Maximum Energy Subsampling: A General Scheme For Multi-resolution Image Representation And Analysis
Image descriptors play an important role in image representation and analysis. Multi-resolution image descriptors can effectively characterize complex images and extract their hidden information.
Wavelet descriptors have been widely used in multi-resolution image analysis. However, making the wavelet transform shift and rotation invariant produces redundancy and requires complex matching processes. As to other multi-resolution descriptors, they usually depend on other methods, such as filtering function, prior-domain knowledge, etc.; that not only increases the computation complexity, but also generates errors.
We propose a novel multi-resolution scheme that is capable of transforming any kind of image descriptor into its multi-resolution structure with high computation accuracy and efficiency. Our multi-resolution scheme is based on sub-sampling each image into an odd-even image tree. Through applying image descriptors to the odd-even image tree, we get the relative multi-resolution image descriptors. Multi-resolution analysis is based on downsampling expansion with maximum energy extraction followed by upsampling reconstruction. Since the maximum energy usually retained in the lowest frequency coefficients; we do maximum energy extraction through keeping the lowest coefficients from each resolution level.
Our multi-resolution scheme can analyze images recursively and effectively without introducing artifacts or changes to the original images, produce multi-resolution representations, obtain higher resolution images only using information from lower resolutions, compress data, filter noise, extract effective image features and be implemented in parallel processing.