| 1. |
- Ardö, Håkan, et al.
(författare)
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Bayesian Formulation of Image Patch Matching Using Cross-correlation
- 2012
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Ingår i: Journal of Mathematical Imaging and Vision. - : Springer Science and Business Media LLC. - 0924-9907 .- 1573-7683. ; 43:1, s. 72-87
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Tidskriftsartikel (refereegranskat)abstract
- A classical solution for matching two image patches is to use the cross-correlation coefficient. This works well if there is a lot of structure within the patches, but not so well if the patches are close to uniform. This means that some patches are matched with more confidence than others. By estimating this uncertainty, more weight can be put on the confident matches than those that are more uncertain. To enable this two distribution functions for two different cases are used: (i) the correlation between two patches showing the same object but with different lighting conditions and different noise realisations and (ii) the correlation between two unrelated patches.Using these two distributions the patch matching problem is, in this paper, formulated as a binary classification problem. The probability of two patches matching is derived. The model depends on the signal to noise ratio. The noise level is reasonably invariant over time, while the signal level, represented by the amount of structure in the patch or its spatial variance, has to be measured for every frame.A common application where this is useful is feature point matching between different images. Another application is background/foreground segmentation. This paper will concentrate on the latter application. It is shown how the theory can be used to implement a very fast background/foreground segmentation algorithm by transforming the calculations to the DCT-domain and processing a motion-JPEG stream without uncompressing it. This allows the algorithm to be embedded on a 150 MHz ARM based network camera. It is also suggested to use recursive quantile estimation to estimate the background model. This gives very accurate background models even if there is a lot of foreground present during the initialisation of the model.
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| 2. |
- Benn, J., et al.
(författare)
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Currents and Finite Elements as Tools for Shape Space
- 2019
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Ingår i: Journal of Mathematical Imaging and Vision. - : Springer Science and Business Media LLC. - 0924-9907 .- 1573-7683. ; 61:8, s. 1197-1220
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Tidskriftsartikel (refereegranskat)abstract
- The nonlinear spaces of shapes (unparameterized immersed curves or submanifolds) are of interest for many applications in image analysis, such as the identification of shapes that are similar modulo the action of some group. In this paper, we study a general representation of shapes as currents, which are based on linear spaces and are suitable for numerical discretization, being robust to noise. We develop the theory of currents for shape spaces by considering both the analytic and numerical aspects of the problem. In particular, we study the analytical properties of the current map and the norm that it induces on shapes. We determine the conditions under which the current determines the shape. We then provide a finite element-based discretization of the currents that is a practical computational tool for shapes. Finally, we demonstrate this approach on a variety of examples.
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| 3. |
- Bergholm, Fredrik, et al.
(författare)
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Analysis of Bias in the Apparent Correlation Coefficient Between Image Pairs Corrupted by Severe Noise
- 2010
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Ingår i: Journal of Mathematical Imaging and Vision. - : Springer Science and Business Media LLC. - 0924-9907 .- 1573-7683. ; 37:3, s. 204-219
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Tidskriftsartikel (refereegranskat)abstract
- The correlation coefficient r is a measure of similarity used to compare regions of interest in image pairs. In fluorescence microscopy there is a basic tradeoff between the degree of image noise and the frequency with which images can be acquired and therefore the ability to follow dynamic events. The correlation coefficient r is commonly used in fluorescence microscopy for colocalization measurements, when the relative distributions of two fluorophores are of interest. Unfortunately, r is known to be biased understating the true correlation when noise is present. A better measure of correlation is needed. This article analyses the expected value of r and comes up with a procedure for evaluating the bias of r, expected value formulas. A Taylor series of so-called invariant factors is analyzed in detail. These formulas indicate ways to correct r and thereby obtain a corrected value free from the influence of noise that is on average accurate (unbiased). One possible correction is the attenuated corrected correlation coefficient R, introduced heuristically by Spearman (in Am. J. Psychol. 15:72-101, 1904). An ideal correction formula in terms of expected values is derived. For large samples R tends towards the ideal correction formula and the true noise-free correlation. Correlation measurements using simulation based on the types of noise found in fluorescence microscopy images illustrate both the power of the method and the variance of R. We conclude that the correction formula is valid and is particularly useful for making correct analyses from very noisy datasets.
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| 4. |
- Brynte, Lucas, 1990, et al.
(författare)
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On the Tightness of Semidefinite Relaxations for Rotation Estimation
- 2022
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Ingår i: Journal of Mathematical Imaging and Vision. - : Springer Science and Business Media LLC. - 1573-7683 .- 0924-9907. ; 64:1, s. 57-67
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Tidskriftsartikel (refereegranskat)abstract
- Why is it that semidefinite relaxations have been so successful in numerous applications in computer vision and robotics for solving non-convex optimization problems involving rotations? In studying the empirical performance, we note that there are few failure cases reported in the literature, in particular for estimation problems with a single rotation, motivating us to gain further theoretical understanding. A general framework based on tools from algebraic geometry is introduced for analyzing the power of semidefinite relaxations of problems with quadratic objective functions and rotational constraints. Applications include registration, hand–eye calibration, and rotation averaging. We characterize the extreme points and show that there exist failure cases for which the relaxation is not tight, even in the case of a single rotation. We also show that some problem classes are always tight given an appropriate parametrization. Our theoretical findings are accompanied with numerical simulations, providing further evidence and understanding of the results.
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| 5. |
- Dos Santos Miraldo, Pedro, et al.
(författare)
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On the Generalized Essential Matrix Correction : An Efficient Solution to the Problem and Its Applications
- 2020
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Ingår i: Journal of Mathematical Imaging and Vision. - : Springer. - 0924-9907 .- 1573-7683. ; 62:8, s. 1107-1120
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Tidskriftsartikel (refereegranskat)abstract
- This paper addresses the problem of finding the closest generalized essential matrix from a given 6 × 6 matrix, with respect to the Frobenius norm. To the best of our knowledge, this nonlinear constrained optimization problem has not been addressed in the literature yet. Although it can be solved directly, it involves a large number of constraints, and any optimization method to solve it would require much computational effort. We start by deriving a couple of unconstrained formulations of the problem. After that, we convert the original problem into a new one, involving only orthogonal constraints, and propose an efficient algorithm of steepest descent type to find its solution. To test the algorithms, we evaluate the methods with synthetic data and conclude that the proposed steepest descent-type approach is much faster than the direct application of general optimization techniques to the original formulation with 33 constraints and to the unconstrained ones. To further motivate the relevance of our method, we apply it in two pose problems (relative and absolute) using synthetic and real data.
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| 6. |
- Eriksson, Anders P, et al.
(författare)
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Normalized Cuts Revisited: A Reformulation for Segmentation with Linear Grouping Constraints
- 2011
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Ingår i: Journal of Mathematical Imaging and Vision. - : Springer Science and Business Media LLC. - 0924-9907 .- 1573-7683. ; 39:1, s. 45-61
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Tidskriftsartikel (refereegranskat)abstract
- Indisputably Normalized Cuts is one of the most popular segmentation algorithms in pattern recognition and computer vision. It has been applied to a wide range of segmentation tasks with great success. A number of extensions to this approach have also been proposed, including ones that can deal with multiple classes or that can incorporate a priori information in the form of grouping constraints. However, what is common for all these methods is that they are noticeably limited in the type of constraints that can be incorporated and can only address segmentation problems on a very specific form. In this paper, we present a reformulation of Normalized Cut segmentation that in a unified way can handle linear equality constraints for an arbitrary number of classes. This is done by restating the problem and showing how linear constraints can be enforced exactly in the optimization scheme through duality. This allows us to add group priors, for example, that certain pixels should belong to a given class. In addition, it provides a principled way to perform multi-class segmentation for tasks like interactive segmentation. The method has been tested on real data showing good performance and improvements compared to standard normalized cuts.
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| 7. |
- Felsberg, Michael, 1974-, et al.
(författare)
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The Monogenic Scale-Space : A Unifying Approach to Phase-Based Image Processing in Scale-Space
- 2004
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Ingår i: Journal of Mathematical Imaging and Vision. - 0924-9907 .- 1573-7683. ; 21
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we address the topics of scale-space and phase-based image processing in a unifying framework. In contrast to the common opinion, the Gaussian kernel is not the unique choice for a linear scale-space. Instead, we chose the Poisson kernel since it is closely related to the monogenic signal, a 2D generalization of the analytic signal, where the Riesz transform replaces the Hilbert transform. The Riesz transform itself yields the flux of the Poisson scale-space and the combination of flux and scale-space, the monogenic scale-space, provides the local features phase-vector and attenuation in scale-space. Under certain assumptions, the latter two again form a monogenic scale-space which gives deeper insight to low-level image processing. In particular, we discuss edge detection by a new approach to phase congruency and its relation to amplitude based methods, reconstruction from local amplitude and local phase, and the evaluation of the local frequency.
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| 8. |
- Gerosa, Daniele, et al.
(författare)
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Bias Versus Non-Convexity in Compressed Sensing
- 2022
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Ingår i: Journal of Mathematical Imaging and Vision. - : Springer Science and Business Media LLC. - 1573-7683 .- 0924-9907. ; 64:4, s. 379-394
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Tidskriftsartikel (refereegranskat)abstract
- Cardinality and rank functions are ideal ways of regularizing under-determined linear systems, but optimization of the resulting formulations is made difficult since both these penalties are non-convex and discontinuous. The most common remedy is to instead use the ℓ1- and nuclear norms. While these are convex and can therefore be reliably optimized, they suffer from a shrinking bias that degrades the solution quality in the presence of noise. This well-known drawback has given rise to a fauna of non-convex alternatives, which usually features better global minima at the price of maybe getting stuck in undesired local minima. We focus in particular penalties based on the quadratic envelope, which have been shown to have global minima which even coincide with the “oracle solution,” i.e., there is no bias at all. So, which one do we choose, convex with a definite bias, or non-convex with no bias but less predictability? In this article, we develop a framework which allows us to interpolate between these alternatives; that is, we construct sparsity inducing penalties where the degree of non-convexity/bias can be chosen according to the specifics of the particular problem.
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| 9. |
- Hammarstedt, P, et al.
(författare)
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Affine reconstruction from translational motion under various autocalibration constraints
- 2006
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Ingår i: Journal of Mathematical Imaging and Vision. - : Springer Science and Business Media LLC. - 0924-9907 .- 1573-7683. ; 24:2, s. 245-257
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Tidskriftsartikel (refereegranskat)abstract
- In this paper algorithms for affine reconstruction from translational motion under various auto calibration constraints are presented. A general geometric constraint, expressed using the camera matrices, is derived and this constraint is used in a least square solution to the problem. Necessary and sufficient conditions for critical motions are derived and shown to depend on the knowledge of the intrinsic parameters of the camera. Experiments on simulated data are performed to evaluate the noise sensitivity of the algorithms and the reconstruction quality for motions close to being critical. An experiment is performed on real data to illustrate that the method works in practice.
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| 10. |
- Jansson, Ylva, 1983-, et al.
(författare)
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Dynamic texture recognition using time-causal and time-recursive spatio-temporal receptive fields
- 2018
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Ingår i: Journal of Mathematical Imaging and Vision. - : Springer. - 0924-9907 .- 1573-7683. ; 60:9, s. 1369-1398
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Tidskriftsartikel (refereegranskat)abstract
- This work presents a first evaluation of using spatio-temporal receptive fields from a recently proposed time-causal spatiotemporal scale-space framework as primitives for video analysis. We propose a new family of video descriptors based on regional statistics of spatio-temporal receptive field responses and evaluate this approach on the problem of dynamic texture recognition. Our approach generalises a previously used method, based on joint histograms of receptive field responses, from the spatial to the spatio-temporal domain and from object recognition to dynamic texture recognition. The time-recursive formulation enables computationally efficient time-causal recognition. The experimental evaluation demonstrates competitive performance compared to state of the art. In particular, it is shown that binary versions of our dynamic texture descriptors achieve improved performance compared to a large range of similar methods using different primitives either handcrafted or learned from data. Further, our qualitative and quantitative investigation into parameter choices and the use of different sets of receptive fields highlights the robustness and flexibility of our approach. Together, these results support the descriptive power of this family of time-causal spatio-temporal receptive fields, validate our approach for dynamic texture recognition and point towards the possibility of designing a range of video analysis methods based on these new time-causal spatio-temporal primitives.
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