| 1. |
- Chanussot, Jocelyn, et al.
(författare)
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Shape signaturs of fuzzy star-shaped sets based on distance from the centroid
- 2005
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Ingår i: Pattern Recognition Letters. - : Elsevier. - 0167-8655. ; 26:6, s. 735-746
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Tidskriftsartikel (refereegranskat)abstract
- We extend the shape signature based on the distance of the boundary points from the shape centroid, to the case of fuzzy sets. The analysis of the transition from crisp to fuzzy shape descriptor is first given in the continuous case. This is followed by a study of the specific issues induced by the discrete representation of the objects in a computer.We analyze two methods for calculating the signature of a fuzzy shape, derived from two ways of defining a fuzzy set: first, by its membership function, and second, as a stack of its α-cuts. The first approach is based on measuring the length of a fuzzy straight line by integration of the fuzzy membership function, while in the second one we use averaging of the shape signatures obtained for the individual α-cuts of the fuzzy set. The two methods, equivalent in the continuous case for the studied class of fuzzy shapes, produce different results when adjusted to the discrete case. A statistical study, aiming at characterizing the performances of each method in the discrete case, is done. Both methods are shown to provide more precise descriptions than their corresponding crisp versions. The second method (based on averaged Euclidean distance over the α-cuts) outperforms the others.
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| 2. |
- Lindblad, Joakim, et al.
(författare)
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Defuzzification by Feature Distance Minimization Based on DC Programming
- 2007
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Ingår i: 5th International Symposium on Image and Signal Processing and Analysis, 2007. - 9789531841160 ; , s. 373-378
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Konferensbidrag (refereegranskat)abstract
- We introduce the use of DC programming, in combination with convex-concave regularization, as a deterministic approach for solving the optimization problem imposed by defuzzification by feature distance minimization. We provide a DC based algorithm for finding a solution to the defuzzification problem by expressing the objective function as a difference of two convex functions and iteratively solving a family of DC programs. We compare the performance with the previously recommended method, simulated annealing, on a number of test images. Encouraging results, together with several advantages of the DC based method, approve use of this approach, and motivate its further exploration.
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| 3. |
- Lindblad, Joakim, et al.
(författare)
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Feature Based Defuzzification at Increased Spatial Resolution
- 2006
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Ingår i: Combinatorial Image Analysis. - Berlin, Heidelberg : Springer Berlin Heidelberg. - 9783540351535 ; , s. 131-143
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Konferensbidrag (refereegranskat)abstract
- Defuzzification of fuzzy spatial sets by feature distance minimization, recently proposed as an alternative to crisp segmentation, is studied further. Fully utilizing information available in a fuzzy (discrete) representation of a continuous shape, we present an improved defuzzification method, such that the crisp discrete representation of a fuzzy set is generated at an increased spatial resolution, compared to the resolution of the fuzzy set. The correspondence between a fuzzy and a crisp set is established through a distance between their representations based on selected features, where the different resolutions of the images to compare are taken into account. The performance of the method is tested on both synthetic and real images.
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| 4. |
- Lindblad, Joakim, et al.
(författare)
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Feature Based Defuzzification in Z² and Z³ Using a Scale Space Approach
- 2006
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Ingår i: Discrete Geometry for Computer Imagery 13th International Conference, DGCI 2006, Szeged, Hungary, October 25-27, 2006. Proceedings. - Berlin, Heidelberg : Springer Berlin Heidelberg. - 9783540476511 ; , s. 379-390
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Konferensbidrag (refereegranskat)abstract
- A defuzzification method based on feature distance minimization is further improved by incorporating into the distance function feature values measured on object representations at different scales. It is noticed that such an approach can improve defuzzification results by better preserving the properties of a fuzzy set; area preservation at scales in-between local (pixel-size) and global (the whole object) provides that characteristics of the fuzzy object are more appropriately exhibited in the defuzzification. For the purpose of comparing sets of different resolution, we propose a feature vector representation of a (fuzzy and crisp) set, utilizing a resolution pyramid. The distance measure is accordingly adjusted. The defuzzification method is extended to the 3D case. Illustrative examples are given.
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| 5. |
- Lindblad, Joakim, 1973-, et al.
(författare)
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Improved Quantification of Bone Remodelling by Utilizing Fuzzy Based Segmentation
- 2009
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Ingår i: Image Analysis. - Berlin : Springer Verlag. - 9783642022296 ; 5575, s. 750-759
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Konferensbidrag (refereegranskat)abstract
- We present a novel fuzzy theory based method for the segmentation of images required in histomorphometrical investigations of bone implant integration. The suggested method combines discriminant analysis classification controlled by an introduced uncertainty measure, and fuzzy connectedness segmentation method, so that the former is used for automatic seeding of the later. A thorough evaluation of the proposed segmentation method is performed. Comparison with previously published automatically obtained measurements, as well as with manually obtained ones, is presented. The proposed method improves the segmentation and, consequently, the accuracy of the automatic measurements, while keeping advantages with respect to the manual ones, by being fast, repeatable, and objective.
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| 6. |
- Lindblad, Joakim, et al.
(författare)
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On set distances and their application to image registration
- 2009
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Ingår i: Proc. 6th International Symposium on Image and Signal Processing and Analysis. - Salzburg, Austria : IEEE. - 9789531841351 ; , s. 449-454
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Konferensbidrag (refereegranskat)abstract
- In this paper we study set distances that are used in image processing. We propose a generalization of Sum of minimal distances and show that its special cases include a metric by Symmetric difference. The Hausdorff metric and the Chamfer matching distances are also closely related with the presented framework. In addition, we define the Complement set distance of a given distance. We evaluate the observed distance with respect to applicability to image object registration. We perform comparative evaluations with respect to noise sensitivity, as well as with respect to rigid body transformations. We conclude that the family of Generalized sum of minimal distances has many desirable properties for this application.
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| 7. |
- Lukic, Tibor, et al.
(författare)
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Deterministic Defuzzification based on Spectral Projected Gradient Optimization
- 2008
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Ingår i: 30th Symposium of the German Association for Pattern Recognition (DAGM). - Berlin / Heidelberg : Springer. - 9783540693208 ; , s. 476-485
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Konferensbidrag (refereegranskat)abstract
- We apply deterministic optimization based on Spectral Projected Gradient method in combination with concave regularization to solve the minimization problem imposed by defuzzification by feature distance minimization. We compare the performance of the proposed algorithm with the methods previously recommended for the same task, (non-deterministic) simulated annealing and (deterministic) DC based algorithm. The evaluation, including numerical tests performed on synthetic and real images, shows advantages of the new method in terms of speed and flexibility regarding inclusion of additional features in defuzzification. Its relatively low memory requirements allow the application of the suggested method for defuzzification of 3D objects.
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| 8. |
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| 9. |
- Sladoje, Natasa, et al.
(författare)
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Estimation of moments of digitized objects with fuzzy borders
- 2005
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Ingår i: Proc. of 13th International Conference on Image Analysis and Processing. - Berlin, Heidelberg : Springer. - 9783540318668 ; , s. 188-195
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Konferensbidrag (refereegranskat)abstract
- Error bounds for estimation of moments from a fuzzy representation of a shape are derived, and compared with estimations from a crisp representation. It is shown that a fuzzy membership function based on the pixel area coverage provides higher accuracy of the estimates, compared to binary Gauss digitization at the same spatial image resolution. Theoretical results are confirmed by a statistical study of disks and squares, where the moments of the shape, up to order two, are estimated from its fuzzy discrete representation. The errors of the estimates decrease both with increased size of a shape (spatial resolution) and increased membership resolution (number of available grey-levels).
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| 10. |
- Sladoje, Natasa, et al.
(författare)
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High-precision boundary length estimation by utilizing gray-level information
- 2009
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Ingår i: IEEE Transactions on Pattern Analysis and Machine Intelligence. - 0162-8828 .- 1939-3539. ; 31:2, s. 357-363
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Tidskriftsartikel (refereegranskat)abstract
- We present a novel method that provides an accurate and precise estimate of the length of the boundary (perimeter) of an object by taking into account gray levels on the boundary of the digitization of the same object. Assuming a model where pixel intensity is proportional to the coverage of a pixel, we show that the presented method provides error-free measurements of the length of straight boundary segments in the case of nonquantized pixel values. For a more realistic situation, where pixel values are quantized, we derive optimal estimates that minimize the maximal estimation error. We show that the estimate converges toward a correct value as the number of gray levels tends toward infinity. The method is easy to implement; we provide the complete pseudocode. Since the method utilizes only a small neighborhood, it is very easy to parallelize. We evaluate the estimator on a set of concave and convex shapes with known perimeters, digitized at increasing resolution. In addition, we provide an example of applicability of the method on real images, by suggesting appropriate preprocessing steps and presenting results of a comparison of the suggested method with other local approaches.
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| 11. |
- Sladoje, Natasa, et al.
(författare)
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Measurements of digitized objects with fuzzy borders in 2D and 3D
- 2005
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Ingår i: Image and Vision Computing. - : Elsevier BV. - 0262-8856. ; 23:2, s. 123-132
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Tidskriftsartikel (refereegranskat)abstract
- The results of our investigation of several measurements on digitized 2D and 3D objects with fuzzy borders are presented. The performance of surface area, volume, and roundness measure estimators for digitized balls with fuzzy borders is analyzed. The method we suggest provides significant improvement in precision, compared to analogous estimation results obtained on a crisp (hard) segmentation, especially in the case of low resolution images.
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| 12. |
- Sladoje, Natasa, et al.
(författare)
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Perimeter estimation based on grey level object representation
- 2008
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We present a novel method that provides an accurate and precise estimate of the length of the boundary (perimeter) of an object, by taking into account gray-levels on the boundary of the digitization of the same object. Assuming a model where pixel intensity is proportional to the coverage of a pixel, we show that the presented method provides error-free measurements of the length of straight boundary segments in the case of non-quantized pixel values. For a more realistic situation, where pixel values are quantized, we derive optimal estimates that minimize the maximal estimation error. We show that the estimate converges toward a correct value as the number of gray-levels tends toward infinity. The method is easy to implement; we provide complete pseudo-code. Since the method utilizes only a small neighborhood, it is very easy to parallelize. We evaluate the estimator on a set of concave and convex shapes with known perimeters, digitized at increasing resolution.
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| 13. |
- Sladoje, Natasa, et al.
(författare)
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Pixel Coverage Segmentation for Improved Feature Estimation
- 2009
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Ingår i: 15th International Conference on Image Analysis and Processing. - Berlin / Heidelberg : Springer. - 9783642041457 ; 5716, s. 929-938
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Konferensbidrag (refereegranskat)abstract
- By utilizing intensity information available in images, partial coverage of pixels at object borders can be estimated. Such information can, in turn, provide more precise feature estimates. We present a pixel coverage segmentation method which assigns pixel values corresponding to the area of a pixel that is covered by the imaged object(s). Starting from any suitable crisp segmentation, we extract a one-pixel thin 4-connected boundary between the observed image components where a local linear mixture model is used for estimating fractional pixel coverage values. We evaluate the presented segmentation method, as well as its usefulness for subsequent precise feature estimation, on synthetic test objects with increasing levels of noise added. We conclude that for reasonable noise levels the presented method outperforms the achievable results of a perfect crisp segmentation. Finally, we illustrate the application of the suggested method on a real histological colour image.
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| 14. |
- Sladoje, Natasa, et al.
(författare)
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Representation and Reconstruction of Fuzzy Disks by Moments
- 2007
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Ingår i: Fuzzy sets and systems (Print). - : Elsevier BV. - 0165-0114 .- 1872-6801. ; 158:5, s. 517-534
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we analyze the representation and reconstruction of fuzzy disks by using moments. Both continuous and digital fuzzy disks are considered. A fuzzy disk is a convex fuzzy spatial set, where the membership of a point to the fuzzy disk depends only on the distance of the point to the centre of the disk. We show that, for a certain class of membership functions defining a fuzzy disk, there exists a one-to-one correspondence between the set of fuzzy disks and the set of their generalized moment representations. Theoretical error bounds for the accuracy of the estimation of generalized moments of a continuous fuzzy disk from the generalized moments of its digitization and, in connection with that, the accuracy of an approximate reconstruction of a continuous fuzzy disk from the generalized moments of its digitization, are derived. Defuzzification (reduction of a continuous fuzzy disk to a crisp representative) is also considered. A statistical study of generated synthetic objects complements the theoretical results.
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| 15. |
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| 16. |
- Tanács, Attila, et al.
(författare)
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Recovering Affine Deformations of Fuzzy Shapes
- 2009
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Ingår i: 16th Scandinavian Conference on Image Analysis. - Berlin / Heidelberg : Springer. - 9783642022296 ; , s. 735-744, s. 735-744
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Konferensbidrag (refereegranskat)abstract
- Fuzzy sets and fuzzy techniques are attracting increasing attention nowadays in the field of image processing and analysis. It has been shown that the information preserved by using fuzzy representation based on area coverage may be successfully utilized to improve precision and accuracy of several shape descriptors; geometric moments of a shape are among them. We propose to extend an existing binary shape matching method to take advantage of fuzzy object representation. The result of a synthetic test show that fuzzy representation yields smaller registration errors in average. A segmentation method is also presented to generate fuzzy segmentations of real images. The applicability of the proposed methods is demonstrated on real X-ray images of hip replacement implants.
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