This shows two input images (from left) stitched
together using the proposed method (right). Credit:
original image: Blanka M. Lukes, Prague Private Guides;
modified image: Wei Wang and Michael Ng.
A photo captures only as much as the camera in use
will allow, and is therefore limited by the field of view
of the camera's lens. In the case of smartphones and
many advanced cameras, the view from the lens is
much smaller than the view from your own eyes.
Panoramic photographs were invented to capture large
objects or scenes that could not otherwise fit within
the constraints of a single photo. Panoramic
photography is achieved through image stitching, a
process that combines two or more photographs,
seamlessly blending input images with overlapping
regions into one picture. A paper published by Wei
Wang and Michael Ng in the SIAM Journal on
Imaging Sciences this summer aims to develop an
algorithm for image stitching.
Image stitching involves two steps: image alignment
and image blending. Image alignment finds point pairs
in the overlapping region of two images that
correspond to one another. Image blending combines
the two aligned images seamlessly. This step is
important if the pixel intensities in the different images
vary enough to produce artifacts such as varying
lighting conditions and different exposure settings. In
this paper, the authors focus on image blending,
assuming that the images have been aligned.
Many different approaches for image blending are
seen in the literature. "The traditional method is to
search for a curve in the overlapping area in which
the differences among the input images are minimal,"
explains author Michael Ng. "However, the curve may
not be determined accurately because of light
intensity, color inconsistency, parallax, occlusion, etc."
The approach used in this paper instead minimizes
seam artifacts by smoothing the transition between the
images. The mosaic image here is a weighted
combination of the input images. This means the pixel
values from the two overlapping images are combined
using a weighted average for qualities such as
exposure, local contrast, saturation, etc.
How is this achieved?
Many systems, both natural and man-made, seek out
the lowest energy state, such as, a ball rolling down a
hill, or a snow-laden tree branch bending to maintain
the lowest possible energy in the system. The concept
of minimizing the energy of a given system is also used
in image processing. For a given image, an energy
function is defined and minimized to get a better
image (i.e. less noise, better sharpness, higher
contrast, etc.). This is the approach the authors use in
the paper. Seamless combination of images is achieved
by minimizing an energy function based on intensity or
gradient differences of the two images.
"According to the model, we construct a weighting
function over the overlapping area so that a
panoramic image can be generated," says Ng. "The
optimal weighting function can be obtained by
minimizing the overall energy of the mathematical
model." Thus, in the proposed model, both the
weighting function and the ?nal blending in the
overlapping region are based on solving an energy
minimizing problem. The authors show how to define
an energy function and develop an algorithm to
minimize it.
This variational method—based on achieving the
lowest energy or ground state—is seen to produce a
more visually appealing photo in comparison to other
existing methods.
Future work may extend the scope of this research
beyond two-dimensional images. "It is interesting to
consider extending the current variational approach to
tackle the problem of three-dimensional image
stitching in medical imaging applications and stitching
video in computer applications," Ng says.
More information: A Variational Approach for Image
Stitching I, Wei Wang and Michael K. Ng SIAM
Journal on Imaging Sciences , 6(3), 1318 (Online
publish date: 11 July 2013). http://epubs.siam.org/doi/
abs/10.1137/110819871
To read related research published by the authors
about further developing an image stitching algorithm
using the gradients of input images, view: A Variational
Approach for Image Stitching II: Using Image Gradients
http://epubs.siam.org/doi/abs/10.1137/120872140
SIAM Journal on Imaging Sciences, 6(3), 1345
Provided by Society for Industrial and Applied
Mathematics
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