Fractional Order Model of the Two Dimensional Heat Transfer Process

In this paper, a new, state space, fractional order model of a heat transfer in two dimensional plate is addressed. The proposed model derives directly from a two dimensional heat transfer equation. It employes the Caputo operator to express the fractional order differences along time. The spectrum decomposition and stability of the model are analysed. The formulae of impluse and step responses of the model are proved. Theoretical results are verified using experimental data from thermal camera. Comparison model vs experiment shows that the proposed fractional model is more accurate in the sense of MSE cost function than integer order model.

Spectrum decomposition in Gaussian scale space for uneven illumination image binarization

Although most images in industrial applications have fewer targets and simple image backgrounds, binarization is still a challenging task, and the corresponding results are usually unsatisfactory because of uneven illumination interference. In order to efficiently threshold images with nonuniform illumination, this paper proposes an efficient global binarization algorithm that estimates the inhomogeneous background surface of the original image constructed from the first k leading principal components in the Gaussian scale space (GSS). Then, we use the difference operator to extract the distinct foreground of the original image in which the interference of uneven illumination is effectively eliminated. Finally, the image can be effortlessly binarized by an existing global thresholding algorithm such as the Otsu method. In order to qualitatively and quantitatively verify the segmentation performance of the presented scheme, experiments were performed on a dataset collected from a nonuniform illumination environment. Compared with classical binarization methods, in some metrics, the experimental results demonstrate the effectiveness of the introduced algorithm in providing promising binarization outcomes and low computational costs.