How do you calculate the residual? Is it literally the difference between the blurred image and the original of the same size?
Is Laplacian up-sampling truly lossless? I see how since the smaller image is downsampled from a blurry image with lower frequency then we're not losing that much information, and the stuff we do lose is added back with the residual, but it still feels like in the upsampling process we'll lose some information.
mpotoole
Yes---it is literally the difference between the blurry and original image.
If the downsampling operation is invertible (i.e., an upsampling operation produces the blurry image exactly), this procedure is lossless. But for this to work, you have to be a little careful with how the blur/downsampling/upsampling operations are implemented here. For example, if you don't apply enough blur to the images, then you will lose some information in the downsampling process.
thuspake
It makes sense but I'm still shocked it works. Wow.
mpotoole
Here's one way to ensure that the Laplacian pyramid is lossless, i.e., reproduce the image exactly according to this slide. Step 1: Construct a Gaussian pyramid and store $f_k$ (the original image at every level $k$). Step 2: Upsample each image $f_{k+1}$ and store the resulting blurry image $b_{k}$. Step 3: Compute the Laplacian image at level $k$ by taking the difference $f_{k+1}$ and $b_{k}$.
I have a few questions
How do you calculate the residual? Is it literally the difference between the blurred image and the original of the same size?
Is Laplacian up-sampling truly lossless? I see how since the smaller image is downsampled from a blurry image with lower frequency then we're not losing that much information, and the stuff we do lose is added back with the residual, but it still feels like in the upsampling process we'll lose some information.
It makes sense but I'm still shocked it works. Wow.
Here's one way to ensure that the Laplacian pyramid is lossless, i.e., reproduce the image exactly according to this slide. Step 1: Construct a Gaussian pyramid and store $f_k$ (the original image at every level $k$). Step 2: Upsample each image $f_{k+1}$ and store the resulting blurry image $b_{k}$. Step 3: Compute the Laplacian image at level $k$ by taking the difference $f_{k+1}$ and $b_{k}$.