The influence of different wavelet transformations and decomposition on edge detection was examined, using convenient operators to images of various complexities. Berkeley Segmentation Database images with the corresponding ground truth were used. The categorization of those images was accomplished according to the degree of complexity in three groups (small, medium, and large number of details), by using discrete cosine transformation and discrete wavelet transformation. Three levels of decomposition for eight wavelet transformations and five operators for edge detection were applied on these images. As an objective measure of the quality for edge detection, the parameters “performance ratio” and “F-measure” were used.
The obtained results showed that edge detection operators behaved differently in images with a different number of details. Decomposition significantly degrades the image, but useful information can be extracted at the third level of decomposition, because the image with a different number of details behaves differently at each level. For an image with a certain number of details, decomposition Level 3 in some cases gives better results than Level 2. The obtained results can be applied to image compression with different complexity. By selecting a certain combination of operators and decomposition levels, a higher compression ratio with preserving a larger amount of useful image information can be achieved. Depending on the image resolution whereby the number of details varies, an operator optimization can be performed according to the decomposition level in order to obtain the best possible edge detection.
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