Now, what's the gradient vector?
现在，梯度向量是什么呢？
So, if you prefer, that's where the gradient vector is zero.
认为梯度向量为零也是可以的。
The gradient vector would be going perpendicular to the level.
梯度向量应该垂直于等值线。
If I fix a point, then the gradient vector at that point is given to me.
确定一点，那么对我来说，这点的梯度向量就是确定的。
So, we said when we have a function of two variables, we have the gradient vector.
我们说，当一个二元函数存在时，就有梯度向量。
And we have learned how to package partial derivatives into a vector, the gradient vector.
我们也知道了，如何将各个偏导组合成一个梯度向量。
We discuss several different definitions of directional derivative and gradient vector.
讨论了几种不同的方向导数和梯度的定义。
In this thesis, a new deformable model called Iterative Gradient Vector Flow (IGVF) is developed.
本文提出了迭代梯度矢量流参数变形模型(IGVF)。
We presented a novel and fast convergent skeleton snake model based on gradient vector flow (GVF).
提出了一种基于梯度矢量流(GVF)的快速收敛骨架snake算法。
This indicates that there is more profound physical meaning of the gradient vector potential of electromagnetic field.
因此，它表明电磁场的梯度矢势具有更明显的物理意义。
The discrete gradient vector filed based on the Morse theory is presented, and is applied to visualization of topologies.
研究了基于莫尔斯理论的离散梯度向量域方法，并将其应用于拓扑可视化。
And we know how to find a normal vector to the level set, namely the gradient vector is always perpendicular to the level set.
我们是知道如何去求水平集的法向量的，也就是垂直于水平集的法向量。
OK, the best way to it, now that we have the gradient vector, is actually to directly say oh, we know the normal vector to this plane.
最好的方法是，既然我们已经有了梯度向量，就可以直接说,我们知道了切平面的法向量。
A new ellipse extraction algorithm based on the ellipse-special deformable templates and gradient vector flow (GVF) was proposed.
给出一种结合梯度矢量流(GVF)及椭圆变形模板的椭圆提取新算法。
In this paper the transmission of paraxial light beams was analyzed based on the gradient vector potential of electromagnetic field.
本文运用电磁场的梯度矢势分析了一般情况下傍轴光束的衍射传输问题。
After simplifying the gradient vector formula THC quasi-gradient vector formula is inferred according to the feature of power systems.
并根据电力系统的特点对该公式进行了简化，得到准梯度向量公式。
According to features of edge gradient maps of face images, a new eye feature extraction algorithm based on gradient vector flow field was proposed.
根据人脸图像的边缘梯度图提出了一种新的基于梯度向量流场的眼睛特征提取方法。
OK, so the new definition for today is the definition of the gradient vector. And, our goal will be to understand a bit better what does this vector mean?
所以今天我们的新定义，就是梯度向量，目的就是更好的理解这一定义，这个向量的含义是什么？
The optimal real power flow is computed on the basis of the quasi-gradient vector by means of gradient method, conjugate gradient method and DPF method.
并用算例用基于准梯度向量的准梯度法、准共轭梯度法和变尺度法求解有功优化潮流。
Objective To put forward an improved gradient vector flow (GVF) snake model based on the edge flow for segmentation of medical ultrasonic images of the lymph node.
目的提出一种基于边缘流的梯度矢量流（gradientvectorflow，GVF）形变模型的图像分割方法，并用于淋巴结超声图像的分割。
The formula of the gradient vector of every performance function is derived, and the iterative and recurrence formulas of collapse probability of section are obtained.
由截面各类复合内力的极限状态建立截面破坏的各类功能函数，导出了各类功能函数的梯度向量计算公式，以及破坏概率计算的迭代、递推公式。
At the same time, how to get the approximate road hollow position is solved to realize the road contour extraction by gradient vector flow model with iterative solution.
通过梯度矢量流模型迭代求解，解决道路凹陷位置逼近问题，最终实现道路提取。
In this paper, on the basis of Gradient Vector flow (GVF) snakes, a fully automatic image segmentation algorithm based on the analysis of flow field and the minimal path method is proposed.
人工干预使蛇模型只能用于半自动的图像分割，该文在梯度向量流(GVF)蛇模型的基础上提出一种基于流场节点与最小路径方法的全自动图像分割算法。
We know that the gradient is perpendicular to this vector that's tangent to the level surface What about other vectors tangent to the level surface?
我们知道梯度向量垂直于这个向量，而速度向量是相切于等值面的，其他相切于等值面的向量，又如何呢？
And I can rewrite this in vector form as the gradient dot product the amount by which the position vector has changed.
可以把这些用向量形式重新写下来，就是梯度向量和位置改变量的点积。
Well, we've seen this criterion that if a curl of the vector field is zero and it's defined in the entire plane, then the vector field is conservative, and it's a gradient field.
我们已经知道了一个准则，如果向量场的旋度为零，而且它在整个平面上有定义，那么这个向量场是保守的，而且它是个梯度场。
The problem is not every vector field is a gradient.
问题是，不是所有向量场都是梯度。
If we have a vector field that cannot possibly be a gradient then we shouldn't try to look for a potential.
如果一个向量场不可能是梯度场，那我们就不应该尝试去找势函数。
So, if the gradient of a function is a vector, the divergence of a vector field is a function.
如果说函数的梯度是向量，那么向量场的散度就是函数。
Well, actually here it is not very hard to find a function whose gradient is this vector field.
实际上，找出一个函数，其梯度是这个向量场并不难。
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