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Image Pyramids for generating pseudo band-pass filters

An image pyramid is the representation of an image at different resolutions. The idea behind image pyramids is to generate a number of homogeneous parameters that represent the response of a bank of filters at different scales and possibly different orientations. There are many different filters that can be used for this purpose. The Gaussian Pyramid decomposes the image into a set of low pass filtered images. The Laplacian Pyramid decomposes the image into a set of band pass filter [18], while the Oriented Laplacian Pyramid is decomposes the Laplacian Pyramid into a number of orientations [19]. A continuous reduction of image resolution with respect to the original image can be achieved by smoothing the image with a Gaussian smoothing kernel, the scale parameter corresponding to the standard deviation $\sigma$. Such successive smoothing of the original image gives a set of low-pass filtered images, which when stacked one on top of the other give rise to the Gaussian pyramid. The Laplacian pyramid images are then obtained as the difference between successive Gaussian levels. Each image of the Laplacian pyramid, which has been obtained as the difference of two low-pass filtered images, can thus be considered to be a band-pass filtered image. A more detailed description of the Gaussian filter which is the basis for the Gabor filter is provided in the next section.

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2002-06-03