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 1Carhino_c=1.jpg

Einstein + Marilyn Hybrid – Cutoff Level 1Marilyn+Einstein_c=1.jpg

Cat + Dog Hybrid – Cutoff Level 2

Cat+Dog_c=2.jpg