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134 3 Image processing

I O

H 0 H 0
H Q F

L Ļ2 L 1 L 1 2 I

H H 1 Q H 1 F

L Ļ2 L 2 Q L 2 2 I

(a)

H 0 Q H 0
–
I 2

L Ļ2 L 1 L 1 2 I

(b)

Figure 3.34 The Laplacian pyramid: (a) The conceptual flow of images through processing stages: images are
high-pass and low-pass filtered, and the low-pass filtered images are processed in the next stage of the pyramid.
During reconstruction, the interpolated image and the (optionally filtered) high-pass image are added back to-
gether. The Q box indicates quantization or some other pyramid processing, e.g., noise removal by coring (setting
small wavelet values to 0). (b) The actual computation of the high-pass filter involves first interpolating the down-
sampled low-pass image and then subtracting it. This results in perfect reconstruction when Q is the identity.
The high-pass (or band-pass) images are typically called Laplacian images, while the low-pass images are called
Gaussian images.