1,119 research outputs found
Wavelet-based video codec using human visual system coefficients for 3G mobiles
A new wavelet based video codec that uses human visual system coefficients is presented. In INTRA mode of operation, wavelet transform is used to split the input frame into a number of subbands. Human Visual system coefficients are designed for handheld videophone devices and used to regulate the quantization stepsize in the pixel quantization of the high frequency subbandsâ coefficients. The quantized coefficients are coded using quadtreecoding scheme. In the INTER mode of operation, the displaced frame difference is generated and a wavelet transform decorrelates it into a number of subbands. These subbands are coded using adaptive vector quantization scheme. Results indicate a significant improvement in frame quality compared to motion JPEG200
Squarepants in a Tree: Sum of Subtree Clustering and Hyperbolic Pants Decomposition
We provide efficient constant factor approximation algorithms for the
problems of finding a hierarchical clustering of a point set in any metric
space, minimizing the sum of minimimum spanning tree lengths within each
cluster, and in the hyperbolic or Euclidean planes, minimizing the sum of
cluster perimeters. Our algorithms for the hyperbolic and Euclidean planes can
also be used to provide a pants decomposition, that is, a set of disjoint
simple closed curves partitioning the plane minus the input points into subsets
with exactly three boundary components, with approximately minimum total
length. In the Euclidean case, these curves are squares; in the hyperbolic
case, they combine our Euclidean square pants decomposition with our tree
clustering method for general metric spaces.Comment: 22 pages, 14 figures. This version replaces the proof of what is now
Lemma 5.2, as the previous proof was erroneou
Robust Proximity Search for Balls using Sublinear Space
Given a set of n disjoint balls b1, . . ., bn in IRd, we provide a data
structure, of near linear size, that can answer (1 \pm \epsilon)-approximate
kth-nearest neighbor queries in O(log n + 1/\epsilon^d) time, where k and
\epsilon are provided at query time. If k and \epsilon are provided in advance,
we provide a data structure to answer such queries, that requires (roughly)
O(n/k) space; that is, the data structure has sublinear space requirement if k
is sufficiently large
Down the Rabbit Hole: Robust Proximity Search and Density Estimation in Sublinear Space
For a set of points in , and parameters and \eps, we present
a data structure that answers (1+\eps,k)-\ANN queries in logarithmic time.
Surprisingly, the space used by the data-structure is \Otilde (n /k); that
is, the space used is sublinear in the input size if is sufficiently large.
Our approach provides a novel way to summarize geometric data, such that
meaningful proximity queries on the data can be carried out using this sketch.
Using this, we provide a sublinear space data-structure that can estimate the
density of a point set under various measures, including:
\begin{inparaenum}[(i)]
\item sum of distances of closest points to the query point, and
\item sum of squared distances of closest points to the query point.
\end{inparaenum}
Our approach generalizes to other distance based estimation of densities of
similar flavor. We also study the problem of approximating some of these
quantities when using sampling. In particular, we show that a sample of size
\Otilde (n /k) is sufficient, in some restricted cases, to estimate the above
quantities. Remarkably, the sample size has only linear dependency on the
dimension
Quadtrees, transforms and image coding
Transforms and quadtrees are both methods of representing information in an
image in terms of the presence of information at differing length scales. This paper
presents a mathematical relationship between these two approaches to describing
images in the particular case when Walsh transforms are used. Furthermore, both
methods have been used for the compression of images for transmission. This paper
notes that under certain circumstances, quadtree compression produces identical
results to Walsh transform coding, but requires less computational effort to do so.
Remarks are also made about the differences between these approaches
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