86 research outputs found
Geometrical Image Denoising Using Quadtree Segmentation
We propose a quadtree segmentation based denoising algo- rithm, which attempts to capture the underlying geometrical structure hidden in real images corrupted by random noise. The algorithm is based on the quadtree coding scheme pro- posed in our earlier work [12, 13] and on the key insight that the lossy compression of a noisy signal can provide the fil- tered/denoised signal. The key idea is to treat the denoising problem as the compression problem at low rates. The in- tuition is that, at low rates, the coding scheme captures the smooth features only, which basically belong to the origi- nal signal. We present simulation results for the proposed scheme and compare these results with the performance of wavelet based schemes. Our simulations show that the pro- posed denoising scheme is competitive with wavelet based schemes and achieves improved visual quality due to better representation for edges
Discrete denoising of heterogenous two-dimensional data
We consider discrete denoising of two-dimensional data with characteristics
that may be varying abruptly between regions.
Using a quadtree decomposition technique and space-filling curves, we extend
the recently developed S-DUDE (Shifting Discrete Universal DEnoiser), which was
tailored to one-dimensional data, to the two-dimensional case. Our scheme
competes with a genie that has access, in addition to the noisy data, also to
the underlying noiseless data, and can employ different two-dimensional
sliding window denoisers along distinct regions obtained by a quadtree
decomposition with leaves, in a way that minimizes the overall loss. We
show that, regardless of what the underlying noiseless data may be, the
two-dimensional S-DUDE performs essentially as well as this genie, provided
that the number of distinct regions satisfies , where is the total
size of the data. The resulting algorithm complexity is still linear in both
and , as in the one-dimensional case. Our experimental results show that
the two-dimensional S-DUDE can be effective when the characteristics of the
underlying clean image vary across different regions in the data.Comment: 16 pages, submitted to IEEE Transactions on Information Theor
Rate-distortion optimized geometrical image processing
Since geometrical features, like edges, represent one of the most important perceptual information in an image, efficient exploitation of such geometrical information is a key ingredient of many image processing tasks, including compression, denoising and feature extraction. Therefore, the challenge for the image processing community is to design efficient geometrical schemes which can capture the intrinsic geometrical structure of natural images. This thesis focuses on developing computationally efficient tree based algorithms for attaining the optimal rate-distortion (R-D) behavior for certain simple classes of geometrical images, such as piecewise polynomial images with polynomial boundaries. A good approximation of this class allows to develop good approximation and compression schemes for images with strong geometrical features, and as experimental results show, also for real life images. We first investigate both the one dimensional (1-D) and two dimensional (2-D) piecewise polynomials signals. For the 1-D case, our scheme is based on binary tree segmentation of the signal. This scheme approximates the signal segments using polynomial models and utilizes an R-D optimal bit allocation strategy among the different signal segments. The scheme further encodes similar neighbors jointly and is called prune-join algorithm. This allows to achieve the correct exponentially decaying R-D behavior, D(R) ~ 2-cR, thus improving over classical wavelet schemes. We also show that the computational complexity of the scheme is of O(N logN). We then extend this scheme to the 2-D case using a quadtree, which also achieves an exponentially decaying R-D behavior, for the piecewise polynomial image model, with a low computational cost of O(N logN). Again, the key is an R-D optimized prune and join strategy. We further analyze the R-D performance of the proposed tree algorithms for piecewise smooth signals. We show that the proposed algorithms achieve the oracle like polynomially decaying asymptotic R-D behavior for both the 1-D and 2-D scenarios. Theoretical as well as numerical results show that the proposed schemes outperform wavelet based coders in the 2-D case. We then consider two interesting image processing problems, namely denoising and stereo image compression, in the framework of the tree structured segmentation. For the denoising problem, we present a tree based algorithm which performs denoising by compressing the noisy image and achieves improved visual quality by capturing geometrical features, like edges, of images more precisely compared to wavelet based schemes. We then develop a novel rate-distortion optimized disparity based coding scheme for stereo images. The main novelty of the proposed algorithm is that it performs the joint coding of disparity information and the residual image to achieve better R-D performance in comparison to standard block based stereo image coder
A Review of Bandlet Methods for Geometrical Image Representation
International audienceThis article reviews bandlet approaches to geometric image repre- sentations. Orthogonal bandlets using an adaptive segmentation and a local geometric flow well suited to capture the anisotropic regularity of edge struc- tures. They are constructed with a “bandletization” which is a local orthogonal transformation applied to wavelet coeffi cients. The approximation in these bandlet bases exhibits an asymptotically optimal decay for images that are regular outside a set of regular edges. These bandlets can be used to perform image compression and noise removal. More flexible orthogonal bandlets with less vanishing moments are constructed with orthogonal grouplets that group wavelet coeffi cients alon a multiscale association field. Applying a translation invariant grouplet transform over a translation invariant wavelet frame leads to state of the art results for image denoising and super-resolution
Reverse Digital Typography
In this project, we study the problem of reconstructing parametrized fonts from scanned images. In the first part, we investigate high-resolution noise-free images. In the second part, we study the noisy images, where artefacts such as low-resolution and blurry edges come into play. We present the quad-tree spline fitting method to robustly reconstruct parametrized fonts in the presence of print-scan artefacts
Moments-Based Fast Wedgelet Transform
In the paper the moments-based fast wedgelet
transform has been presented. In order to perform the classical
wedgelet transform one searches the whole wedgelets’
dictionary to find the best matching. Whereas in the proposed
method the parameters of wedgelet are computed directly
from an image basing on moments computation. Such
parameters describe wedgelet reflecting the edge present in
the image. However, such wedgelet is not necessarily the
best one in the meaning of Mean Square Error. So, to overcome
that drawback, the method which improves the matching
result has also been proposed. It works in the way that
the better matching one needs to obtain the longer time it
takes. The proposed transform works in linear time with respect
to the number of pixels of the full quadtree decomposition
of an image. More precisely, for an image of size
N ×N pixels the time complexity of the proposed wedgelet
transform is O(N2 log2 N)
A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity
The richness of natural images makes the quest for optimal representations in
image processing and computer vision challenging. The latter observation has
not prevented the design of image representations, which trade off between
efficiency and complexity, while achieving accurate rendering of smooth regions
as well as reproducing faithful contours and textures. The most recent ones,
proposed in the past decade, share an hybrid heritage highlighting the
multiscale and oriented nature of edges and patterns in images. This paper
presents a panorama of the aforementioned literature on decompositions in
multiscale, multi-orientation bases or dictionaries. They typically exhibit
redundancy to improve sparsity in the transformed domain and sometimes its
invariance with respect to simple geometric deformations (translation,
rotation). Oriented multiscale dictionaries extend traditional wavelet
processing and may offer rotation invariance. Highly redundant dictionaries
require specific algorithms to simplify the search for an efficient (sparse)
representation. We also discuss the extension of multiscale geometric
decompositions to non-Euclidean domains such as the sphere or arbitrary meshed
surfaces. The etymology of panorama suggests an overview, based on a choice of
partially overlapping "pictures". We hope that this paper will contribute to
the appreciation and apprehension of a stream of current research directions in
image understanding.Comment: 65 pages, 33 figures, 303 reference
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