
should be merged). We propose a rigorous definition of segment
homogeneity which is scale-free and adaptive to the geometry of segments.
We motivate this definition using random walk theory and show
how segment homogeneity facilitates the quantification of violations of
the conditions (i) and (ii) which are referred to as under-segmentation
and over-segmentation, respectively. We describe the theoretical foundations
of our approach and present a proof of concept on a few natural
images.
-
M. Hanselmann, U. Köthe, M. Kirchner, B.Y. Renard, E.R. Amstalden, K. Glunde, R.M.A. Heeren, F.A. Hamprecht:
- Towards Digital Staining using Imaging Mass Spectrometry and Random Forests ,
Journal of Proteome Research, 8(7):3558-3567, 2009
Abstract | PDF
We show on imaging mass spectrometry (IMS) data that the Random Forest classifier can be used for automated tissue classification and that it results in predictions with high sensitivities and positive predictive values, even when intersample variability is present in the data. We further demonstrate how Markov Random Fields and vector-valued median filtering can be applied to reduce noise effects to further improve the classification results in a posthoc smoothing step. Our study gives clear evidence that digital staining by means of IMS constitutes a promising complement to chemical staining techniques.
-
M. Frank, M. Plaue, H. Rapp, U. Köthe, B. Jähne, F.A. Hamprecht:
- Theoretical and Experimental Error Analysis of Continuous-Wave Time-Of-Flight Range Cameras,
Optical Engineering, 48(1):013602, 2009
Abstract | PDF
This paper offers a formal investigation of the measurement principle of time-of-flight
(TOF) 3D cameras using correlation of amplitude-modulated continuous-wave signals. These sensors
can provide both depth maps and IR intensity pictures simultaneously and in real-time. We
examine the theory of the data acquisition in detail. The variance of the range measurements is derived
in a concise way and we show that the computed range follows an Offset Normal distribution.
The impact of quantization of that distribution is discussed. All theoretically investigated errors
like the behavior of the variance, depth bias, saturation and quantization effects are supported by
experimental results.
-
H. Meine, U. Köthe, P. Stelldinger:
- A Topological Sampling Theorem for Robust Boundary Reconstruction and Image Segmentation,
Discrete Applied Mathematics (DGCI Special Issue), 157(3):524-541, 2009.
Abstract | PDF
Existing theories on shape digitization impose strong constraints on admissible
shapes, and require error-free data. Consequently, these theories are not applicable
to most real-world situations. In this paper, we propose a new approach that overcomes
many of these limitations. It assumes that segmentation algorithms represent
the detected boundary by a set of points whose deviation from the true contours is
bounded. Given these error bounds, we reconstruct boundary connectivity by means
of Delaunay triangulation and alpha-shapes. We prove that this procedure is guaranteed
to result in topologically correct image segmentations under certain realistic conditions.
Experiments on real and synthetic images demonstrate the good performance
of the new method and confirm the predictions of our theory.
-
B. Andres, C. Kondermann, D. Kondermann, U. Köthe, F.A. Hamprecht, C.S. Garbe:
- On Errors-In-Variables Regression with Arbitrary Covariance and its Application to Optical Flow Estimation,
in: IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2008, pages 1-6, 2008.
Abstract | BibTeX | PDF
Linear inverse problems in computer vision, including motion estimation, shape fitting and image reconstruction, give rise to parameter estimation problems with highly correlated errors in variables. Established total least squares methods estimate the most likely corrections A' and b' to a given data matrix [A, b] perturbed by additive Gaussian noise, such that there exists a solution y with [A + A', b +b']y = 0. In practice, regression imposes a more restrictive constraint namely the existence of a solution x with [A + A']x = [b + b']. In addition, more complicated correlations arise canonically from the use of linear filters. We, therefore, propose a maximum likelihood estimator for regression in the general case of arbitrary positive definite covariance matrices. We show that A', b' and x can be found simultaneously by the unconstrained minimization of a multivariate polynomial which can, in principle, be carried out by means of a Grobner basis. Results for plane fitting and optical flow computation indicate the superiority of the proposed method.
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B. Andres, U. Köthe, M. Helmstaedter, W. Denk, F.A. Hamprecht:
- Segmentation of SBFSEM Volume Data of Neural Tissue by Hierarchical Classification,
in: G. Rigoll (Ed.): Pattern Recognition, Proc. DAGM 2008, Lecture Notes in Computer Science 5096 , pp. 142-152, Berlin: Springer, 2008. (note: this article is © Springer-Verlag)
Abstract | BibTeX | PDF
Received a Best Paper Award from the German Association for Pattern Recognition (DAGM)
Three-dimensional electron-microscopic image stacks with
almost isotropic resolution allow, for the first time, to determine the complete
connection matrix of parts of the brain. In spite of major advances
in staining, correct segmentation of these stacks remains challenging, because
very few local mistakes can lead to severe global errors. We propose
a hierarchical segmentation procedure based on statistical learning and
topology-preserving grouping. Edge probability maps are computed by a
random forest classifier (trained on hand-labeled data) and partitioned
into supervoxels by the watershed transform. Over-segmentation is then
resolved by another random forest. Careful validation shows that the
results of our algorithm are close to human labelings.
-
U. Köthe:
- What Can We Learn from Discrete Images about the Continuous World?,
in: D. Coeurjolly, I. Sivignon, L. Tougne, F. Dupont (Eds.): Discrete Geometry for Computer Imagery, Proc. DGCI 2008, Lecture Notes in Computer Science 4992, pp. 4-19, Berlin: Springer, 2008. (note: this article is © Springer-Verlag)
Abstract | PDF
Image analysis attempts to perceive properties of the continuous real
world by means of digital algorithms. Since discretization discards
an infinite amount of information, it is difficult to predict if and
when digital methods will produce reliable results. This paper reviews
theories which establish explicit connections between the continuous
and digital domains (such as Shannon's sampling theorem and a recent
geometric sampling theorem) and describes some of their consequences
for image analysis. Although many problems are still open, we can
already conclude that adherence to these theories leads to significantly
more stable and accurate algorithms.
-
U. Köthe, P. Stelldinger, H. Meine:
- Provably Correct Edgel Linking and Subpixel Boundary Reconstruction,
in: K. Franke, K.-R. Müller, B. Nikolay, R. Schäfer (Eds.): Pattern Recognition, Proc. DAGM 2006, Lecture Notes in Computer Science 4174, pp. 81-90, Berlin: Springer, 2006. (note: this article is © Springer-Verlag)
Abstract | PDF
Existing methods for segmentation by edgel linking are based on heuristics and give no guarantee for a topologically correct result. In this paper, we propose an edgel linking algorithm based on a new sampling theorem for shape digitization, which guarantees a topologically correct reconstruction of regions and boundaries if the edgels approximate true object edges with a known maximal error. Experiments on real and generated images demonstrate the good performance of the new method and confirm the predictions of our theory.
-
P. Stelldinger, U. Köthe, H. Meine:
- Topologically Correct Image Segmentation Using Alpha Shapes,
in: A. Kuba, L. Nyul, K. Palagyi (Eds.): Discrete Geometry for Computer Imagery, Proc. DGCI 2006, Lecture Notes in Computer Science 4245, pp. 542-554, Berlin: Springer, 2006. (note: this article is © Springer-Verlag)
Abstract | PDF
Existing theories on shape digitization impose strong constraints on feasible shapes and require error-free measurements. We use Delaunay triangulation and alpha-shapes to prove that topologically correct segmentations can be obtained under much more realistic conditions. Our key assumption is that sampling points represent object boundaries with a certain maximum error. Experiments on real and generated images demonstrate the good performance and correctness of the new method.
-
U. Köthe, H. Meine:
- Merkmalsextraktion für eine automatische Bildsuche,
in: G. Stanke, A. Bienert, J. Hemsley, V. Cappellini (Eds.): Konferenzband EVA 2006 Berlin, Elektronische Bildverarbeitung und Kunst, Kultur, Historie, pp 47-53, ISBN 3-9809212-7-1, Berlin, 2006 (in German)
Abstract | PDF
Many applications of content-based image retrieval require very accurate local image features. We describe how the measurement accuracy of geometrical and topological features can be optimized by means of appropriate image resolution, interpolation, and subpixel-accurate edge detection.
Für viele Anwendungen der Bildsuche werden hochgenaue lokale Bildmerkmale benötigt. Wir beschreiben, wie man durch hinreichende Bildauflösung, Interpolation, und subpixel-genaue Kantendetektion die Messgenauigkeit für geometrische und topologische Merkmale optimieren kann.
-
H. Meine, U. Köthe:
- A New Sub-pixel Map for Image Analysis,
in: R. Reulke, U. Eckhardt, B. Flach, U. Knauer, K. Polthier (Eds.): Combinatorial Image Analysis, Proc. IWCIA 2006, Lecture Notes in Computer Science 4040, pp. 116-130, Berlin: Springer, 2006. (note: this article is © Springer-Verlag)
Abstract | PDF
Planar maps have been proposed as a powerful and easy-to-use representation
for various kinds of image analysis results, but so far they are restricted
to pixel accuracy.
This leads to limitations in the representation of complex structures (such
as junctions, triangulations, and skeletons) and discards the sub-pixel
information available in grayvalue and color images.
We extend the planar map formalism to sub-pixel accuracy and introduce
various algorithms to create such a map, thereby demonstrating significant
gains over the existing approaches.
-
P.Stelldinger, U. Köthe:
- Connectivity preserving digitization of blurred binary images in 2D and 3D,
Computers & Graphics, Volume 30, Issue 1, Pages 70-76 (February 2006) (note: this article is © Elsevier B.V.)
Abstract | official Elsevier page | paper draft PDF format
Connectivity and neighborhood are fundamental topological properties of
objects in pictures. Since the input for any image analysis algorithm is
a digital image, which does not need to have the same topological
characteristics as the imaged real world, it is important to know, which
shapes can be digitized without change of such topological properties.
Most existing approaches do not take into account the unavoidable blurring
in real image acquisition systems or use extremely simplified and thus
unrealistic models of digitization with blurring. In some previous work
we showed that certain shapes can be digitized topologically correctly with
a square grid when some blurring with an arbitrary non-negative radially
symmetric point spread function is involved. Now we extend this result to
other common sampling grids in the two and even in the three dimensional
space, including hexagonal, bcc and fcc grids.
-
U. Köthe:
- Low-level Feature Detection Using the Boundary Tensor,
in: J. Weickert, H. Hagen (Eds.): Visualization and Processing of Tensor Fields, Series on Mathematics and Visualization, pp. 63-79, Berlin: Springer, 2006 (note: this article is © Springer-Verlag)
Abstract |
PDF
Tensors are a useful tool for the detection of low-level features such as edges, lines, corners, and junctions because they can represent feature strength and orientation in a way that is easy to work with. However, traditional approaches to define feature tensors have a number of disadvantages. By means of the first and second order Riesz transforms, we propose a new approach called the boundary tensor. Using quadratic convolution equations, we show that the boundary tensor overcomes some problems of the older tensor definitions. When the Riesz transform is combined with the Laplacian of Gaussian, the boundary tensor can be efficiently computed in the spatial domain. The usefulness of the new method is demonstrated for a number of application examples.
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G. Kedenburg, C. Cocosco, U. Köthe, W. Niessen, E. Vonken, M. Viergever:
- Automatic cardiac MRI myocardium segmentation using graphcut,
in: J. Reinhardt, J. Pluim (Eds.): Proc. Medical Imaging 2006: Image Processing, SPIE vol. 6144, pp. 85-96, 2006
Abstract |
PDF
Segmentation of the left myocardium in four-dimensional (space-time) cardiac MRI data sets is a prerequisite of many diagnostic tasks. We propose a fully automatic method based on global minimization of an energy functional by means of the graphcut algorithm. Starting from automatically obtained segmentations of the left and right ventricles and a cardiac region of interest, a spatial model is constructed using simple and plausible assumptions. This model is used to learn the appearance of different tissue types by non parametric robust estimation. Our method does not require previously trained shape or appearance models. Processing takes 30-40s on current hardware. We evaluated our method on 11 clinical cardiac MRI data sets acquired using cine balanced fast field echo. Linear regression of the automatically segmented myocardium volume against manual segmentations (performed by a radiologist) showed an RMS error of about 12ml.
-
H. Meine, U. Köthe:
- Image Segmentation with the Exact Watershed Transform,
in: J.J. Villanueva (Ed.): VIIP 2005, Proc. 5th IASTED International Conference on Visualization, Imaging, and Image Processing, pp. 400-405, ACTA Press, 2005. (note: this article is © ACTA Press)
Abstract |
PDF
Discrete algorithms for low-level boundary detection are
geometrically inaccurate and topologically unreliable. Corresponding
continuous methods are often more accurate
and need fewer or no heuristics. Thus, we transfer discrete
boundary indicators into a continuous form by means of
differentiable spline interpolation and detect boundaries using
the exact watershed transform. We demonstrate that this
significantly improves the obtained segmentations.
-
U. Köthe, M. Felsberg:
- Riesz-Transforms Versus Derivatives: On the Relationship Between the Boundary Tensor and the Energy Tensor,
in: R. Kimmel, N. Sochen, J. Weickert (Eds.): Scale Space and PDE Methods in Computer Vision, Proc. Scale-Space 2005, Lecture Notes in Computer Science 3459, pp. 179-191, Berlin: Springer, 2005. (note: this article is © Springer-Verlag)
Abstract |
PDF
Traditionally, quadrature filters and derivatives have been considered as alternative approaches to low-level image analysis. In this paper we show that there actually exist close connections: We define the quadrature-based boundary tensor and the derivative-based gradient energy tensor which exhibit very similar behavior. We analyse the reason for this and determine how to minimize the difference. These insights lead to a simple and very efficient integrated feature detection algorithm.
-
M. Felsberg, U. Köthe:
- GET: The Connection Between Monogenic Scale-Space and Gaussian Derivatives,
in: R. Kimmel, N. Sochen, J. Weickert (Eds.): Scale Space and PDE Methods in Computer Vision, Proc. Scale-Space 2005, Lecture Notes in Computer Science 3459, pp. 192-203, Berlin: Springer, 2005. (note: this article is © Springer-Verlag)
Abstract |
PDF
In this paper we propose a new operator which combines advantages of monogenic scale-space and Gaussian scale-space, of the monogenic signal and the structure tensor. The gradient energy tensor (GET) defined in this paper is based on Gaussian derivatives up to third order using different scales. These filters are commonly available, separable, and have an optimal uncertainty. The response of this new operator can be used like the monogenic signal to estimate the local amplitude, the local phase, and the local orientation of an image, but it also allows to measure the coherence of image regions as in the case of the structure tensor. Both theoretically and in experiments the new approach compares favourably with existing methods.
-
H. Meine, U. Köthe:
- The GeoMap: A Unified Representation for Topology and Geometry,
in: L. Brun, M. Vento (Eds.): Graph-Based Representations in Pattern Recognition, Proc. GbR 2005, Lecture Notes in Computer Science 3434, pp. 132-141, Berlin: Springer, 2005. (note: this article is © Springer-Verlag)
Abstract |
PDF
We propose the GeoMap abstract data type as a unified representation for image segmentation purposes. It manages both topology (based on XPMaps) and pixel-based information, and its interface is carefully designed to support a variety of automatic and interactive segmentation methods. We have successfully used the abstract concept of a GeoMap as a foundation for the implementation of well-known segmentation methods.
-
P.Stelldinger, U. Köthe:
- Shape Preserving Digitization of Binary Images After Blurring,
in: E. Andres, G. Damiand, P. Lienhardt (Eds.): Discrete Geometry for Computer Imagery, Proc. DGCI 2005, Lecture Notes in Computer Science 3429, pp. 383-391, Berlin: Springer, 2005. (note: this article is © Springer-Verlag)
Abstract |
PDF
Topology is a fundamental property of shapes in pictures. Since the input for any image analysis algorithm is a digital image, which does not need to have the same topological characteristics as the imaged real world, it is important to know, which shapes can be digitized without topological changes. Most existing approaches do not take into account the unavoidable blurring in real image acquisition systems or use extremely simplified and thus unrealistic models of digitization with blurring. In case of the mostly used square grids we show which binary images can be digitized topologically correctly after blurring with an arbitrary non-negative radially symmetric point spread function, which is an important step forward to real digitization.
-
P. Stelldinger, U. Köthe:
- Towards a general sampling theory for shape preservation,
Image and Vision Computing,
Special Issue on Discrete Geometry for Computer Vision, Volume 23, Issue 2, Pages 237-248, 1 February 2005. (note: this article is © Elsevier B.V.)
Abstract | official Elsevier page | PDF format
Computerized image analysis makes statements about the continuous world by looking at a discrete representation. Therefore, it is important to know precisely which information is preserved during digitization. We analyze this question in the context of shape recognition. Existing results in this area are based on very restricted models and thus not applicable to real imaging situations. We present generalizations in several directions: first, we introduce a new shape similarity measure that approximates human perception better. Second, we prove a geometric sampling theorem for arbitrary dimensional spaces. Third, we extend our sampling theorem to two-dimensional images that are subjected to blurring by a disk point spread function. Our findings are steps towards a general sampling theory for shapes that shall ultimately describe the behavior of real optical systems.
This article brings together and extends the conference papers "Shape Preserving Digitization of Ideal and Blurred Binary Images" and "Shape Preservation During Digitization: Tight Bounds Based on the Morphing Distance".
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U. Köthe:
- Boundary Characterization within the Wedge-Channel Representation ,
in: B. Jähne, R. Mester, E. Barth, H. Scharr (Eds.): Complex Motion, Proc. of
1st International Workshop on Complex Motion, Günzburg 2004, Lecture Notes in Computer Science 3417, pp. 42-53, Berlin: Springer, 2004. (note: this article is © Springer-Verlag)
Abstract |
PDF
Junctions play an important role in motion analysis. Approaches based on the structure tensor have become the standard for junction detection. However, the structure tensor is not able to classify junctions into different types (L, T, Y, X etc.). We propose to solve this problem by the wedge channel representation. It is based on the same computational steps as used for the (anisotropic) structure tensor, but stores results into channel vectors rather than tensors. Due to one-sided channel smoothing, these channel vectors not only represent edge orientation (as existing channel approaches do) but edge direction. Thus junctions cannot only be detected, but also fully characterized.
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U. Köthe:
- Accurate and Efficient Approximation of the Continuous Gaussian Scale-Space,
in: C.E. Rasmussen, H. Bülthoff, M. Giese, B. Schölkopf (Eds.): Pattern Recognition, Proc. of 26th DAGM Symposium, Tübingen 2004, Lecture Notes in Computer Science 3175, pp. 350-358, Berlin: Springer, 2004. (note: this article is © Springer-Verlag)
Abstract |
PDF
The Gaussian scale-space is a standard tool in image analysis. While continuous in theory, it is generally realized with fixed regular grids in practice. This prevents the use of algorithms which require continuous and differentiable data and adaptive step size control, such as numerical path following. We propose an efficient continuous approximation of the Gaussian scale-space that removes this restriction and opens up new ways to subpixel feature detection and scale adaptation.
-
H. Meine, U. Köthe, H.S. Stiehl:
- Fast and Accurate Interactive Image Segmentation in the GeoMap Framework,
in: T. Tolxdorff, J. Braun, H. Handels, A. Horsch, H.-P. Meinzer (Eds.): Proc. Bildverarbeitung für die Medizin 2004, pp. 60-64, Berlin: Springer, 2004. (note: this article is © Springer-Verlag)
Abstract |
PDF
Although many interactive segmentation methods exists, none
can be considered a silver bullet for all clinical tasks. Moreover, incompatible data representations prevent multiple algorithms from being combined as desired. We propose the GeoMap as a unified representation
for segmentation results and illustrate how it facilitates the design of
an integrated framework for interactive medical image analysis. Results
show the high flexibility and performance of the new framework.
-
U. Köthe:
- Integrated Edge and Junction Detection with the Boundary Tensor,
in: ICCV 03, Proc. of 9th Intl. Conf. on Computer Vision, Nice 2003, vol. 1, pp. 424-431, Los Alamitos: IEEE Computer Society, 2003. (note: this article is © IEEE)
Abstract |
PDF
The boundaries of image regions necessarily consist of
edges (in particular, step and roof edges), corners, and
junctions. Currently, different algorithms are used to detect
each boundary type separately, but the integration of
the results into a single boundary representation is difficult.
Therefore, a method for the simultaneous detection of all
boundary types is needed. We propose to combine responses
of suitable polar separable filters into what we will call the
boundary tensor. The trace of this tensor is a measure of
boundary strength, while the small eigenvalue and its difference
to the large one represent corner/junction and edge
strengths respectively. We prove that the edge strength measure
behaves like a rotationally invariant quadrature filter.
A number of examples demonstrate the properties of the new
method and illustrate its application to image segmentation.
-
U. Köthe:
- Edge and Junction Detection with an Improved Structure Tensor,
in: B. Michaelis, G. Krell (Eds.): Pattern Recognition, Proc. of 25th DAGM Symposium, Magdeburg 2003, Lecture Notes in Computer Science 2781, pp. 25-32, Berlin: Springer, 2003. (note: this article is © Springer-Verlag)
Abstract |
PDF
Awarded the main prize of the German Pattern Recognition Society (DAGM) 2003
We describe three modifications to the structure tensor approach
to lowlevel feature extraction. We first show that the structure
tensor must be represented at a higher resolution than the original image.
Second, we propose a nonlinear filter for structure tensor computation
that avoids undesirable blurring. Third, we introduce a method to
simultaneously extract edge and junction information. Examples demonstrate
significant improvements in the quality of the extracted features.
-
U. Köthe, P. Stelldinger:
- Shape Preserving Digitization of Ideal and Blurred Binary Images,
in: I. Nyström, G. Sanniti di Baja, S. Svensson (Eds.): Discrete Geometry for Computer Imagery, Proc. of 11th DGCI Conference, Naples 2003, Lecture Notes in Computer Science 2886, pp. 82-91, Berlin: Springer, 2003. (note: this article is © Springer-Verlag)
Abstract | PDF
In order to make image analysis methods more reliable it
is important to analyse to what extend shape information is preserved
during image digitization. Most existing approaches to this problem consider
topology preservation and are restricted to ideal binary images. We
extend these results in two ways. First, we characterize the set of binary
images which can be correctly digitized by both regular and irregular
sampling grids, such that not only topology is preserved but also the
Hausdorff distance between the original image and the reconstruction is
bounded. Second, we prove an analogous theorem for gray scale images
that arise from blurring of binary images with a certain filter type. These
results are steps towards a theory of shape digitization applicable to real
optical systems.
-
P. Stelldinger, U. Köthe:
- Shape Preservation During Digitization: Tight Bounds Based on the Morphing Distance,
in: B. Michaelis, G. Krell (Eds.): Pattern Recognition, Proc. of 25th DAGM Symposium, Magdeburg 2003, Lecture Notes in Computer Science 2781, pp. 108-115, Berlin: Springer, 2003. (note: this article is © Springer-Verlag)
(this paper builds on the DGCI paper above)
Abstract | PDF
We define strong rsimilarity and the morphing distance to
bound geometric distortions between shapes of equal topology. We then
derive a necessary and su#cient condition for a set and its digitizations
to be rsimilar, regardless of the sampling grid. We also extend these
results to certain gray scale images. Our findings are steps towards a
theory of shape digitization for real optical systems.
This paper builds on the paper "Shape Preserving Digitization of Ideal and Blurred Binary Images" which should be read before.
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U. Köthe:
- Deriving Topological Representations from Edge Images,
in: T. Asano, R. Klette, C. Ronse (Eds.): Geometry, Morphology, and Computational Imaging, 11th Intl. Workshop on Theoretical Foundations of Computer Vision, Lecture Notes in Computer Science 2616, pp. 320-334, Berlin: Springer, 2003. (note: this article is © Springer-Verlag)
Abstract | PDF
In order to guarantee consistent descriptions of image structure, it is
desirable to base such descriptions on topological principles. Thus, we
want to be able to derive topological representations from segmented
images. This paper discusses two methods to achieve this goal by means of
the recently introduced XPMaps. First, it improves an existing algorithm
that derives topological representations from region images and crack
edges, and second, it presents a new algorithm that can be applied to
standard 8-connected edge images.
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U. Köthe:
- XPMaps and Topological Segmentation - a Unified Approach to Finite Topologies in the Plane,
in: A. Braquelaire, J.-O. Lachaud, A. Vialard (Eds.): Proc. of 10th International Conference on Discrete Geometry for Computer Imagery (DGCI 2002), Lecture Notes in Computer Science 2301, pp. 22-33, Berlin: Springer, 2002. (note: this article is © Springer-Verlag)
Abstract | PDF
Long version with proofs: Technical Report FBI-HH-M-308/01, Department of Informatics, University of Hamburg, December 2001 (PDF)
Finite topological spaces are now widely recognized as a valuable
tool of image analysis. However, their practical application is complicated
because there are so many different approaches. We show that there are
close relationships between those approaches which motivate the
introduction of XPMaps as a concept that subsumes the important
characteristics of the other approaches. The notion of topological
segmentations then extends this concept to a particular class of labelings
of XPMaps. We show that the new notions lead to significant simplifications
from both a theoretical and practical viewpoint.
-
U. Köthe:
- Local Appropriate Scale in Morphological Scale-Space,
in: B. Buxton, R. Cipolla (Eds.): Computer Vision, Proc. of 4th European
Conference on Computer Vision, vol. 1, Lecture Notes in Computer Science 1064, pp. 219-228, Berlin: Springer, 1996. (note: this article is © Springer-Verlag)
Abstract | PDF
Long version with proofs: Fraunhofer IGD Technical Report 96i001-FEGD, 1996. (PDF)
This paper presents a novel approach to selecting appropriate scales
for region detection prior to feature localization. We develop and
formalize a number of requirements that should be fulfilled by such an
appropriate scale operator and show by theoretical considerations and
experiments that a morphological opening-closing scale-space meets
these requirements better than Gaussian scale-space.
As a prerequisite for appropriate scale measurements we generalize
morphological decomposition methods and introduce a morphological
band-pass filter. It decomposes an image into structures of different
size and different curvature polarity ("light and dark blobs"). It may
thus be seen as a morphological analogy to the important Laplacian of
Gaussian operator. The local appropriate scale is than defined as the
scale that maximizes the response of the band-pass filter at each point.
This operator has a number of interesting properties. Most notably it
gives constant scale values in a region of constant width, and its zero-
crossings coincide with local maxima of the gradient magnitudes.
Some example applications show that the new operator is very useful to tune subsequent operators towards optimal scales.
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U. Köthe:
- Morphological Appropriate Scale Measurements for Region
Segmentation,
in: P. Johansen (ed.): Proc. of Copenhagen WS on Gaussian
Scale-Space Theory, U of Copenhagen, Dept. of Computer Science,
Technical Report Nr. 96/19, 1996.
Abstract | PDF
This paper presents a novel approach to selecting appropriate scales in
morphological openingclosing scalespace. It is based on a morphological
bandpass filter that decomposes an image into structures of different size
and different curvature polarity ("light and dark blobs"). Appropriate
scale is defined as the scale that maximizes the response of the bandpass.
The resulting scale measurements allow to automatically select window
sizes (scales) for segmentation operators. The application of this idea to
region segmentation gives very satisfying results.
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U. Köthe:
- Parameterfreie Merkmalsextraktion durch automatische
Skalenselektion,
in: F. K. List (Hrsg.): Vorträge
16. Wissenschaftlich-Technische Jahrestagung der Deutschen Gesellschaft
für Photogrammetrie und Fernerkundung 1996, Publikationen der
Deutschen Gesellschaft für Photogrammetrie und Fernerkundung, Band 5,
pp. 29-36, 1997. (in German)
Abstract | PDF
Der vorliegende Artikel diskutiert Möglichkeiten, parameterfreie Merkmalsdetektoren zu definieren, indem diese mit einem Mechanismus zur
Selektion optimaler Skalen in einem geeigneten Skalenraum kombiniert werden. Als
optimale Skala wird dabei für jedes Pixel diejenige Skala gewählt, die ein geeignetes Auffälligkeitsmaß maximiert. Verschiedene Beispiele zeigen die sehr interessanten Eigenschaften dieser neuen Technik.
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U. Köthe:
- Inhaltsbasierte Suche in Bilddatenbanken,
Forschungsbericht 95i004-FEGD, Fraunhofer Institute for Computer Graphics Rostock, Joachim-Jungius-Str. 9, 18059 Rostock, Germany, 1995. (in German)
Abstract | PDF
Der vorliegende Artikel beschäftigt sich mit einer neuen Art intelligenter
Informationssysteme, den Bilddatenbanken mit inhaltsbasierter Suchoption. Die inhaltsbasierte Suche gilt als vielversprechender Lösungsansatz für das Finden relevanter Daten in großen Datenbeständen. Die grundlegenden Konzepte in Bezug auf Bilddatenbanken werden beschrieben und anhand eines Modellbeispiels, einer Datenbank mit Brillengestellen, überprüft. Es zeigt sich, daß der Nutzen von inhaltsbasierter Suche entscheidend davon abhängt, daß das Retrievalsystem ähnliche Suchkriterien anwendet wie der Mensch. Aufgrund einfacher Experimente werden geeignete Kriterien, die auf Richtungshistogrammen und Skelettlinien beruhen, identifiziert. Die experimentelle Evaluierung des darauf aufbauenden Demonstrationssystems zeigt eine gute Übereinstimmung der Suchergebnisse mit den Erwartungen des Nutzers.
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U. Köthe:
- Primary Image Segmentation,
in: G. Sagerer, S. Posch, F. Kummert (Hrsg.): Mustererkennung 1995, 17. DAGM-Symposium, pp. 554-561, Berlin: Springer, 1995. (note: this article is © Springer-Verlag)
Abstract | PDF
This paper introduces the notion of primary image segmentation which serves as a well defined link between low- and high-level image analysis. A general algorithmic framework based on priority queues is proposed that allows for the integration of a variety of different segmentation algorithms. A seeded region growing approach, along with a number of improved seed selection methods and foveation of critical areas, is chosen to realize this framework. Experimental evaluation shows very good performance of these algorithms on a relatively large number of outdoor photographs without the need to adjust parameters.
