R. Wilson and G. H. Granlund, "The Uncertainty Principle in Image Processing", IEEE Trans. PAMI, Vol. 6, No. 6, November 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....as basis functions in transforms to pro vide information about image frequency content at specific points within the image. The degree to which a function is simultaneously local in both space and frequency is limited by the uncertainty principle, which plays an important role in image processing[7]. Gabor has formalized this principle by measuring the uncertainty of a signal in each domain as the variance of the signal power normalized by the signal energy[2] In 1D, the product of the spatial and spectral uncertainty then has a lower bound of 0. The now famous Gabor functions are complex ....

H. R. Wilson and G. H. Granlund. The uncertainty principle in image processing. 1EEE Trans. PAM1, 6:758-767, 1984.

....in band frequency response and sharp off band attenuation. But, such a filter may have a longer support in time domain, and thus offer less time domain separation. Such contradictory construction requirements are well demonstrated by the Heisenberg uncertainty principle. Please see Wilson et al. [34] [35] for a further discussion on how the selection of frequency localization can effect the performance of several image processing applications. In this investigation, we selected Lemari e Battle wavelets, which are symmetric and quadrature mirror filters (QMF) The high pass filter G 0 ( is ....

R.Wilson and G.H.Granlund. "the uncertainty principle in image processing" IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, pp. 758--767, 1984.

....CAM algorithm is that it dynamically adjusts all of its internal parameters in response to the image data. Many algorithms give spurious or incorrect outputs when presented with image data that is only mildly corrupted by noise, and few exhibit useful behaviour as noise becomes more severe. What [12] term the Uncertainty Principle in image processing is the solution the greater the difficulty of the statistical decision task, the coarser the scale at which it can be reliably made. It is therefore important that all region boundaries are only represented at an appropriate scale for the ....

R. Wilson and G. Granlund. The Uncertainty Principle in image processing. IEEE Trans. Pattern Analysis and Machine Intell., 6(6), November 1984.

....The quality of the features, on the other hand, depends on the spatial extent of the data from which the features are extracted. However, large spatial extent, in turn, deteriorates localization of the structures. This interdependence is also known as the uncertainty principle in image processing [63]. There are a number of methods to extract texture features. These can be categorized into geometrical, statistical, signal processing, and model based methods [56] Geometrical methods include the structural methods [66, 16, 58, 5, 54] and Voronoi tessellation features [55] Co occurrence ....

R. Wilson and G. Granlund, "The uncertainty principle in image processing," IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, pp. 758-767, 1984.

....any calculations involving these values automatically inherit NaN without slowing down the computations. The algorithm (in Matlab on an HP 735) takes about 6 s per repetition for a pair of 320 240 images. C. Exploiting Commutativity for Parameter Estimation There is a fundamental uncertainty [37] involved in the simultaneous estimation of parameters of a noncommutative group, akin to the Heisenberg uncertainty relation of quantum mechanics. In contrast, for a commutative 13 group (in the absence of noise) we can obtain the exact coordinate transformation. Segman [38] considered the ....

R. Wilson and G. H. Granlund, "The uncertainty principle in image processing," IEEE Trans. Pattern Anal. Machine Intell., Nov. 1984.

....depends on the size of the sampling windows. As for the Canny edge detector [4] the desirable size of these windows depends on a trade off between the conflicting goals of maximizing the signal to noise ratio and locating the boundaries accurately. This gives rise to an uncertaincy principle [42]. We show how optimally sized windows can be chosen to minimize this uncertainty. Like many algorithms, the performance of region competition will depends on the initial conditions more precisely on the choice of initial seeds . We discuss criteria for choosing such seeds. We also describe an ....

....with high contrast regions (i.e. high SNR) where Delta oe, we can simply choose m = 1. This explains why region growing algorithms work for certain images. But 0 cannot be reduced without limit by selecting the window. This corresponds to the general uncertainty principle in image processing [42]. We choose the window size to be the smallest m which satisfies the inequalities (25,26) So far the analysis has assumed square windows, though our algorithm uses circular windows. Then Pi (x) will be slightly different for x 2 ( Gamma =2; 2) and, as shown in figure (10.b) it will no longer ....

R.Wilson and G.Granlund. "The uncertainty principle in image processing". IEEE.trans.on PAMI vol. 6, No.6, Nov.1984.

....A specific texture may be modeled as a realization of a random function. We propose to define a random function as homogeneous if, with probability one, spatial averages of any local operator are constant with respect to space in the limit of infinite size of the averaging region. To quote Wilson [8, 9], when the scale of averaging is infinite the class localization of the texture pattern must become infinitely accurate. Of course, in practical circumstances we cannot take averages over infinite regions: for practical purposes the averaged texture features (i.e. the averaged output of the local ....

R. Wilson and G.H. Granlund. The uncertainty principle in image processing. IEEE Trans. Pattern Anal. Machine Intell., 6(6):758--767, Nov. 1984.

....calculations involving these values automatically inherit NaN without slowing down the computations. The algorithm (in Matlab on an HP 735) takes about six seconds per iteration for a pair of 320x240 images. 4. 3 Exploiting commutativity for parameter estimation There is a fundamental uncertainty [37] involved in the simultaneous estimation of parameters of a noncommutative group, akin to the Heisenberg uncertainty relation of quantum mechanics. In contrast, for a commutative 13 group (in the absence of noise) we can obtain the exact coordinate transformation. 13 A commutative (or Abelian) ....

R. Wilson and G. H. Granlund, "The Uncertainty Principle in Image Processing ," IEEE Transactions on Pattern Analysis and Machine Intelligence, November 1984.

....in band frequency response and sharp off band attenuation. But, such a filter may have a longer support in time domain, and thus offer less time domain separation. Such contradictory construction requirements are well demonstrated by the Heisenberg uncertainty principle. Please see Wilson et al. [34] [35] for a further discussion on how the selection of frequency localization can effect the performance of several image processing applications. In this investigation, we selected Lemari e Battle wavelets, which are symmetric and quadrature mirror filters (QMF) The high pass filter G 0 ( is ....

R.Wilson and G.H.Granlund. "the uncertainty principle in image processing" IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, pp. 758--767, 1984.

....E[f (x) becomes more horizontal around zero. This makes the thick line segment grow. In summary, the above two points indicate that the uncertainty of the boundary cannot be reduced without limit by selecting the window. This corresponds to the general uncertainty principle in image processing[36]. The window size is chosen to be the smallest m which satisfies the inequalities (26,27) So far the analyses are based on square windows, in fact, we are using circular ( s = s = s ) 1 2 E(f ) x) D(f ) x) a o x 2 w w 2 ( s = s = s ) 1 2 E(f ) x) D(f ) x) a o x 2 w w 2 ....

R.Wilson and G.Granlund. "The uncertainty principle in image processing". IEEE.trans.on PAMI vol. 6, No.6, Nov.1984.

....Data Figure 1: Propagation of Uncertainty 2 Sensor and Image Processing Uncertainties In this section we develop and discuss modeling the uncertainties in 2 D feature displacement vectors. There are many sources of errors and ways to model uncertainties in image processing and sensing in general [5,8,15,16]. The uncertainty in the recovered values results from sensor uncertainties, noise, and the image processing techniques used to extract and track world features. When dealing with measurements of any sort, it is always the case that the measurements are accompanied by some error. Mistakes also ....

R. Wilson and G. H. Granlund, "The Uncertainty Principle in Image Processing", IEEE Trans. PAMI, Vol. 6, No. 6, November 1984.

....depends on the size of the sampling windows. As for the Canny edge detector [4] the desirable size of these windows depends on a tradeoff between the conflicting goals of maximizing the signal to noise ratio and locating the boundaries accurately. This gives rise to an uncertaincy principle [36]. We describe how optimally sized windows can be chosen to minimize this uncertainty. Like many algorithms, the performance of region competition will depends on the initial conditions more precisely on the choice of initial seeds . We discuss criteria for choosing such seeds. We also ....

....regions (i.e. high SNR) where Delta oe, we can simply choose m = 1. This explains why region growing algorithms work for certain images. But once the window is big enough, 0 becomes a constant (see equation (23) This corresponds to the general uncertainty principle in image processing[36]. We choose the window size to be the smallest m which satisfies the inequalities (24,25) 0 R 1 2 R f(x) G ( s = s = s ) 1 2 E(f ) x) D(f ) x) a o x 2 w w 2 x Figure 10 When an ellipse window is used with the same size (area) m, the uncertainty interval shown by the thick line ....

R.Wilson and G.Granlund. "The uncertainty principle in image processing". IEEE.trans.on PAMI vol. 6, No.6, Nov.1984.

....the image iterativelly using local averages where the brightness gradient is not too big while averaging is inhibited at location where the gradient is too strong, i.e. where an edge is very likely to exist. The choice of an appropriate scale of segmentation is related to the uncertainty principle [56]. That is, a large scale allows a good class localization (as long as we do not mix statistics from different regions) but deteriorates the spatial information about the localization of boundaries. In other words, it is possible to rely on accurate measurment of the parameters of the image model ....

R. Wilson and G.H. Granlund. The uncertainty principle in image processing. IEEE Trans. Pattern Anal. Machine Intell., 6(6):758--767, Nov. 1984.

....way the benefit of large smoothing to detect the major features could be combined with precise localisation. In a way these linkages across scale are used to overcome the uncertainty principle which states that spatial localisation and frequency domain localisation are conflicting requirements [8]. A defining feature of scale space theory, in contrast to other multiscale approaches, is the property that a signal feature, once present at some scale, must persist all the way through scale space to zero scale (otherwise the feature would be spurious: being caused by the filter and not the ....

Roland Wilson and Goesta H. Granlund, "The uncertainty principle in image processing", IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-6, pp. 758--767, 1984.`

....of the analysis window, is a trade off between frequency and spatial resolution. Due to Heisenberg s uncertainty principle, which gives an upper bound for the product of the spatial and frequency resolutions, it is not possible to get simultaneous arbitrarily high spatial and frequency resolutions [24]. One popular multiresolution representation is the Wavelet Transform (WT) 16] 19] The WT is a space scale representation which means that each coefficient of the WT is identified by a position and a scale. The WT decomposes the signal onto a set of analysis functions that are all obtained ....

R. G. Wilson and G. H. Granlund. The uncertainty principle in image processing. IEEE Trans. P.A.M.I, 6(6):758--767, November 1984. 42

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R. Wilson and G.H. Granlund,"The Uncertainty Principle in Image Processing", IEEE Trans. Patt. Anal. and Machine Intell., 6. pp. 758-767, 1984.

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R. Wilson and G. H. Granlund, "The Uncertainty Principle in Image Processing", IEEE Trans. PAMI, Vol. 6, No. 6, November 1984.

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