Some recent methods, like the Empirical Mode De-composition (EMD), propose to decompose a signal accordingly to its contained information. Even though its adaptability seems useful for many applications, the main issue with this approach is its lack of theory. This paper presents a new approach to build adaptive wavelets. The main idea is to extract the different modes of a signal by designing an appropriate wavelet filter bank. This construction leads us to a new wavelet transform, called the empirical wavelet transform. Many experiments are presented showing the usefulness of this method compared to the classic EMD.

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In this paper, we present an algorithm to automatically detect meaningful modes in a histogram. The proposed method is based on the behavior of local minima in a scale-space representation. We show that the detection of such meaningful modes is equivalent in a two classes clustering problem on the length of minima scale-space curves. The algorithm is easy to implement, fast and does not require any parameter. We present several results on histogram and spectrum segmentation, grayscale image segmentation and color image reduction.

Carboranethiol molecules self-assemble into upright molecular monolayers on Au{111} with aligned dipoles in two dimensions. The positions and offsets of each molecule's geometric apex and local dipole moment are measured and correlated with sub-Ångström precision. Juxtaposing simultaneously acquired images, we observe monodirectional offsets between the molecular apexes and dipole extrema. We determine dipole orientations using efficient new image analysis techniques and find aligned dipoles to be highly defect tolerant, crossing molecular domain boundaries and substrate step edges. The alignment observed, consistent with Monte Carlo simulations, forms through favorable intermolecular dipoleÀdipole interactions.