An adaptive approach for texture enhancement based on a fractional differential operator with non-integer step and order

Depth Image Vibration Filtering and Shadow Detection Based on Fusion and Fractional Differential

The depth image generated by Kinect sensor always contains vibration and shadow noises which limit the related usage. In this research, a method based on image fusion and fractional differential is proposed for the vibration filtering and shadow detection. First, an image fusion method based on pixel level is put forward to filter the vibration noises. This method can achieve the best quality of every pixel according to the depth images sequence. Second, an improved operator based on fractional differential is studied to extract the shadow noises, which can enhance the boundaries of shadow regions significantly to accomplish the shadow detection effectively. Finally, a comparison is made with other traditional and state-of-the-art methods and our experimental results indicate that the proposed method can filter out the vibration and shadow noises effectively based on the [Formula: see text]-measure system.

Nonlinear information data mining based on time series for fractional differential operators

The use of mathematical methods has become an indispensable research tool and method in the establishment and improvement of many disciplines. Therefore, mathematical methods have also been included in the intelligence analysis system of public security information science. Intelligence is a summary of information that exists in all aspects of our lives. This information is distributed according to time based on certain rules. The application of mathematical analysis methods can more accurately extract effective information and predict future trends. As we all know, classical calculus is a powerful tool for dealing with many dynamic processes in the field of applied science. However, there are many complex systems in nature that cannot be characterized by classical integer-order calculus models, especially in information processing analysis. The fractional-order system model can better describe its system performance. This paper introduces the time series analysis method into the public security intelligence analysis system, combines the fractional differential operator to construct the mathematical model, analyzes the network intelligence, predicts the future occurrence of the case, and compares the predicted data with the actual data to verify. The method is predictive of the true credibility of the results.