The human eye can perceive a vast array of colors. Whether light or dark, the colors that our eyes can see are supposedly unlimited. However, this is not the case. In reality, every image has two aspects or descriptors to it, a reflectance and an illumination. While the reflectance essentially shows an images true color, the illumination is what causes the colors to seem different to the human eye. This effect, originally discovered by Helmholtz, is known as Color Constancy. Color Constancy ensures that the color the Human Visual System (HVS) receives is the true color of the image, regardless of illumination. As a result of this effect, in 1971, Land and McCann created the Retinex theory. Using the pixels in the image, Land tried to estimate the value of the reflectances and thus reveal the true color of the image. This theory was basically a color constancy algorithm that tried to explain why colors look different when exposed to lighting. By calculating the pixels, Land was able to depict the sameness in a gradient of colors in an image. However, the algorithm is both inefficient and complicated. Following their footsteps, many other people have tried to formulate new algorithms around the Lands original Retinex algorithm. In this paper, different methods such as least squares and discrete cosine transform are explained as well as how to enhance images using both Lands idea and histogram equalization.

We derive pointwise curvature estimates for graphical mean curvature flows in higher codimensions. To the best of our knowledge, this is the first such estimates without assuming smallness of first derivatives of the defining map. An immediate application is a convergence theorem of the mean curvature flow of the graph of an area decreasing map between flat Riemann surfaces.

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This paper studies the convergence of the adaptively iterative thresholding (AIT) algorithm for compressed sensing. We first introduce a generalized restricted isometry property (gRIP). Then, we prove that the AIT algorithm converges to the original sparse solution at a linear rate under a certain gRIP condition in the noise free case. While in the noisy case, its convergence rate is also linear until attaining a certain error bound. Moreover, as by-products, we also provide some sufficient conditions for the convergence of the AIT algorithm based on the two well-known properties, i.e., the coherence property and the restricted isometry property (RIP), respectively. It should be pointed out that such two properties are special cases of gRIP. The solid improvements on the theoretical results are demonstrated and compared with the known results. Finally, we provide a series of simulations to verify the correctness of the theoretical assertions as well as the effectiveness of the AIT algorithm.