英语翻译If every point of the brightness pattern can move indepe

英语翻译
If every point of the brightness pattern can move independently,there is little hope of recovering the velocities.More commonly we view opaque objects of finite size
undergoing rigid motion or deformation.In this case neighboring points on the
objects have similar velocities and the velocity field of the brightness patterns
in the image varies smoothly almost everywhere.Discontinuities in flow can be expected where one object occludes another.An algorithm based on a smoothness
constraint is likely to have difficulties with occluding edges as a result.
One way to express the additional constraint is to minimize the square of the magnitude of the gradient of the optical flow velocity:
Another measure of the smoothness of the optical flow field is the sum of the squares of the Laplacians of the X- and y-components of the flow.The Laplacians of u and v are defined as
In simple situations,both Laplacians are zero.If the viewer translates parallel
to a flat object,rotates about a line perpendicular to the surface or travels
orthogonally to the surface,then the second partial derivatives of both u and v
vanish (assuming perspective projection in the image formation).
We will use here the square of the magnitude of the gradient as smoothness
measure.Note that our approach is in contrast with that of Fennema and
Thompson [5],who propose an algorithm that incorporates additional assump-
tions such as constant flow velocities within discrete regions of the image.Their
method,based on cluster analysis,cannot deal with rotating objects,since these
give rise to a continuum of flow velocities.

如果亮度模式的每一点都可以独立地移动,有没有希望恢复速度.通常我们认为有限尺寸的不透明的物体
经历刚体运动或变形.在这种情况下的邻点
对象具有相似的速度和亮度图案的速度场
在图像的平滑变化几乎无处不在.不连续性的流量可以预计,在哪里一个对象的阻塞.一种基于平滑算法
约束可能遮挡边缘由于困难.
表达附加约束的方法之一是减少对光学流速梯度幅值的平方：
对光流场的平整度的另一措施是对X -拉普拉斯算子的平方和的流量y分量.U和V的拉普拉斯算子定义为
在简单的情况下,两个拉普拉斯算子是零.如果观众转换并行
一个平面物体,绕垂直于表面的线或旅行
垂直于表面,然后u和v的二阶偏导数
消失（假设透视投影的图像形成）.
我们将在这里使用的梯度的大小为平滑的方
测量.请注意,我们的方法是,介绍和对比
汤普森[ 5 ],他提出了一个算法,采用额外的假设—
tions如恒流速度的图像的离散区域内.他们的
方法,基于聚类分析,不能处理旋转对象,因为这些
产生一个连续的流动速度.