D. Saupe, "Accelerating Fractal Image Compression by Multidimensional Nearest Neighbor Search", in Proc. IEEE Data Compression Conf., J.A. Storer and M. Cohn, Eds. Snowbird, UT, Mar. 1995, pp. 222-231;  Home/Search   Document Details and Download   Summary   Related Articles   Check

....generalized to gray level images. In Section 4 a comparative analysis of the method proposed with the classical quad tree decomposition is presented together with some experimental results. A final Section closes the paper tracking directions for future related works and applications [8] 9] 10][11][12] 13] Figure 1. An example of Trapezoidal Region and its boundary representation. 2. BUILDING FUNCTION TREES Function trees are connected with the key concept of quad tree decomposition. In particular a function tree can be defined as a quad tree with four possible kinds of subnodes: each ....

D. Saupe, "Accelerating Fractal Image Compression by Multidimensional Nearest Neighbor Search", in Proc. IEEE Data Compression Conf., J.A. Storer and M. Cohn, Eds. Snowbird, UT, Mar. 1995, pp. 222-231;

....to that of the domain block. Most speed ups have, in some way, reduced the size of the pool that the coder must search for each domain block. Reducing the size of the search pool, however, can have an adverse effect on reconstructed image quality since the range block pool is not as rich. Saupe [21] uses the theory of multi dimensional keys to perform an approximate nearest neighbour search. Since this search can be completed in O(logN) time, the range pool need not be depleted to achieve a speed up. Saupe s basic idea is that of a (d Gamma 1) Gammadimensional projection on d where d ....

D. Saupe. Accelerating Fractal Image Compression by Multi-Dimensional Nearest Neighbour Search. In Proceedings DCC'95 Data Compression Conference, 1995.

....ffl we are free to classify the domain blocks in any number of classes; ffl we know exactly in which classes the matching domain blocks are. The use of angles in an n dimensional space as classification indices is also very closely related to the feature vectors approach of Dietmar Saupe (see [21] and [22] His classification is based on the value of the inner products of each domain CHAPTER 4. FRACTAL IMAGE COMPRESSION 87 block 9 with a small number of fixed orthogonal unit vectors. The values of all these inner products gives the so called feature vector. The components of this vector ....

Dietmar Saupe. Accelerating fractal image compression by multi-dimensional nearest neighbor search. In Storer [24].

....error of minp;i kr Mpd i k. The problem may be simpli ed by constructing an appropriate invariant representation for each image block. Transforming range and contracted domain blocks to this representation allows direct distance comparisons between them to determine the best possible match [88]. The standard invariant representation for the block intensity transform 14 is constructed by applying the orthogonal projection onto the orthogonal complement of the space spanned by the xed block terms, followed by normalisation. Alternative representations 15 for the single constant ....

....allowing the vector in the search set closest (the invariant representation of range and domain blocks is used) to the speci ed vector to be located without actually examining every point in the set. Existing techniques [102, ch. 2, 3] 103] have been applied to domain searching [16, pp. 179 200] [88] [92] 104] 105] as have algorithms speci cally designed for this purpose [95] 106] 107] VII. Transform Representation Domain positions, and any additional partition information required in an adaptive partition, are represented by discrete values and are not subjected to quantisation. ....

D. Saupe, \Accelerating fractal image compression by multidimensional nearest neighbor search," in Proceedings DCC '95 (IEEE Data Compression Conference), J. A. Storer and M. Cohn, Eds., Snowbird, UT, USA, Mar. 1995, pp. 222-231.

....much higher than that of transform coders and vector quantizers. The most time consuming part of the encoding procedure is usually the search for finding the best matching domain blocks. Different techniques have been studied for limiting, structuring or approximating the search procedure [114, 116, 115]. In many implementations of fractal image coders the search is limited to the neighborhood of the range block where finding a good match is more likely. In the extreme case, the search may be totally avoided by using a predetermined domain block at the location of the range block. The search in ....

D. Saupe. Accelerating fractal image compression by multi-dimensional nearest neighbor search. In J. A. Storer and M. Cohn, editors, DCC'95: Data Compression Conference, Snowbird, Utah, Mar. 28--30, 1995. 302 Chapter 7

....the matching primitive is recorded. However, for unsatisfying distortions, the conventional fractal coder is employed to find a better match, after which the primitive dictionary is updated with the new primitive (contracted domain block) and fractal code (affine transformation) Many researches [1, 15, 18, 23, 6, 22, 20] (and many more) have already suggested and established methods to improve the image qualities and search schemes of both coders. However, we restricted ourselves to basic and uncomplicated implementations of the base methods in order to introduce and establish the FVQ coder. This was done because ....

D. Saupe. Accelerating fractal image compression by multidimensional nearest neigbor search. In J. A. Storer and M. Cohn, editors, IEEE Data Compression Conference, DCC, pages 222--231, UT, USA, March 1995. Snowbird.

....an appropriate search algorithm is described in 2.2. Finally experimental results are presented and commented in section 2.4. 1. 2 A Fast General Method Using Feature Vectors A good method to solve the problem of finding the best domain block for each range has been described in several papers ([17], 22] 13] with different formulations and features. The general scheme is as follows : 1. find an operator mapping image blocks to feature vectors, so that minimizing the distance (e.g. the euclidean distance) between a feature vector corresponding to a range and a feature vector corresponding ....

....different operators to compute the feature vectors, and different structures to perform the search. In [22] and [2] the feature vectors used are the normalized DCT coefficients of the blocks, in [13] the structure used for the search is a R tree, and the feature vectors used are the same as in [17]. We review the different methods in the following paragraphs. Normalization The simplest way of finding good feature vectors might be the one described in [17] and also used in [13] Suppose that x is a vector obtained by an ordering of the pixels values of a block (e.g. in scan line order) and ....

[Article contains additional citation context not shown here]

Saupe, D., "Accelerating fractal image compression by multi-dimensional nearestneighbour search", in: Proceedings DCC'95 Data Compression Conference, J.A. Storer and M.Cohn (eds.), IEEE Comp. Soc. Press, 1998.

....order of the search. There are anyway a lot of methods that achieve this goal, often with a slight quality loss (see e.g. 1] 1. 2 A Fast General Method Using Feature Vectors A good method to solve the problem of finding the best domain block for each range has been described in several papers ([18], 23] 13] 9] using sometimes different formulations and features. The general scheme is as follows : 1. find an operator mapping image blocks to feature vectors, so that minimizing the distance (e.g. the euclidean distance) between a feature vector corresponding to a range and a feature vector ....

....operators to compute the feature vectors, and different structures to perform the search. In [23] and [2] the feature vectors used are the normalized DCT coefficients of the blocks, in [13] the structure used for the search is a R tree, and the feature vectors used are the same than in [18]. In [9] the feature vectors used are invariant to the isometry transformations used in some compression scheme. We review the different methods in the following paragraphs. Normalization The simplest way of finding good feature vectors is maybe the one described in [18] and also used in [13] ....

[Article contains additional citation context not shown here]

Saupe, D., "Accelerating fractal image compression by multi-dimensional nearestneighbour search", in: Proceedings DCC'95 Data Compression Conference, J.A. Storer and M.Cohn (eds.), IEEE Comp. Soc. Press, March 1995.

....ffl we are free to classify the domain blocks in any number of classes; ffl we know exactly in which classes the matching domain blocks are. The use of angles in an n dimensional space as classification indices is also very closely related to the feature vectors approach of Dietmar Saupe (see [7] and [8] His classification is based on the value of the inner products of each domain block 5 with a small number of fixed orthogonal unit vectors. The values of all these inner products gives the so called feature vector. The components of this vector are nothing but the direction cosines in ....

Dietmar Saupe. Accelerating fractal image compression by multidimensional nearest neighbor search. In James Storer, editor, IEEE Data Compression Conference Proceedings. IEEE Computer Society Press, March 1995.

....on the three major approaches are [2, 3, 4, 5] Let us mention the review [6] as well. There are two types of accelerating techniques: those which are lossless, i.e. which do not sacrifice any image quality for the sake of the speedup, such as [7, 8] or [9] those which are not, such as [10], 11] or the present one. At the same time, new transformations such as square isometries [12] or modifications of the initial scheme [13] have been introduced in order to improve the quality of the images. Pessimistic general studies such as [14] or [15] help in keeping enthusiastic papers at a ....

Dietmar Saupe. Accelerating fractal image compression by multi-dimensional nearest neighbor search. In Data Compression Conference, Freiburg, Germany, March 1995. IEEE.

....optimal load distribution. In addition to pre computed load distribution the proposed technique may be used for dynamic load balancing in a multi user environment with varying load conditions. Future research will be conducted on how to employ multidimensional nearest neighbour search techniques [18] (which is currently the most efficient sequential speedup technique) within parallel algorithms. Acknowledgements The first author was partially supported by Osterreichische Nationalbank, Jubil aumsfonds project no. 6900. We thank the Paderborn Center for Parallel Computing for providing access ....

D. Saupe. Accelerating fractal image compression by multi-dimensional nearest neighbor search. In J.A. Storer and M.A. Cohn, editors, Proceedings Data Compression Conference (DCC'95), pages 222--231. IEEE Computer Society Press, March 1995.

....and by Fisher in [7] Throughout this paper, when we refer to fractal block coders, we will be referring to such Jacquin style schemes. The second problem is to find fast and effective algorithms for associating a given image to a contraction map of which the image is an approximate fixed point[8] [9]. The third problem is to analyze the convergence properties of various families of maps and to establish error bounds for decoded images[10] 11] In this paper we address the issues of finding effective families of maps and convergence properties of fractal schemes. More importantly, we address ....

Dietmar Saupe, "Accelerating fractal image compression by multi-dimensional nearest neighbor search", in Proc. Data Compression Conference, Snowbird, Utah, James A. Storer and Martin Cohn, Eds. IEEE Computer Society, Mar. 1995, pp. 222--231.

....with the initialization, the second one with the data handling during the region merging process. In the initialization phase a fractal encoding for a uniform partition is sought. Here, an acceleration method can be employed, especially since all ranges have the same size. The method of Saupe [43] is particularly well suited for this case. We will briefly outline this method. For a range R 2 R m nspanf1g and a codebook block D 2 R m nspanf1g the collage error kR Gamma( sD o1)k 2 2 using unquantized luminance parameters can be expressed as hR; Ri Gamma 1 m hR; 1i 2 ....

D. Saupe, "Accelerating fractal image compression by multi-dimensional nearest neighbor search," Proc. IEEE Data Compression Conference, J. Storer and M. Cohn (eds.), Snowbird, Utah, pp. 222-231, 1995.

....range only those domains are considered whose values are within some distance of the value of the given range [11] b) Feature vectors. The domains and ranges are assigned a multi dimensional feature vector and for a given range only a few domains that are closest in feature space are considered [12, 13, 14]. These approaches reduce the factor of proportionality in the O(ND ) time complexity for a search in the domain pool, except for the method based on feature vectors which can be organized such that it yields an O(log ND ) complexity. All the above methods are designed with the goal of a large ....

....k k 1 . 5. Check all domains D k with k 0 k k 1 . In this procedure a list of candidate domains D k is produced in O(log ND ) time while the full scan rejecting the domains that do not pass the test takes O(ND ) time. 3. 4 Feature vectors In the feature vector approach introduced by Saupe in [12, 13, 14] a small set of d real valued keys is devised for each domain which make up a d dimensional feature vector. These keys are carefully constructed such that searching in the domain pool can be restricted to the nearest neighbors of a query point, i.e. the feature vector of the current range. ....

[Article contains additional citation context not shown here]

Saupe, D., Accelerating fractal image compression by multidimensional nearest neighbor search, submitted, Nov. 1994.

....of E(D;R) occurs when the squared inner product hOE(D) OE(R)i 2 is maximal. Since hOE(D) OE(R)i 2 = cos 2 6 (OE(D) OE(R) this means minimizing the angle 6 (OE(D) OE(R) or, equivalently 6 (OD;OR) 3. 2 Feature vectors In the feature vector approach introduced by Saupe in [Saup94a, Saup94b, Saup95a] a small set of d real valued keys is devised for each domain which make up a d dimensional feature vector. These keys are carefully constructed such that searching in the domain pool can be restricted to the nearest neighbors of a query point, i.e. the feature vector of the current range. ....

Saupe, D., Accelerating fractal image compression by multi-dimensional nearest neighbor search, in: Proceedings DCC'95 Data Compression Conference, J. A. Storer and M. Cohn (eds.), IEEE Comp. Soc. Press, March 1995.

No context found.

Saupe, D., Accelerating fractal image compression by multi-dimensional nearest neighbor search, in: Proceedings DCC'95 Data Compression Conference, J. A. Storer and M. Cohn (eds.), IEEE Comp. Soc. Press, March 1995.

....of the feature vectors which results in a reduction of the dimensionality of the search space. New results from numerical simulations are reported. Also we provide a brief overview of related work and other complexity reduction methods. This paper is an extended version of the article [34]. 1 Introduction With the ever increasing demand for images, sound, video sequences, computer animations and volume visualization, data compression remains a critical issue regarding the cost of data storage and transmission times. While JPEG currently provides the industry standard for still ....

....symmetric in the sense that the encoding and decoding phases require about the same number of operations. On the contrary, fractal image compression allows fast decoding but su#ers from long encoding times. In our papers [32, 33] we introduced and discussed a new twist for the encoding process. In [34] we demonstrated its e#ciency by a series of empirical studies. In this expository article we review the material in [34] and extend the discussion of the acceleration technique. During encoding a large pool of image subsets, the domain pool, has to be searched repeatedly many times, which by ....

[Article contains additional citation context not shown here]

Saupe, D., Accelerating fractal image compression by multi-dimensional nearest neighbor search, in: Proceedings Data Compression Conference, March 28--30, 1995 . Snowbird, Utah, J. A. Storer, M. Cohn (eds.), IEEE Computer Society Press, 1995.

No context found.

D. Saupe, U. Freiburg, "Accelerating Fractal Image Compression by Multi-Dimensional Nearest Neighbor Search."

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Dietmar Saupe. Accelerating fractal image compression by multi dimensional nearest neighbor search. In ASI NATO 95 on Fractal image encoding and analysis, Trondheim, to be published in a Springer-Verlag book, 1995.

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Saupe, D. (1995a). Accelerating fractal image compression by multi-dimensional nearest neighbour search. Proceedings of the Data Compression Conference. 47

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