Hybrid Images with Laplacian Pyramids
Kyle Cackett
Gaussian/Laplacian image pyramids
are constructed by applying low/high pass filters to a base image and subsampling the low pass filtered image to use as the base
image for the next level in the pyramid. To build my Gaussian and Laplacian pyramids I used a Guassian
filter of size=13 and sigma=HalfSize/3=2 and sub-sampled
every other pixel (the high pass Laplacian pyramid
was constructed by subtracting the Gaussian filtered image from the base image).
I
selected my filter parameters by transforming a number of Gaussian filters into
the frequency domain and picking the filter which seemed to adhere most closely
to the Nyquist limit. I looked for a filter that wiped out
frequencies higher than half of the sampling rate which in this case was half
the image size. For simplicity I used a
square Guassian filter but better results might be
obtained using a filter whose dimensions more closely match the base image's
dimensions.
Hybrid images are constructed by combining the high
frequencies of one image with the low frequencies of a second image. This results in an image whose interpretation
depends on the viewing distance. To construct
hybrid images from the Gaussian/Laplacian pyramids we
combine the top levels of the Laplacian pyramid of
one image (which contains the highest frequencies in that image) with the
bottom portion of the Gaussian pyramid of the other image (which contains the
lowest frequencies in that image). All
of the pyramids I used had 8 levels and I selected a pyramid cutoff level for
each image by testing a number of different cutoffs and qualitatively
evaluating which cutoff produced a hybrid image that best transformed with
distance. My results are included below.
Car + Rhino Hybrid – Cutoff Level 1
Einstein + Marilyn Hybrid – Cutoff Level
1
Cat + Dog Hybrid – Cutoff Level 2