1,459 research outputs found
Fast O(1) bilateral filtering using trigonometric range kernels
It is well-known that spatial averaging can be realized (in space or
frequency domain) using algorithms whose complexity does not depend on the size
or shape of the filter. These fast algorithms are generally referred to as
constant-time or O(1) algorithms in the image processing literature. Along with
the spatial filter, the edge-preserving bilateral filter [Tomasi1998] involves
an additional range kernel. This is used to restrict the averaging to those
neighborhood pixels whose intensity are similar or close to that of the pixel
of interest. The range kernel operates by acting on the pixel intensities. This
makes the averaging process non-linear and computationally intensive,
especially when the spatial filter is large. In this paper, we show how the
O(1) averaging algorithms can be leveraged for realizing the bilateral filter
in constant-time, by using trigonometric range kernels. This is done by
generalizing the idea in [Porikli2008] of using polynomial range kernels. The
class of trigonometric kernels turns out to be sufficiently rich, allowing for
the approximation of the standard Gaussian bilateral filter. The attractive
feature of our approach is that, for a fixed number of terms, the quality of
approximation achieved using trigonometric kernels is much superior to that
obtained in [Porikli2008] using polynomials.Comment: Accepted in IEEE Transactions on Image Processing. Also see addendum:
https://sites.google.com/site/kunalspage/home/Addendum.pd
Constant-time filtering using shiftable kernels
It was recently demonstrated in [5] that the non-linear bilateral filter [14]
can be efficiently implemented using a constant-time or O(1) algorithm. At the
heart of this algorithm was the idea of approximating the Gaussian range kernel
of the bilateral filter using trigonometric functions. In this letter, we
explain how the idea in [5] can be extended to few other linear and non-linear
filters [14, 17, 2]. While some of these filters have received a lot of
attention in recent years, they are known to be computationally intensive. To
extend the idea in [5], we identify a central property of trigonometric
functions, called shiftability, that allows us to exploit the redundancy
inherent in the filtering operations. In particular, using shiftable kernels,
we show how certain complex filtering can be reduced to simply that of
computing the moving sum of a stack of images. Each image in the stack is
obtained through an elementary pointwise transform of the input image. This has
a two-fold advantage. First, we can use fast recursive algorithms for computing
the moving sum [15, 6], and, secondly, we can use parallel computation to
further speed up the computation. We also show how shiftable kernels can also
be used to approximate the (non-shiftable) Gaussian kernel that is ubiquitously
used in image filtering.Comment: Accepted in IEEE Signal Processing Letter
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
Spectral Characterization of functional MRI data on voxel-resolution cortical graphs
The human cortical layer exhibits a convoluted morphology that is unique to
each individual. Conventional volumetric fMRI processing schemes take for
granted the rich information provided by the underlying anatomy. We present a
method to study fMRI data on subject-specific cerebral hemisphere cortex (CHC)
graphs, which encode the cortical morphology at the resolution of voxels in
3-D. We study graph spectral energy metrics associated to fMRI data of 100
subjects from the Human Connectome Project database, across seven tasks.
Experimental results signify the strength of CHC graphs' Laplacian eigenvector
bases in capturing subtle spatial patterns specific to different functional
loads as well as experimental conditions within each task.Comment: Fixed two typos in the equations; (1) definition of L in section 2.1,
paragraph 1. (2) signal de-meaning and normalization in section 2.4,
paragraph
Bilateral Filter: Graph Spectral Interpretation and Extensions
In this paper we study the bilateral filter proposed by Tomasi and Manduchi,
as a spectral domain transform defined on a weighted graph. The nodes of this
graph represent the pixels in the image and a graph signal defined on the nodes
represents the intensity values. Edge weights in the graph correspond to the
bilateral filter coefficients and hence are data adaptive. Spectrum of a graph
is defined in terms of the eigenvalues and eigenvectors of the graph Laplacian
matrix. We use this spectral interpretation to generalize the bilateral filter
and propose more flexible and application specific spectral designs of
bilateral-like filters. We show that these spectral filters can be implemented
with k-iterative bilateral filtering operations and do not require expensive
diagonalization of the Laplacian matrix
Efficient SDP Inference for Fully-connected CRFs Based on Low-rank Decomposition
Conditional Random Fields (CRF) have been widely used in a variety of
computer vision tasks. Conventional CRFs typically define edges on neighboring
image pixels, resulting in a sparse graph such that efficient inference can be
performed. However, these CRFs fail to model long-range contextual
relationships. Fully-connected CRFs have thus been proposed. While there are
efficient approximate inference methods for such CRFs, usually they are
sensitive to initialization and make strong assumptions. In this work, we
develop an efficient, yet general algorithm for inference on fully-connected
CRFs. The algorithm is based on a scalable SDP algorithm and the low- rank
approximation of the similarity/kernel matrix. The core of the proposed
algorithm is a tailored quasi-Newton method that takes advantage of the
low-rank matrix approximation when solving the specialized SDP dual problem.
Experiments demonstrate that our method can be applied on fully-connected CRFs
that cannot be solved previously, such as pixel-level image co-segmentation.Comment: 15 pages. A conference version of this work appears in Proc. IEEE
Conference on Computer Vision and Pattern Recognition, 201
- …