BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

General Discrete Centered Image Pyramids

P. Brigger, M. Unser

Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet Applications in Signal and Image Processing V, San Diego CA, USA, July 30-August 1, 1997, vol. 3169, pp. 212–223.

We present an improved type of image pyramid based on general approximation functions. The type of pyramid proposed maintains the good properties of symmetry and consistent boundary conditions of the Haar pyramid. Moreover, it is not restricted to a piece-wise constant image model, but allows the use of any generating sequence. The centered topology guarantees a clearly defined up-projection of labels and may be employed in applications for contour detection, object recognition and segmentation. We start by introducing the general discrete framework for the design of least squares pyramids using the standard filtering and decimation tools based on arbitrary basis functions. Our design criterion is to minimize the l2 norm of the approximation error. We then define the centered pyramid and give explicit filter coefficients for odd and even spline approximation functions. Finally, we compare the centered pyramid to the ordinary one and highlight some applications. 

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