We present an algorithm to approximate a set of unorganized points with a simple curve without self-intersections. The moving least-squares method has a good ability to reduce a point cloud to a thin curve-like shape which is a near-best approximation of the point set. In this paper, an improved moving least-squares technique is suggested using Euclidean minimum spanning tree, region expansion and refining iteration. After thinning a given point cloud using the improved moving least-squares technique we can easily reconstruct a smooth curve. As an application, a pipe surface reconstruction algorithm is presented.

Offset curves have diverse engineering applications, which have consequently motivated extensive research concerning various offset techniques. Offset research in the early 1980s focused on approximation techniques to solve immediate application problems in practice. This trend continued until 1988, when Hoschek [1, 2] applied non-linear optimization techniques to the offset approximation problem. Since then, it has become quite difficult to improve the state-of-the-art of offset approximation. Offset research in the 1990s has been more theoretical. The foundational work of Farouki and Neff [3] clarified the fundamental difficulty of exact offset computation. Farouki and Sakkalis [4] suggested the Pythagorean Hodograph curves which allow simple rational representation of their exact offset curves.

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An image is a very effective tool for conveying emotions. Many researchers have investigated in computing the image emotions by using various features extracted from images. In this paper, we focus on two high level features, the object and the background, and assume that the semantic information of images is a good cue for predicting emotion. An object is one of the most important elements that define an image, and we find out through experiments that there is a high correlation between the object and the emotion in images. Even with the same object, there may be slight difference in emotion due to different backgrounds, and we use the semantic information of the background to improve the prediction performance. By combining the different levels of features, we build an emotion based feed forward deep neural network which produces the emotion values of a given image. The output emotion values in our framework are continuous values in the 2-dimensional space (Valence and Arousal), which are more effective than using a few number of emotion categories in describing emotions. Experiments confirm the effectiveness of our network in predicting the emotion of images.

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Many visualization techniques use images containing meaningful color sequences. If such images are converted to grayscale, the sequence is often distorted, compromising the information in the image. We preserve the significance of a color sequence during decolorization by mapping the colors from a source image to a grid in the CIELAB color space. We then identify the most significant hues, and thin the corresponding cells of the grid to approximate a curve in the color space, eliminating outliers using a weighted Laplacian eigenmap. This curve is then mapped to a monotonic sequence of gray levels. The saturation values of the resulting image are combined with the original intensity channels to restore details such as text. Our approach can also be used to recolor images containing color sequences, for instance for viewers with color‐deficient vision, or to interpolate between two images that use the same geometry and color sequence to present different data.