Image Line Groove Machine Keygenl
Rivka Licklider
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Medical image segmentation is crucial in diagnosing and treating diseases, but automatic segmentation of complex images is very challenging. Here we present a method, called the crack propagation method (CPM), based on the principles of fracture mechanics. This unique method converts the image segmentation problem into a mechanical one, extracting the boundary information of the target area by tracing the crack propagation on a thin plate with grooves corresponding to the area edge. The greatest advantage of CPM is in segmenting images involving blurred or even discontinuous boundaries, a task difficult to achieve by existing auto-segmentation methods. The segmentation results for synthesized images and real medical images show that CPM has high accuracy in segmenting complex boundaries. With increasing demand for medical imaging in clinical practice and research, this method will show its unique potential.
With the rapid development of modern imaging techniques, medical image segmentation plays an increasingly important role in the diagnosis and treatment of various diseases1. When computer models are used to simulate physiological phenomena, explore pathogenesis, and design personalized surgery, image segmentation is an essential step for reconstructing the anatomical structure of relevant tissues and organs2,3,4. Some typical segmentation technologies, such as the active contour model5,6,7,8,9,10, atlas-based registration11,12,13,14, and neural network-based segmentation15,16,17,18, have become more mature over the past several decades. Other strategies, such as fuzzy clustering19, the superpixel method20,21, and graph-cut method22,23, are also well applied to medical image segmentation. These autosegmentation methods have promoted the development of medical imaging-based diagnostic and treatment techniques. However, automatic image segmentation of certain complex images, such as soft tissues with blurred and discontinuous boundaries, remains challenging today. A general solution for the myriad of complex medical images that need to be segmented is still wanting. As a result, many complex medical images still rely on manual segmentation, greatly limiting the applications of medical imaging in a wider range of medical study and clinical practice.
One example of a segmentation problem that is difficult to solve can be found in head and neck magnetic resonance (MR) images. We see that the epimysium appears as a white bright line between dark-gray muscle tissues, and the grayscale color of these muscles is quite similar24. This dividing line between the muscles may be fuzzy and even discontinuous. No existing automatic methods can identify such a boundary correctly, and it currently must be segmented manually. So the question is, can we segment it automatically with the limited information that we have?
At present, the field of segmentation method study focuses on incremental improvements of existing mature algorithms according to characteristics of the target region7,8,9,10. Although these improvements can enhance the performance of segmentation methods to some extent, it is difficult to achieve a real breakthrough while being trapped in the existing frameworks. We propose a fresh way to think about the problem: can we solve the segmentation problem easily by transforming it into a problem in another field, such as a mechanics problem? This may sound farfetched because image processing and mechanics seem completely unrelated. But consider the following well-known real-life phenomenon: after we scored a glass surface using a glass cutter, the glass will crack along the scored line under an appropriate load. Therefore, if we convert the grayscale image into a thin plate and transform the boundary line between tissues into a groove or crack on its surface, then we can make this plate fracture along the groove just like cutting glass. Thus, the image segmentation problem transforms into a mechanical calculation of crack propagation on a thin plate. Compared with boundary-overflow issues caused by other algorithms, such as level sets, this mechanical method has an outstanding advantage when there are discontinuities or small grayscale gradients at the edge of the target area in the image. Due to stress concentration at its tip, when subject to external load, the crack can penetrate small gaps of groove-free regions in the thin-plane structure to connect to the crack on the other side of the gap, forming a continuous trace representing the boundary that we want to segment.
Based on the above analysis, we propose a unique method, named the crack-propagation method (CPM), for image segmentation. The core idea of this method is to transform the image segmentation problem into a mechanical problem of crack propagation on a thin plate. Using the principles of fracture mechanics, we can obtain the boundary coordinates of the target area in an image by tracing the cracks along the edge of the relevant region in a thin-plate model. This paper establishes this unique method, and demonstrates its great advantage and potential in image segmentation by segmenting synthetic and realistic medical images, especially those including soft tissues with blurred and broken boundaries.
The basic principle for converting grayscale to plate thickness is to transform the boundaries of the target region into grooves on the surface of a plate. Under external load, stress will concentrate at the groove, and the material cracks when the stress value exceeds a certain threshold25,26. By extracting coordinates of the crack and mapping it onto the original image, we can obtain the boundary of the target area. Here we construct the geometry of the thin plate based on not the grayscale value itself, but the gradient of the grayscale image, which can transform the boundary into grooves because the edge of the object region generally has substantial variation in grayscale level, and therefore a higher gradient, as shown in Fig. 1a.
a From left to right: original image, gradient image, grayscale trend of the gradient image, and mechanical model established from the gradient image. b From left to right: original image, images after intensity transformation, grayscale trend of the images in the second column, and perspective mechanical models corresponding to those same images. c From left to right: magnetic resonance image of head and neck muscles, grayscale trend of the one-sided model, grayscale trend of the two-sided model, and bilateral symmetric mechanical model.
The deeper the groove, the higher the stress concentration and the greater the tendency of crack propagation along the groove, and therefore the higher the accuracy of the segmentation result. Thus, when transforming an image into a plate, the height difference between the groove and its surrounding structures should be increased as much as possible. In order to increase the height difference, we can increase the grayscale contrast of the image. Figure 1b shows the results from linear and nonlinear transformations. Although a linear transformation can increase the overall grayscale contrast, the left boundary of the image is still blurred. When we perform a nonlinear transformation, the left boundary is further enhanced. We can achieve a much higher overall contrast compared to using a linear transformation, and additionally the grooves formed in the plate model are deeper.
The models established above are one-sided models, characterized by a flat lower and a curved upper surface with grooves. Because the stress distribution on two sides is different, the crack generated on the lower surface does not necessarily coincide with the grooves on the upper surface, which may cause deviations in the path of crack propagation. Figure 1c shows a symmetric model with grooves on the both sides of the thin plate. In the double-sided model, both surfaces reflect the same grayscale gradient, and therefore we can avoid the problem caused by an asymmetric stress distribution along the thickness of the plate in the one-sided model. Therefore, the results of the double-sided model can be more consistent with the boundary of the target area in the image.
The key for image segmentation using CPM is that the crack propagation in the plate due to stress concentration matches the boundary of the target area in the original image. Figure 2a shows the cross-sectional stress distribution under a distributed pulling force perpendicular to the groove in the plate, showing a strong stress concentration at the bottom of the groove. As shown in Fig. 2b, the deeper the groove, the greater the maximum stress. Therefore, when the boundary of the target area on the image is converted into a groove on a plate, the stress at the groove position will be much higher than in other areas under external load.
For the brittle materials, damage and breakage will occur at the location where the stress value reaches the strength limit of the material27. The stress concentration at the groove region allows it to reach the damage threshold first, causing it to crack. The crack continues to expand along the groove, tracing a path reflecting the boundary position. Figure 2c is a mechanical model for a thin plate with an arc-like groove. Under the external load F near the groove, stress concentration occurs at the groove region marked by the red circle. The local stress value increases rapidly as F increases, and a crack is generated there when the stress limit is reached (Fig. 2d). Persistently applying tensile force, the crack will continuously extend along the groove due to stress concentration, and finally will trace along the entire arc of the groove (Fig. 2e). After mapping the crack back to the original image, we can obtain the coordinates of the arc on the two-dimensional plane (Fig. 2f).
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