Embedded zerotrees of wavelet transforms: Difference between revisions

Revision as of 03:36, 21 November 2023

Revision as of 03:37, 21 November 2023

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{{Short description|Lossy image compression algorithm}}

'''Embedded Zerotrees''' of '''Waveletwavelet transforms''' ('''EZW''') is a lossy [[image compression]] [[algorithm]]. At low bit rates, i.e. high compression ratios, most of the coefficients produced by a [[Sub-band coding|subband transform]] (such as the [[wavelet transform]]) will be zero, or very close to zero. This occurs because "real world" images tend to contain mostly low frequency information (highly correlated). However where high frequency information does occur (such as edges in the image) this is particularly important in terms of human perception of the image quality, and thus must be represented accurately in any high quality coding scheme.

will be zero, or very close to zero. This occurs because "real world" images tend to contain mostly low frequency information (highly correlated). However where high frequency information does occur (such as edges in the image) this is particularly important in terms of human perception of the image quality, and thus must be represented accurately in any high quality coding scheme.

By considering the transformed coefficients as a [[Tree (graph theory)|tree]] (or trees) with the lowest frequency coefficients at the root node and with the children of each tree node being the spatially related coefficients in the next higher frequency subband, there is a high probability that one or more subtrees will consist entirely of coefficients which are zero or nearly zero, such subtrees are called '''zerotrees'''. Due to this, we use the terms node and coefficient interchangeably, and when we refer to the children of a coefficient, we mean the child coefficients of the node in the tree where that coefficient is located. We use '''children''' to refer to directly connected nodes lower in the tree and '''descendants''' to refer to all nodes which are below a particular node in the tree, even if not directly connected.