Planning: how to learn the horizontal set algorithm in Image Segmentation

The Level Set method was proposed by Osher and sethian in 1988 [1]. It was initially applied to fluid mechanics and has been widely used in various scientific research and engineering fields related to the same curve evolution. In 1997, CASELLES and others took the lead in applying this theory to the field of Image Science and began the research of image processing technology based on the level set method.

In order to improve the robustness of segmentation, a geometric Contour Model Based on Boundary edge, a region-based geometric contour model, and a geometric contour model based on prior shape knowledge are proposed, texture Image segmentation models, motion image segmentation models, and the integrated image segmentation models of these models. Multi-model component integration is an important trend in the development of this academic genre in recent years.

The horizontal set method is used to solve the problem of image segmentation by combining with the Geometric Active Contour Model. First, the continuous curve is used to describe the image edge directly, at the same time, the image information is used to define an Energy Functional independent variable including the boundary contour curve, and then the curve evolution equation corresponding to the Energy Functional is obtained by applying the dynamic format of the Euler-Langar equation, that is to say, the method of the horizontal set method is used to simulate the process of evolution of the initial curve along the fastest energy descent direction for a class of Hamilton-Kalton equations, so as to obtain the best boundary profile curve. This method can belong to a class of edge detection segmentation methods.

The key to implementing the level set method is the forward speed design of interface evolution, which is usually called a speed function. CASELLES, catte, coll, dibos, malladi, sethian, and vemuri are profile-basedMean Curvature motion and image gradientAs the main component to construct the speed function of the level set method, the Geometric Active Contour Model for image segmentation was first established;

Kichenassamy, Kumar, Olver, Tannenbaum, yezzi, CASELLES, Kimmel, and sapiro are based onMinimum geographic distanceClassic geometric contour models are obtained. These models are all geometric deformation models based on the contour edge. The common feature of the above method is to first establish an energy function that contains contour (surface) and Image Edge-related information, so that when the energy reaches the minimum value, the contour line exactly matches the boundary of the object to be separated, the shortest speed can be used as the speed function of the level set. Because many medical images and satellite remote sensing images contain a large amount of noise, it is inevitable that there will be strong edges or weak boundaries of objects to be separated. This method is mainly based on the local information at the edge contour, although we all consider adding frequent speed items for improvement, but the effect is limited, its natural improvement is to fully consider regional information. (Horizontal set class in Itk)

The typical image segmentation model based on the variational method is the Mumford-Shah model. The Mumford-Shah functional consists of three parts, the first is to express the data items that are similar to the observed data, the second is to express the smoothing items of the data within the region, and the third is the Constraint item with the minimum length of the model contour. The first two items are based on region information, and the third item is based on contour information. Due to the difficulties in theoretical analysis and practical application, different approximation or simplification are made in specific use. The first is to use the functional sequence defined in the sobolevspace to approximate the original functional sequence, so that the new functional sequence converges to the original functional sequence in the sense of Gamma convergence.

Chan-vese proposed an Active Contour Model without gradient items based on the simplified Mumford-Shah model and the horizontal set method for segmented constant-value images. The principles of this model are as follows: yezzi, Tsai, the two-phase and three-phase image segmentation proposed by willskyStatistical methodsThey are very similar, while the latter not only considers the average image strength of different regions, but also considers the average standard deviation of different regions. Zhu, yuille's Integrated Active Contour Model, regional growth model, energy model/Bayes model/minimum descriptive length model of regional competition model and paragios Based on the location measurement Active Contour Model and Maximum Posterior ProbabilityActive location Measurement Model, Sifakis, Garcia, and tziritas, a combination of the Bayes model and the horizontal set method, image segmentation model.

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The above region-based geometric deformation model assumes that the image to be split is a segmentation constant value, or that the image strength in different regions conforms to the Gauss distribution. In fact, the distribution model of images obtained from different devices or even images obtained from the same device in different environments may be different. Sarti, Corsi, and Mazzini use the maximum likelihood estimation to establish a method for the segmentation of ultrasonic images that conform to the distribution.

The fusion of region information enhances the robustness of the model. However, when the part of the object to be split is blocked or partially defective, even if the deformation model of the border and region information fusion cannot be split to produce correct results. The fusion of prior shape knowledge can not only effectively overcome this difficulty, but also further improve the behavior of the deformation model. Based on a variational horizontal set, a study on prior shape energy is integrated based on contour-based energy or region-based energy functions.