L. Haglund, Adaptive Multidimensional Filtering, PhD thesis, Linkoping University, Sweden, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... and surface area in 3 D, and shape descriptors such as bending energy and Euler number can be measured using Gaussian derivative filters [5] Local anisotropy and orientation can be measured in a Gaussian smoothed tensor image constructed from the dyadic product of a gradient vector with itself [6, 7]. These applications will benefit from a recursive implementation of Gaussian derivative filters. Recursive filters are fast and scale independent. Deriche [11 13] has proposed a stable recursive implementation by decomposing the transfer function into a sum (parallel interconnection) of a stable ....

L. Haglund, "Adaptive multidimensional filtering," Linkping University, Sweden, 1992.

....be re estimated at the higher resolution level until a single feature is found or the specific level, where the block is too small to be analysed, is reached. 3.5 Locating the features To locate a feature, both the feature s orientation and the centroid are to be calculated. Some researchers [3] [5] [13] have used inertia tensor [1] to estimate feature orientation with satisfactory results. In this work, we estimate local feature orientation by calculating the argument of the centroid vector of the half plane starting at angle 1 in equation (11) For the blocks containing single feature, ....

Leif Haglund. Adaptive Multidimensional Filtering. PhD thesis, Department of Electrical Engineering, Linkoping University, Sweden, 1992.

....The coordinate system defined in this way is displayed in figure 1. It is the same real part u i i part j part Figure 1: Coordinate system of the 2D phase approach as in [10] but Granlund and Knutsson use the 2D phase in the context of orientation adaptive filtering (see also [11]) Consider a given quaternion q, how can we extract the two phases, described just above In fact, the answer of this question defines the introduced coordinate system. 7 Definition 1 Let arg(z) be the function which evaluates the complex phase of z in the interval [0; 2 ) and let q s be a ....

HAGLUND, L. Adaptive Multidimensional Filtering. PhD thesis, Link oping University, 1992.

.... the structure tensor, but without being nonlinear [4] Using this real two dimensional analytic signal (the monogenic signal) it is easy to apply approaches based on the one dimensional analytic signal to twodimensional signals without sampling the orientation or using adaptive ltering (e.g. [7]) As an example, we applied the phase congruency [10, 11] in order to obtain an edge detector which is independent of the local contrast. Additionally to the information of local amplitude and local phase, the monogenic signal includes geometric properties, e.g. the orientation of an ....

Haglund, L. Adaptive Multidimensional Filtering. PhD thesis, Linkoping University, 1992.

....(see [7] such that it is not possible to create a real 2D quadrature lter. To overcome this problem, several approaches has been developed in the past, all using the quadrature lters with respect to a preference direction: 1. orientation adaptive ltering using the structure tensor, e.g. [7, 8] 2. sampling of the orientation, e.g. 12, 13] 3. steerable lters, e.g. 5, 16] The rst two approaches are non linear and the corresponding algorithms have high complexities (compared to convolutions) The steerable lters are linear and fast, but they are not related to a generalized ....

Haglund, L. Adaptive Multidimensional Filtering. PhD thesis, Linkoping University, 1992.

....Spatiotemporal filtering and parametric motion models, in particular affine motion, are today standard components of motion estimation algorithms. The use of orientation tensors is, however, less common. The basic relations between 3D orientation tensors and motion have been explored in e.g. [3, 10, 9, 20, 8]. A more sophisticated tensor based algorithm has been presented by Karlholm [14] His algorithm has some elements in common with the one presented here, but differs in the method for estimation of tensors and in that it uses a maximum likelihood approach to estimate motion model parameters. A ....

L. Haglund. Adaptive Multidimensional Filtering. PhD thesis, Linkoping University, Sweden, SE-581 83 Linkoping, Sweden, October 1992. Dissertation No 284, ISBN 917870 -988-1.

....plane. c) d) Averaging of tensors ( symbolically shown in (c) gives as result an estimate of the true motion, now from the eigenvector corresponding to the smallest eigenvalue of the tensor (d) which ideally is of rank 2. In general it is more robust to estimate normal flow than true flow [2, 6], and due to phase interference this is true also when using quadrature filters. We consequently do not want to use points outside line edge segments. Since our method uses a rather costly eigenvalue decomposition we need a way to eliminate points which are not part of oriented 4 0 5 10 15 20 25 ....

L. Haglund. Adaptive Multidimensional Filtering. PhD thesis, Linkoping University, Sweden, S--581 83 Linkoping, Sweden, October 1992. Dissertation No 284, ISBN 91--7870--988--1.

.... synthesized filters, can be controlled by the proposed method, but unfortunately this extension requires a vast increase of the number of basis filters [20] A more efficient method to obtain estimates in scale space is to apply the same basis filters at subsampled versions of the original image [1, 12]. Step 2 and 3 above are of course depending on each other. The requirement on the basis filters are, however, fairly general and the presentation of the synthesized filters is postponed to section 4. 2 Basis Filters A 3 D basis filter set is required to support a uniform approximation of ....

L. Haglund. Adaptive Multidimensional Filtering. PhD thesis, Linkoping University, Sweden, SE-581 83 Linkoping, Sweden, October 1992. Dissertation No 284, ISBN 91-7870-988-1.

....di erentiation, which involve a signi cant amount of storage and computation, as well as a temporal delay. Low pass pre lters are required by di erential techniques for reliable numerical di erentiation, while band pass lters are an essential ingredient of energybased and phase based approaches [1, 2, 8, 9, 11, 12]. Despite the use of separable lters and reasonably ecient implementations, the lters are a major computational burden of these methods. We concentrate on gradient based methods here because of their lower computational demands, which make them good candidates for real time implementations. This ....

....of about 6 [9] 7.2 Results Our quantitative results are derived from two synthetic image sequences with smooth motion elds for which the true 2d motion elds are known. They are convenient since they have been used in the extensive comparative study of Barron et al. 3] and by others (e.g. [11]) Each sequence depicts a textured plane moving with respect to a camera. The textured plane and the known 2d motion elds are shown in Figure 3. Table 2 shows results reported by others on the same sequences. The gradient based implementation by Barron et al. described above in Section 2, uses ....

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Haglund L. (1992) Adaptive Multidimensional Filtering. PhD Dissertation, Dept. Electrical Engineering, Univ. of Linkoping (ISSN 0345-7524)

....being some constant. We also report error statistics for subsets of the velocity estimates from step 1 (2.19) with a threshold based on the largest eigenvalue of S c (2.20) 2. 3 Energy Based Methods A third class of optical flow techniques is based on the output energy of velocity tuned filters [2, 7, 11, 27, 30, 34]. These are also called frequency based methods owing to the design of velocity tuned filters in the Fourier domain [1, 23, 49, 59] The Fourier transform of a translating 2 d pattern (2.1) is I(k; I 0 (k) ffi( v T k) 2.25) where I 0 (k) is the Fourier transform of I(x; 0) ....

....2 d pattern lies on a plane through the origin in frequency space. Interestingly, it has been shown that certain energy based methods are equivalent to correlation based methods [1, 49] and to the gradient based approach of Lucas and Kanade [2, 53] Indeed, as mentioned below, results reported in [27, 53] with our image sequences are close to those for our implementation of the Lucas and Kanade gradient based method and therefore support this claim. Heeger Here we consider the method developed by Heeger [29, 30] formulated as a least squares fit of spatiotemporal energy to a plane in frequency ....

[Article contains additional citation context not shown here]

Haglund L. (1992) Adaptive Multidimensional Filtering. PhD Dissertation, Dept. Electrical Engineering, Univ. of Linkoping (ISSN 0345-7524)

....of this study [14] was to analyze the performance of different optical flow methods and to and to encourage others to compare numerical results with theirs. Towards this end, several authors now compare the performance of their techniques with those of this study for the same image sequences [27, 58, 156, 89, 26, 161, 57, 49]. In addition, some experimental work evaluating differential techniques has recently appeared [59] Unfortunately, a quantitative analysis is often impossible for real image data (to obtain the correct optical flow, one needs the 3 d motion parameters as well as the 3 d depth values everywhere) ....

L. Haglund. Adaptive Multidimensional Filtering. PhD thesis, Dept. Electrical Engineering, Univ. of Linkoping, 1992.

....related method is that of phase correlation [83, 135] where the product of the spectra is normalised before the inverse FT, thus in the ideal case resulting in an impulse at the position corresponding to the motion vector. Another frequency domain technique is that of spatio temporal filtering [1, 54, 56]. The basic idea is based on the observation that motion corresponds to orientation in spacetime. In frequency space all energy corresponding to the 2 D motion of some patch will lie on a plane through the origin. The orientation of such a plane can, for example, be estimated fitting a plane to ....

L. Haglund. Adaptive multidimensional filtering. PhD thesis, Linkoping University, Sweden, 1992.

.... for constructing multiple levels of images by means of averaging and subsampling, where the averaging procedure usually corresponds to band pass filtering, is the wavelet transform, introduced to image processing by Daubechies [10] and Mallat [35] and implemented by e.g. Fleet [14] and Haglund [23]. One of the more common averaging procedures for multiresolution hierarchies employs Gaussian weights, which has the interesting property of enabling a sequence of levels that is continuous rather than discrete. This is the scale space, introduced in image processing by Witkin [48] and further ....

....corresponds to complete uncertainty of the average orientation. arg(z) Figure 1.5 The standard double angle representation of local orientation. Introduction 23 The vector representation has been used successfully also as a representation of for local frequency, Nappa Granlund [36] and Haglund [23], and for circular symmetries, Bigun [5] 1.4.2 Tensor representation When it comes to representation of multi dimensional orientation, the vector representation is insufficient for dimensions greater than two, at least for two reasons. Let us assume that we want to represent the orientation of a ....

L. Haglund. Adaptive Multidimensional Filtering. PhD thesis, Linkoping University, Sweden, S--581 83 Linkoping, Sweden, October 1992. Dissertation No 284, ISBN 91--7870--988--1.

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L. Haglund, Adaptive Multidimensional Filtering, PhD thesis, Linkoping University, Sweden, 1992.

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L. Haglund, Adaptive Multidimensional Filtering, PhD thesis, Linkoping University, Sweden, 1992.

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L. Haglund, Adaptive multi-dimensional filtering, PhD Thesis, Linkking, 1992.

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L. Haglund, Adaptive Multidimensional Filtering, PhD thesis, Linkoping University, Sweden, 1992.

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L. Haglund. Adaptive Multidimensional Filtering. PhD thesis, Linkoping University, Sweden, SE-581 83 Linkoping, Sweden, October 1992. Dissertation No 284, ISBN 91-7870-988-1.

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