We propose and analyze a nonparametric regionbased active contour model for segmenting cluttered scenes. The proposed model is unsupervised and assumes pixel intensity is independently identically distributed. Our proposed energy functional consists of a geometric regularization term that penalizes the length of the partition boundaries and a region-based image term that uses histograms of pixel intensity to distinguish different regions. More specifically, the region data encourages segmentation so that local histograms within each region are approximately homogeneous. An advantage of using local histograms in the data term is that histogram differentiation is not required to solve the energy minimization problem. We use Wasserstein distance with exponent 1 to determine the dissimilarity between two histograms. The Wasserstein distance is a metric and is able to faithfully measure the distance between two histograms, compared to many pointwise distances. Moreover, it is insensitive to oscillations, and therefore our model is robust to noise. A fast global minimization method based on is employed to solve the proposed model. The advantages of using this method are two-fold. First, the computational time is less than that of the method by gradient descent of the associated Euler-Lagrange equation (Chan et al. in Proc. of SSVM, pp. 697-708, 2007). Second, it is able to find a global minimizer. Finally, we propose a variant of our model that is able to properly segment a cluttered scene with local illumination changes.

Abstract. In this paper, we propose a new nonparametric region-based active contour model for clutter image segmentation. To quantify the similarity between two clutter regions, we propose to compare their respective histograms using the Wasserstein distance. Our first segmentation model is based on minimizing the Wasserstein distance between the object (resp. background) histogram and the object (resp. background) reference histogram, together with a geometric regularization term that penalizes complicated region boundaries. The minimization is achieved by computing the gradient of the level set formulation for the energy. Our second model does not require reference histograms and assumes that the image can be partitioned into two regions in each of which the local histograms are similar everywhere.

A recently proposed approach for compressed sensing, or compressive sampling, with deterministic measurement matrices made of chirps is applied to images that possess varying degrees of sparsity in their wavelet representations. The "fast reconstruction" algorithm enabled by this deterministic sampling scheme as developed by Applebaum et al.[1] produces accurate results, but its speed is hampered when the degree of sparsity is not sufficiently high. This paper proposes an efficient reconstruction algorithm that utilizes discrete chirp-Fourier transform (DCFT) and updated linear least squares solutions and is suitable for medical images, which have good sparsity properties. Several experiments show the proposed algorithm is effective in both reconstruction fidelity and speed.

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A recent approach to compressed sensing using deterministic sensing matrices formed from discrete frequency-modulated chirps or from Reed-Muller codes is extended to support efficient deterministic reconstruction of signals that are much less sparse than envisioned in the original work. In particular, this allows the application of this approach in imaging. The reconstruction algorithm developed for images incorporates several new elements to improve computational complexity and reconstruction fidelity in this application regime. Introduction.In the few years since the foundational ideas of compressed sensing were set forth by Donoho [19] and Candès and Tao [15,11], the methodology has inspired a substantial body of research seeking to exploit sparsity in various classes of signals to enable efficient measurement approaches [27,32,33]. While most of the emphasis has been connected with the use of stochastic measurement matrices, a few researchers have sought to develop deterministic measurement strategies. Among these is an approach introduced by Applebaum et al.[2] and extended by Howard, Calderbank, and Searle [25] in which the columns of the measurement matrix consist of sampled linear frequency-modulated chirps or the closely related second-order Reed-Muller codes. This approach includes a deterministic algorithm for reconstructing the original sparse signal from measurements that is shown to compare favorably to reconstruction methods used in other compressed sensing contexts, particularly so when the signal is extremely sparse. The performance of this algorithm deteriorates significantly, both in speed and fidelity, when the signal is less sparse. In most image processing applications, intrinsic compressibility of classes of images using a suitable basis (e.g., wavelets) typically makes high-accuracy approximation by a sparse image possible only if the sparsity is 5-20% or higher. Thus, the reconstruction algorithm for chirp compressed sensing given in [2] and the closely related algorithm for Reed-Muller compressed sensing given in [25] are not suitable