In forward warping the source image
mapped onto cylindrical surface, but it can create holes in the
image ( because some pixels may never get mapped there). therefore we
use inverse mapping where each pixel in the destination image is mapped
to the source image. Since either of the mapping is unlikely to be
exact on the
pixel values, bilinear interpolation is used to calculate the colors at
the destination pixels.
Because of the thick lens that are
often used in the camera, it is
necessary to correct the radial distortions in the image. One of
the simplified distortion model that is commonly used is
Xd = Xu( 1 + k1*r^2 + k2*r^4)
Yd = Yu( 1 + k1*r^2 + k2*r^4 )
Where (Xd,Yd) are the distorted image position and (Xu,Yu) are the
undistorted correct position. The values (k1,k2) that depends on the
camera can be calibrated using some standard techniques.
Both inverse mapping and radial distortion correction requires
interpolation to calculate the color values at the destination pixel.o
Interpolation is not only expensive, they also smooth the features,
therefore, this step must be minimized to get high quality final
images. In this application there are two places where interpolated
values are required (1) Cylindrical to image in inverse warping (2)
From undistorted image values to distorted images values. We can
combine these two steps and calculate cylindrical image values directly
from the distorted images and therefore, avoid the intermediate
Ransac algorithm is general purpose
algorithm that can be used to
calculate full homography in the presense of outliers. The use of
cylindrical warping has the advantage that only the translation motion
has to calculated on the warped image. Also for the translation
estimation, only one feature is sufficient. Ransac estimation counts
the inliners based on some tolerance value ( d < eps) which depends
on the noise present in the images. Since our image capturing was high
quality, only two pixel tolerance was sufficient to get good
estimation. ( We found that that in our images only 5-10% outliers).
When different images are stitched
together, for various reasons
(changed lighting conditions, vignette effects) the adjacent pixel
intensities differ enough to produce artifacts as shown in the
following pictures. To remove these artifacts, we experimented with two
algorithms (1) Feathering (2) Image pyramids.
Feathering or center weighting image blending:
In this simplest approach, the the
pixel values in the blended regions
are weighted average from the two overlapping images. Sometimes this
simple approach doesn't work( for example in the presence of exposure
differences ). But in our case, all the images were taken at the same
time and using high quality tripods, therefore, this simple algorithm
produces excellant results.
PB(i,j) = (1-w)*PA(i,j) + w*PB(i,j)
Laplacian pyramid is an algorithm using
Gaussian to blend the image while keeping the significant feature in
the mean time. It downsizes the image into different levels (sizes)
with Gaussian. Later it expands the Gaussian in to the lower lever
and subtracts from the image in that lever to acquire the Laplacian
Very often the first image and the last image in the view don't align
properly. This misalignment can be adjusted by shear warping and other
bundle adjustment algorithm. In our case, we didn't have to do any
adjustment as the misaligment was only 1-2 pixels.
We used Canon SX100 and Kedan tripods provided by Dr. Li Zhang. Some
specific information of the camera are as follows:
resolution : 480x640
focal length : 678.05421
Here is the panoramic image generated from our implemention: panorama1
Software and Usage Guide:
The entire source code is written in C++. The only dependencies to use
this software are "SIFT" and ImageiMagick++ which must be downloaded
separately. Monju has developed Pyramid Blending code in
Click here to download the entire source code.
Step 1: Create one folder, set DataSet.
Step 2: Inside the Dataset folder create some new directories;
DataSet/RawImages : All the raw images goes in this
DataSet/WarpImages: All cylindrical warped images are
stored in this directory.
DataSet/PNGImages : All cylindrical images are converted in
gray scale for feature detection.
: All features keys from the Sift programs are stored in this
Once all the directories are created execute the command
executable <root directory name>
It will generate a panormic image "panimage.jpg" which must be cropped
- R. Szeliski and H.-Y. Shum.
Creating full view panoramic image mosaics and texture-mapped models,
SIGGRAPH 1997, pp251-258.
- M. Brown, D. G. Lowe,
Recognising Panoramas, ICCV 2003.
We worked as a group but distributed the work as follows:
Chaman Singh : Develop the entire C++ code including warping,
ransac, feathering (in C++) , results, performance analysis and
: Image taking, Pyramid blending code in matlab, feathering
code in matlab.