| 1. |
- Asplund, Teo, et al.
(författare)
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A Faster, Unbiased Path Opening by Upper Skeletonization and Weighted Adjacency Graphs
- 2016
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Ingår i: IEEE Transactions on Image Processing. - 1057-7149 .- 1941-0042. ; 25:12, s. 5589-5600
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Tidskriftsartikel (refereegranskat)abstract
- The path opening is a filter that preserves bright regions in the image in which a path of a certain length L fits. A path is a (not necessarily straight) line defined by a specific adjacency relation. The most efficient implementation known scales as O(min(L, d, Q)N) with the length of the path, L, the maximum possible path length, d, the number of graylevels, Q, and the image size, N. An approximation exists (parsimonious path opening) that has an execution time independent of path length. This is achieved by preselecting paths, and applying 1D openings along these paths. However, the preselected paths can miss important structures, as described by its authors. Here, we propose a different approximation, in which we preselect paths using a grayvalue skeleton. The skeleton follows all ridges in the image, meaning that no important line structures will be missed. An H-minima transform simplifies the image to reduce the number of branches in the skeleton. A graph-based version of the traditional path opening operates only on the pixels in the skeleton, yielding speedups up to one order of magnitude, depending on image size and filter parameters. The edges of the graph are weighted in order to minimize bias. Experiments show that the proposed algorithm scales linearly with image size, and that it is often slightly faster for longer paths than for shorter paths. The algorithm also yields the most accurate results- as compared with a number of path opening variants-when measuring length distributions.
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| 2. |
- Asplund, Teo, et al.
(författare)
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A new approach to mathematical morphology on one dimensional sampled signals
- 2016
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Ingår i: Proceedings of the 23rd International Conference on Pattern Recognition ICPR 2016. - Piscataway, NJ : IEEE Communications Society. - 9781509048472 ; , s. 3904-3909
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Konferensbidrag (refereegranskat)abstract
- We present a new approach to approximate continuous-domain mathematical morphology operators. The approach is applicable to irregularly sampled signals. We define a dilation under this new approach, where samples are duplicated and shifted according to the flat, continuous structuring element. We define the erosion by adjunction, and the opening and closing by composition. These new operators will significantly increase precision in image measurements. Experiments show that these operators indeed approximate continuous-domain operators better than the standard operators on sampled one-dimensional signals, and that they may be applied to signals using structuring elements smaller than the distance between samples. We also show that we can apply the operators to scan lines of a two-dimensional image to filter horizontal and vertical linear structures.
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| 3. |
- Asplund, Teo, et al.
(författare)
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Adaptive Mathematical Morphology on Irregularly Sampled Signals in Two Dimensions
- 2020
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Ingår i: Mathematical Morphology : Theory and Applications. - : Walter de Gruyter. - 2353-3390. ; 4:1, s. 108-126
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Tidskriftsartikel (refereegranskat)abstract
- This paper proposes a way of better approximating continuous, two-dimensional morphologyin the discrete domain, by allowing for irregularly sampled input and output signals. We generalizeprevious work to allow for a greater variety of structuring elements, both flat and non-flat. Experimentallywe show improved results over regular, discrete morphology with respect to the approximation ofcontinuous morphology. It is also worth noting that the number of output samples can often be reducedwithout sacrificing the quality of the approximation, since the morphological operators usually generateoutput signals with many plateaus, which, intuitively do not need a large number of samples to be correctlyrepresented. Finally, the paper presents some results showing adaptive morphology on irregularlysampled signals.
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| 4. |
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| 5. |
- Asplund, Teo, et al.
(författare)
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Mathematical Morphology on Irregularly Sampled Data Applied to Segmentation of 3D Point Clouds of Urban Scenes
- 2019
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Ingår i: International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing. - Cham : Springer Nature. - 9783030208660 - 9783030208677
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Konferensbidrag (refereegranskat)abstract
- This paper proposes an extension of mathematical morphology on irregularly sampled signals to 3D point clouds. The proposed method is applied to the segmentation of urban scenes to show its applicability to the analysis of point cloud data. Applying the proposed operators has the desirable side-effect of homogenizing signals that are sampled heterogeneously. In experiments we show that the proposed segmentation algorithm yields good results on the Paris-rue-Madame database and is robust in terms of sampling density, i.e. yielding similar labelings for more sparse samplings of the same scene.
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| 6. |
- Asplund, Teo, et al.
(författare)
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Mathematical Morphology on Irregularly Sampled Data in One Dimension
- 2017
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Ingår i: Mathematical Morphology : Theory and Applications. - : Walter de Gruyter. - 2353-3390. ; 2:1, s. 1-24
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Tidskriftsartikel (refereegranskat)abstract
- Mathematical morphology (MM) on grayscale images is commonly performed in the discretedomain on regularly sampled data. However, if the intention is to characterize or quantify continuousdomainobjects, then the discrete-domain morphology is affected by discretization errors that may bealleviated by considering the underlying continuous signal, given a correctly sampled bandlimited image.Additionally, there are a number of applications where MM would be useful and the data is irregularlysampled. A common way to deal with this is to resample the data onto a regular grid. Often this createsproblems where data is interpolated in areas with too few samples. In this paper, an alternative way ofthinking about the morphological operators is presented. This leads to a new type of discrete operatorsthat work on irregularly sampled data. These operators are shown to be morphological operators thatare consistent with the regular, morphological operators under the same conditions, and yield accurateresults under certain conditions where traditional morphology performs poorly
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| 7. |
- Asplund, Teo, et al.
(författare)
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Mathematical Morphology on Irregularly Sampled Signals
- 2017
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Ingår i: Computer Vision – ACCV 2016 Workshops. - Cham : Springer. - 9783319544267 - 9783319544274 ; , s. 506-520
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Konferensbidrag (refereegranskat)abstract
- This paper introduces a new operator that can be used to ap-proximate continuous-domain mathematical morphology on irregularly sampled surfaces. We define a new way of approximating the continuous domain dilation by duplicating and shifting samples according to a flat continuous structuring element. We show that the proposed algorithm can better approximate continuous dilation, and that dilations may be sampled irregularly to achieve a smaller sampling without greatly com-promising the accuracy of the result.
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| 8. |
- Asplund, Teo
(författare)
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Precise Image-Based Measurements through Irregular Sampling
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Mathematical morphology is a theory that is applicable broadly in signal processing, but in this thesis we focus mainly on image data. Fundamental concepts of morphology include the structuring element and the four operators: dilation, erosion, closing, and opening. One way of thinking about the role of the structuring element is as a probe, which traverses the signal (e.g. the image) systematically and inspects how well it "fits" in a certain sense that depends on the operator.Although morphology is defined in the discrete as well as in the continuous domain, often only the discrete case is considered in practice. However, commonly digital images are a representation of continuous reality and thus it is of interest to maintain a correspondence between mathematical morphology operating in the discrete and in the continuous domain. Therefore, much of this thesis investigates how to better approximate continuous morphology in the discrete domain. We present a number of issues relating to this goal when applying morphology in the regular, discrete case, and show that allowing for irregularly sampled signals can improve this approximation, since moving to irregularly sampled signals frees us from constraints (namely those imposed by the sampling lattice) that harm the correspondence in the regular case. The thesis develops a framework for applying morphology in the irregular case, using a wide range of structuring elements, including non-flat structuring elements (or structuring functions) and adaptive morphology. This proposed framework is then shown to better approximate continuous morphology than its regular, discrete counterpart.Additionally, the thesis contains work dealing with regularly sampled images using regular, discrete morphology and weighting to improve results. However, these cases can be interpreted as specific instances of irregularly sampled signals, thus naturally connecting them to the overarching theme of irregular sampling, precise measurements, and mathematical morphology.
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| 9. |
- Bernander, Karl B., et al.
(författare)
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Improving the stochastic watershed
- 2013
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Ingår i: Pattern Recognition Letters. - : Elsevier BV. - 0167-8655 .- 1872-7344. ; 34:9, s. 993-1000
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Tidskriftsartikel (refereegranskat)abstract
- The stochastic watershed is an unsupervised segmentation tool recently proposed by Angulo and Jeulin. By repeated application of the seeded watershed with randomly placed markers, a probability density function for object boundaries is created. In a second step, the algorithm then generates a meaningful segmentation of the image using this probability density function. The method performs best when the image contains regions of similar size, since it tends to break up larger regions and merge smaller ones. We propose two simple modifications that greatly improve the properties of the stochastic watershed: (1) add noise to the input image at every iteration, and (2) distribute the markers using a randomly placed grid. The noise strength is a new parameter to be set, but the output of the algorithm is not very sensitive to this value. In return, the output becomes less sensitive to the two parameters of the standard algorithm. The improved algorithm does not break up larger regions, effectively making the algorithm useful for a larger class of segmentation problems.
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| 10. |
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