Area and Length Minimizing Flows for Shape Segmentation

©1997 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.Presented at the 1997 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, June 17-19, 1997, San Juan, Puerto Rico.DOI: 10.1109/CVPR.1997.609390Several active contour models have been proposed to unify the curve evolution framework with classical energy minimization techniques for segmentation, such as snakes. The essential idea is to evolve a curve (in 20) or a surface (in 30) under constraints from image forces so that it clings to features of interest in an intensity image. Recently the evolution equation has. been derived from first principles as the gradient flow that minimizes a modified length functional, tailored io features such as edges. However, because the flow may be slow to converge in practice, a constant (hyperbolic) term is added to keep the curve/surface moving in the desired direction. In this paper, we provide a justification for this term based on the gradient flow derived from a weighted area functional, with image dependent weighting factor. When combined with the earlier modified length gradient flow we obtain a pde which offers a number of advantages, as illustrated by several examples of shape segmentation on medical images. In many cases the weighted area flow may be used on its own, with significant computational savings

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Area and Length Minimizing Flows for Shape Segmentation

A number of active contour models have been proposed which unify the curve evolution framework with classical energy minimization techniques for segmentation, such as snakes. The essential idea is to evolve a curve (in 2D) or a surface (in 3D) under constraints from image forces so that it clings to features of interest in an intensity image. Recently the evolution equation has been derived from first principles as the gradient flow that minimizes a modified length functional, tailored to features such as edges. However, because the flow may be slow to converge in practice, a constant (hyperbolic) term is added to keep the curve/surface moving in the desired direction. In this paper, we derive a modification of this term based on the gradient flow derived from a weighted area functional, with image dependent weighting factor. When combined with the earlier modified length gradient flow we obtain a pde which offers a number of advantages, as illustrated by several examples of shape segm..

Additional file 4: Figure S4. of Stimulation of triple negative breast cancer cell migration and metastases formation is prevented by chloroquine in a pre-irradiated mouse model

Quantitative densitometry from Western blots of the expression of (A) LCB3I, (B) LCB3II (Sham-CQ 60 vs IRR-CQ 60; P = 0.0024, CTL-CQ 60 vs IRR-CQ 60; P = 0.0182, IRR-VH vs IRR-CQ 60; P = 0.0009) and (C) p62 autophagy markers calculated using ImageJ Gel Analyze function

Additional file 5: Figure S5. of Stimulation of triple negative breast cancer cell migration and metastases formation is prevented by chloroquine in a pre-irradiated mouse model

Hormonal status of D2A1 cell line was confirmed by immunohistochemistry as described in Materials and Methods. No nuclear (ER and PR) as well as membrane (HER2) staining were observed. D2A1 cells were then revealed to be triple negative by a pathologist of our institution. (TIF 9131 kb

Additional file 1: Figure S1. of Stimulation of triple negative breast cancer cell migration and metastases formation is prevented by chloroquine in a pre-irradiated mouse model

Validation of the mice as its own control in mice pre-irradiated at the right mammary gland. D2A1 tumor volumes of sham irradiated animals (sham tumors) were compared to control tumors (left side) of pre-irradiated animals. Error bars indicate s.e.m. for n = 6 to 15 animals for each group. (TIF 224 kb