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Clustering algorithms by minimizing an object function share a clear drawback that the number of clusters need to be set manually. Although density peak clustering is able to seek the number of clusters, it suffers from memory overflow when it is used for image segmentation because a moderate-size image usually includes a large number of pixels leading to a huge similarity matrix. To address the issue, here we proposed an automatic fuzzy clustering framework (AFCF) for image segmentation. The proposed framework has threefold contributions. Firstly, the idea of superpixel is used for the density peak (DP) algorithm, which efficiently reduces the size of the similarity matrix and thus improves the computational efficiency of the DP algorithm. Secondly, we employ a density balance algorithm to obtain a more robust decision-graph that helps the DP algorithm to achieve fully automatic clustering. Finally, a fuzzy c-means clustering based on prior entropy is used in the framework to improve image segmentation results. Because the spatial neighboring information of both the pixels and membership are considered, the final segmentation result is improved effectively. Experiments show that the proposed framework is not only able to achieve automatic image segmentation, it also provides better segmentation results than state-of-the-art algorithms.Index Terms-Fuzzy clustering, image segmentation, superpixel, density peak (DP) algorithm Tao Lei (M'17) received the Ph.D degree in Information and Communication Engineering from Northwestern

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Total variation method has been widely used in image processing. However, it produces undesirable staircase effect. To alleviate the staircase effect, some fourth order variational models were studied, which lead to the restored images smoothing and some details lost. In this paper, a low-order variational model for image deblurring and denoising is proposed, which is based on the splitting technique for the regularizer. Different from the general split technique, the improved variational model adopts the 1 L norm. To compute the new model effectively, we employ an alternating iterative method for recovering images from the blurry and noisy observations. The iterative algorithm is based on decoupling of deblurring and denoising steps in the restoration process. In the deblurring step, an efficient fast transforms can be employed. In the denoising step, the primal-dual method can be adopted. The numerical experiments show that the new model can obtain better results than those by some recent methods.

This paper considers the following parabolic-elliptic chemotaxisgrowth system with nonlinear diffusion ut = ∇ • (D(u)∇u) − ∇ • (χu q ∇v) + µu(1 − u α), x ∈ Ω, t > 0, 0 = ∆v − v + u γ , x ∈ Ω, t > 0 under homogeneous Neumann boundary conditions for some constants q ≥ 1, α > 0 and γ ≥ 1, where D(u) ≥ c D u m−1 (m ≥ 1) for all u > 0 and D(u) > 0 for all u ≥ 0, and Ω ⊂ R N (N ≥ 1) is a bounded domain with smooth boundary. It is shown that when m > q + γ − 2 N , or α > q + γ − 1, or α = q + γ − 1 and µ > µ * , where µ * = (α+1−m)N −2 (α+1−m)N +2(α−γ) χ, if m ≤ q + γ − 2 N , 0, if m > q + γ − 2 N , then the above system possesses a global bounded classical solution for any sufficiently smooth initial data. The results improve the results by Wang et al.

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In this paper, we present our recent study on the characterization of the elastic properties of several metal alloys fabricated by additive manufacturing method using the line-focus ultrasonic transducer technique. Line-focused ultrasonic transducer has been used to measure leaky surface wave velocity based on the time-resolved defocusing method in recent years. Elastic properties of the materials can be calculated based on the velocities of leaky Rayleigh wave and longitudinal bulk wave, which are generated and detected by the ultrasonic transducer. In this work, a line focus ultrasonic testing system was constructed, using a PVDF thin film piezoelectric transducer, a computer controlled z-stage and a rotary stage, and data acquisition software for precision measurement of the propagation velocity of surface wave in the test materials. The transducer system was calibrated by testing the commercial stainless steel, aluminum, and copper. The surface roughness of the testing samples was measured to eliminate the possible effect on the surface wave velocity. Finally, the transducer system was used to characterize the elastic properties of specimens of nickel alloy and stainless steel which were built by additive manufacturing instruments. The results indicate good agreement with the data measured by traditional method.