04-01-2013, 04:36 PM
New Edge-Directed Interpolation
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Abstract
This paper proposes an edge-directed interpolation
algorithm for natural images. The basic idea is to first estimate
local covariance coefficients from a low-resolution image and
then use these covariance estimates to adapt the interpolation at
a higher resolution based on the geometric duality between the
low-resolution covariance and the high-resolution covariance. The
edge-directed property of covariance-based adaptation attributes
to its capability of tuning the interpolation coefficients to match
an arbitrarily oriented step edge. A hybrid approach of switching
between bilinear interpolation and covariance-based adaptive
interpolation is proposed to reduce the overall computational
complexity. Two important applications of the new interpolation
algorithm are studied: resolution enhancement of grayscale
images and reconstruction of color images from CCD samples.
Simulation results demonstrate that our new interpolation
algorithm substantially improves the subjective quality of the
interpolated images over conventional linear interpolation.
INTRODUCTION
IMAGE interpolation addresses the problem of generating a
high-resolution image from its low-resolution version. The
model employed to describe the relationship between high-resolution
pixels and low-resolution pixels plays the critical role
in the performance of an interpolation algorithm. Conventional
linear interpolation schemes (e.g., bilinear and bicubic) based
on space-invariant models fail to capture the fast evolving statistics
around edges and consequently produce interpolated images
with blurred edges and annoying artifacts. Linear interpolation
is generally preferred not for the performance but for computational
simplicity.
Many algorithms [1]–[12] have been proposed to improve
the subjective quality of the interpolated images by imposing
more accurate models. Adaptive interpolation techniques
[1]–[4] spatially adapt the interpolation coefficients to better
match the local structures around the edges. Iterative methods
such as PDE-based schemes [5], [6] and projection onto convex
sets (POCS) schemes [7], [8], constrain the edge continuity and
find the appropriate solution through iterations. Edge-directed
interpolation techniques [9], [10] employ a source model
that emphasizes the visual integrity of the detected edges
and modify the interpolation to fit the source model. Other
approaches [11], [12] borrow the techniques from vector
quantization (VQ) and morphological filtering to facilitate the
induction of high-resolution images.
Demosaicking of Color CCD Samples
Another important industrial application of new edge-directed
interpolation is the so-called “demosaicking” problem
[17], i.e., the reconstruction of a full-resolution color image
from CCD samples generated by the Bayer color filter array
(CFA), as shown in Fig. 3. It is easy to see that our algorithm
easily lends itself to the demosaicking problem. Two-step
algorithm described in Section III-A can be directly used to
interpolate the missing red and blue pixels; and only the second
step is needed for the green pixels. However, the approaches
of treating (R,G,B) planes independently ignore the strong
dependency among the color planes and annoying artifacts
brought by the color misregistration are often visible in the
reconstructed color images.
SIMULATION RESULTS
As mentioned in the introduction, most existing objective
metrics of image quality cannot take the visual masking effect
around an arbitrarily-oriented edge into account. Therefore,
we shall only rely on subjective evaluation to assess the visual
quality of the interpolated images.We believe that the improvements
on visual quality brought by new edge-directed interpolation
can be easily observed when the images are viewed at a
normal distance.
We have used four photographic images: Airplane, Cap,
Motor, and Parrot as our benchmark images. The original 24-bit
color images are 768 512 (around 1 MB). Photographic images
in this range (with the resolution of 0.25 M–1 M pixels)
are widely available in current digital camera products. Two
sets of experiments have been used to evaluate the effectiveness
of the proposed interpolation algorithm: one for grayscale
images and the other for color images.
CONCLUDING REMARKS
In this paper, we present a novel edge-directed interpolation
algorithm. The interpolation is adapted by the local covariance
and we provide a solution to estimate the high-resolution covariance
from the low-resolution counterpart based on their geometric
duality. A hybrid scheme of combining bilinear interpolationand covariance-based adaptive interpolation is proposed
to alleviate the burden of the computational complexity. We
have studied two important applications of our new interpolation
algorithm: resolution enhancement of grayscale images and
demosaicking of color CCD samples.