In this paper, we propose a new Modified Laplacian Vector Median Filter (MLVMF) for real-time denoising complex images corrupted by “salt and pepper” impulsive noise. The method consists of two rounds with three steps each: the first round starts with the identification of pixels that may be contaminated by noise using a Modified Laplacian Filter. Then, corrupted pixels pass a neighborhood-based validation test. Finally, the Vector Median Filter is used to replace noisy pixels. The MLVMF uses a 5 × 5 window to observe the intensity variations around each pixel of the image with a rotation step of π/8 while the classic Laplacian filters often use rotation steps of π/2 or π/4. We see better identification of noise-corrupted pixels thanks to this rotation step refinement. Despite this advantage, a high percentage of the impulsive noise may cause two or more corrupted pixels (with the same intensity) to collide, preventing the identification of noise-corrupted pixels. A second round is then necessary using a second set of filters, still based on the Laplacian operator, but allowing focusing only on the collision phenomenon. To validate our method, MLVMF is firstly tested on standard images, with a noise percentage varying from 3% to 30%. Obtained performances in terms of processing time, as well as image restoration quality through the PSNR (Peak Signal to Noise Ratio) and the NCD (Normalized Color Difference) metrics, are compared to the performances of VMF (Vector Median Filter), VMRHF (Vector Median-Rational Hybrid Filter), and MSMF (Modified Switching Median Filter). A second test is performed on several noisy chest x-ray images used in cardiovascular disease diagnosis as well as COVID-19 diagnosis. The proposed method shows a very good quality of restoration on this type of image, particularly when the percentage of noise is high. The MLVMF provides a high PSNR value of 5.5% and a low NCD value of 18.2%. Finally, an optimized Field-Programmable Gate Array (FPGA) design is proposed to implement the proposed method for real-time processing. The proposed hardware implementation allows an execution time equal to 9 ms per 256 × 256 color image.
International audience In this paper we are interested in the mathematical and numerical analysis of the timedependent Galbrun equation in a rigid duct. This equation modelizes the acoustic propagation in presence of flow. We prove the well-posedness of the problem for a subsonic uniform flow. Besides, we propose a regularized variational formulation of the problem suitable for an approximation by Lagrange finite elements. Dans ce papier, nous nous intéressons à l'analyse mathématique et à l'approximation numérique de l'équation de Galbrun en régime transitoire dans un conduit rigide. Cette équation modélise la propagation d'ondes acoustiques en présence d écoulement. Nous montrons pour un écoulement porteur uniforme subsonique que ce modèle a une solution unique. En outre, nous proposons une formulation variationnelle régularisée qui se prête à une approximation par éléments finis de Lagrange.
In this paper, we propose 2D dynamic visual servoing (Dynamic IBVS), where a quadrotor UAV tries to track a moving target using a single facing-down perspective camera. As an application, we propose the tracking of a car-type vehicle. In this case, data related to the altitude and the lateral angles have no importance for the visual system. Indeed, to perform the tracking, we only need to know the longitudinal displacements (along the x and y axes) and the orientation along the z-axis. However, those data are necessary for the quadrotor’s guidance problem. Thanks to the concept of differential flatness, we demonstrate that if we manage to extract the displacements according to the three axes and the orientation according to the yaw angle (the vertical axis) of the quadrotor, we can control all the other variables of the system. For this, we consider a camera equipped with a vertical stabilizer that keeps it in a vertical position during its movement (a gimbaled camera). Other specialized sensors measure information regarding altitude and lateral angles. In the case of classic 2D visual servoing, the elaboration of the kinematic torsor of the quadrotor in no way guarantees the physical realization of instructions, given that the quadrotor is an under-actuated system. Indeed, the setpoint has a dimension equal to six, while the quadrotor is controlled only by four inputs. In addition, the dynamics of a quadrotor are generally very fast, which requires a high-frequency control law. Furthermore, the complexity of the image processing stage can cause delays in motion control, which can lead to target loss. A new dynamic 2D visual servoing method (Dynamic IBVS) is proposed. This method makes it possible to generate in real time the necessary movements for the quadrotor in order to carry out the tracking of the target (vehicle) using a single point of this target as visual information. This point can represent the center of gravity of the target or any other part of it. A control by flatness has been proposed, which guarantees the controllability of the system and ensures the asymptotic convergence of the generated trajectory in the image plane. Numerical simulations are presented to show the effectiveness of the proposed control strategy.
This paper introduces a new method for real-time high-density impulsive noise elimination applied to medical images. A double process aimed at the enhancement of local data composed of Nested Filtering followed by a Morphological Operation (NFMO) is proposed. The major problem with heavily noisy images is the lack of color information around corrupted pixels. We show that the classic replacement techniques all come up against this problem, resulting in average restoration quality. We only focus on the corrupt pixel replacement phase. For the detection itself, we use the Modified Laplacian Vector Median Filter (MLVMF). To perform pixel replacement, two-window nested filtering is suggested. All noise pixels in the neighborhood scanned by the first window are investigated using the second window. This investigation phase increases the amount of useful information within the first window. The remaining useful information that the second window failed to produce in the case of a very strong connex noise concentration is then estimated using a morphological operation of dilatation. To validate the proposed method, NFMO is first evaluated on the standard image Lena with a range of 10% to 90% impulsive noise. Using the Peak Signal-to-Noise Ratio metric (PSNR), the image denoising quality obtained is compared to the performance of a wide variety of existing approaches. Several noisy medical images are subjected to a second test. In this test, the computation time and image-restoring quality of NFMO are assessed using the PSNR and the Normalized Color Difference (NCD) criteria. Finally, an optimized design for a field-programmable gate array (FPGA) is suggested to implement the proposed method for real-time processing. The proposed solution performs excellent quality restoration for images with high-density impulsive noise. When the proposed NFMO is used on the standard Lena image with 90% impulsive noise, the PSNR reaches 29.99 dB. Under the same noise conditions, NFMO completely restores medical images in an average time of 23 milliseconds with an average PSNR of 31.62 dB and an average NCD of 0.10.
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