Image transforms

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Paramjeet Singh Jamwal

One-Dimensional & Two dimensional DFT, Cosine, Sine, Hadamard, Haar.

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The desire of better and faster retrieval techniques has always fuelled to the research in content based image retrieval (CBIR). The extended comparison of innovative content based image retrieval (CBIR) techniques based on feature vectors as fractional coefficients of transformed images using various orthogonal transforms is presented in the paper. Here the fairly large numbers of popular transforms are considered along with newly introduced transform. The used transforms are Discrete Cosine, Walsh, Haar, Kekre, Discrete Sine, Slant and Discrete Hartley transforms. The benefit of energy compaction of transforms in higher coefficients is taken to reduce the feature vector size per image by taking fractional coefficients of transformed image. Smaller feature vector size results in less time for comparison of feature vectors resulting in faster retrieval of images. The feature vectors are extracted in fourteen different ways from the transformed image, with the first being all the coefficients of transformed image considered and then fourteen reduced coefficients sets are considered as feature vectors (as 50%, 25%, 12.5%, 6.25%, 3.125%, 1.5625% ,0.7813%, 0.39%, 0.195%, 0.097%, 0.048%, 0.024%, 0.012% and 0.06% of complete transformed image coefficients). To extract Gray and RGB feature sets the seven image transforms are applied on gray image equivalents and the color components of images. Then these fourteen reduced coefficients sets for gray as well as RGB feature vectors are used instead of using all coefficients of transformed images as feature vector for image retrieval, resulting into better performance and lower computations. The Wang image database of 1000 images spread across 11 categories is used to test the performance of proposed CBIR techniques. 55 queries (5 per category) are fired on the database o find net average precision and recall values for all feature sets per transform for each proposed CBIR technique. The results have shown performance improvement (higher precision and recall values) with fractional coefficients compared to complete transform of image at reduced computations resulting in faster retrieval. Finally Kekre transform surpasses all other discussed transforms in performance with highest precision and recall values for fractional coefficients (6.25% and 3.125% of all coefficients) and computation are lowered by 94.08% as compared to Cosine or Sine or Hartlay transforms.

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