A bound on the expected overshoot for some concave boundaries

Albrecht Irle; Vladimir Ivanovich Lotov

doi:10.1007/bf02717178

Phase- and GVF-Based Level Set Segmentation of Ultrasonic Breast Tumors

Journal of Applied Mathematics ◽

10.1155/2012/810805 ◽

2012 ◽

Vol 2012 ◽

pp. 1-22 ◽

Cited By ~ 7

Author(s):

Liang Gao ◽

Xiaoyun Liu ◽

Wufan Chen

Keyword(s):

Level Set ◽

Breast Tumor ◽

Active Contour Model ◽

Speckle Noise ◽

Ultrasound Images ◽

Low Contrast ◽

Good Convergence ◽

Capture Range ◽

Edge Based ◽

Concave Boundaries

Automatically extracting breast tumor boundaries in ultrasound images is a difficult task due to the speckle noise, the low image contrast, the variance in shapes, and the local changes of image intensity. In this paper, an improved edge-based active contour model in a variational level set formulation is proposed for semi-automatically capturing ultrasonic breast tumor boundaries. First, we apply the phase asymmetry approach to enhance the edges, and then we define a new edge stopping function, which can increase the robustness to the intensity inhomogeneities. To extend the capture range of the method and provide good convergence to boundary concavities, we use the phase information to obtain an improved edge map, which can be used to calculate the gradient vector flow (GVF). Combining the edge stopping term and the improved GVF in the level set framework, the proposed method can robustly cope with noise, and it can extract the low contrast and/or concave boundaries well. Experiments on breast ultrasound images show that the proposed method outperforms the state-of-art methods.

Steady inviscid rotational flows with free surfaces

Journal of Fluid Mechanics ◽

10.1017/s0022112094003253 ◽

1994 ◽

Vol 258 ◽

pp. 105-113 ◽

Cited By ~ 3

Author(s):

J.-M. Vanden-Broeck ◽

E. O. Tuck

Keyword(s):

Fluid Velocity ◽

Inviscid Fluid ◽

Single Plane ◽

Free Surfaces ◽

Finite Segment ◽

Velocity Magnitude ◽

Constant Vorticity ◽

Rotational Flows ◽

Parabolic Dish ◽

Concave Boundaries

An inviscid fluid in steady two-dimensional motion in a region bounded by a closed streamline must have constant vorticity. We solve here for some such flows where the boundary is in part free, the fluid velocity magnitude being constant on the free boundary. A trivial example of such a flow is a circular cylinder of fluid rotating about its axis as if rigid, for which the whole circular boundary is free, irrespective of its radius. We now ask what happens to that flow when it comes into contact with solid boundaries. There is no steady flow when the contact is with a finite segment of a single plane wall, but a unique solution exists when the rotating fluid mass is in contact with some concave boundaries. Computed results are obtained for vortices lying inside a parabolic dish, or in a corner between two planes.

Study on the Characteristic Point Location of Depth Average Velocity in Smooth Open Channels: Applied to Channels with Flat or Concave Boundaries

Water ◽

10.3390/w12020430 ◽

2020 ◽

Vol 12 (2) ◽

pp. 430 ◽

Cited By ~ 2

Author(s):

Tongshu Li ◽

Jian Chen ◽

Yu Han ◽

Zhuangzhuang Ma ◽

Jingjing Wu

Keyword(s):

Average Velocity ◽

Characteristic Point ◽

Vertical Direction ◽

Side Wall ◽

Mathematical Expression ◽

Open Channels ◽

Point Location ◽

Flow Measurements ◽

Characteristic Points ◽

Concave Boundaries

Based on the flow partition theory, we derive a mathematical expression by using the log-law for the characteristic point location (CPL) of depth average velocity in channels with flat or concave boundaries. It can manifest the position of the characteristic points in the vertical direction relative to the channel side wall or bed. Taking rectangular and semi-circular channels as research objects, we put forward a method to calculate the discharge of channels with CPL. Additionally, we carried out some experiments on rectangular and semi-circular channel sections. CPL’s analytic expression is validated against experimental results through comparison of velocity and discharge. The proposed formulation of characteristic point location could be extensively employed in flow measurements of flat and concave boundary channels, which has practical application value in simplifying the flow measurement steps of open channels.

Effect of the Forest-Mine Boundary Form on Woody Colonization and Forest Expansion in Degraded Ecosystems

Forests ◽

10.3390/f12060773 ◽

2021 ◽

Vol 12 (6) ◽

pp. 773

Author(s):

Carolina Martínez-Ruiz ◽

Ana I. Milder ◽

Daphne López-Marcos ◽

Pilar Zaldívar ◽

Belén Fernández-Santos

Keyword(s):

Woody Species ◽

Forest Edge ◽

Quercus Petraea ◽

Northern Spain ◽

Forest Expansion ◽

Nurse Plants ◽

Colonization Pattern ◽

Mine Sites ◽

Concave Boundaries ◽

Boundary Form

We evaluated the ecological significance of the boundary form between two patches with contrasting vegetation (mine grassland and adjacent forest) on woody colonization and forest expansion in open-cast coal mines in Northern Spain. Woody colonization and browsing traces were measured on three mine sites, along 24 transects that were laid out perpendicular to the forest-mine boundary and classified according to their shape (concave, convex, straight). Mine sites were colonized from the close forest by woody species, whose colonization intensity depends on the boundary form. The overall colonization intensity decreased with increasing distance to the forest and differed depending on the boundary form. The more intense colonization was found in concave boundaries and the strongest decrease in convex boundaries close to the forest, whereas straight boundaries showed an intermediate colonization pattern. Concave boundaries reached higher woody cover in the basal strata of the mines than convex (up to 2 m) or straight boundaries (up to 1 m) from 11 m to the forest edge, mainly by the presence of dense patches of Cytisus scoparius (L.) Link, with a scattered overstory of Genista florida L. These shrubs might reduce the browsing intensity and act as nurse plants facilitating the establishment of Quercus petraea (Matt.) Liebl. in mine areas at greater distances from the forest edge. The forest-mine boundary form does not affect the forest vertical structure that is homogenous and does not help explain the woody colonization pattern in the mines. We conclude that edge characteristics have a strong potential to be used in the restoration of native forests based on natural processes. The implications of our results for sessile oak (Quercus petraea (Matt.) Liebl.) forest expansion along edges in fragmented Mediterranean forest landscapes were discussed.