人脸对齐算法 [英] face alignment algorithm on images

问题描述

如何在二维图像上进行基本的脸部对准，假设我有嘴巴和眼睛的位置/坐标。

How can I do a basic face alignment on a 2-dimensional image with the assumption that I have the position/coordinates of the mouth and eyes.

有没有任何算法可以实现来纠正图像上的脸部对齐？

Is there any algorithm that I could implement to correct the face alignment on images?

推荐答案

面部（或图像）对齐是指将一个图像参考图像/面）。它也被称为图像配准。您可以使用外观（基于强度的注册）或关键点位置（基于功能的注册）来实现。第二类来自图像运动模型，其中一个图像被认为是另一个的移位版本。

Face (or image) alignment refers to aligning one image (or face in your case) with respect to another (or a reference image/face). It is also referred to as image registration. You can do that using either appearance (intensity-based registration) or key-point locations (feature-based registration). The second category stems from image motion models where one image is considered a displaced version of the other.

在您的情况下，地标位置（眼睛和鼻子的3个点）为简单的基于特征的注册提供了一个很好的参考集。假设您在两个2D图像中都有一组点的位置，则 x_1 和 x_2 相似变换（旋转，平移，缩放），即映射 x_1 S c>到 x_2 。你可以另外添加反射，虽然对于面孔这很可能是不必要的。

In your case the landmark locations (3 points for eyes and nose?) provide a good reference set for straightforward feature-based registration. Assuming you have the location of a set of points in both of the 2D images, x_1 and x_2 you can estimate a similarity transform (rotation, translation, scaling), i.e. a planar 2D transform S that maps x_1 to x_2. You can additionally add reflection to that, though for faces this will most-likely be unnecessary.

估算可以通过形成正态方程并求解 x_1 = Sx_2 系统使用线性回归。对于5个未知参数（2旋转，2平移，1缩放），您将需要3个点（2.5是精确的）来求解5个方程。上述LS的解可以通过直接线性变换（例如通过应用SVD或矩阵伪逆）来获得。对于足够多的参考点（即自动检测）的情况，使用用于点滤波和不确定性消除的RANSAC型方法（尽管这不是您的情况）。

Estimation can be done by forming the normal equations and solving a linear least-squares (LS) problem for the x_1 = Sx_2 system using linear regression. For the 5 unknown parameters (2 rotation, 2 translation, 1 scaling) you will need 3 points (2.5 to be precise) for solving 5 equations. Solution to the above LS can be obtained through Direct Linear Transform (e.g. by applying SVD or a matrix pseudo-inverse). For cases of a sufficiently large number of reference points (i.e. automatically detected) a RANSAC-type method for point filtering and uncertainty removal (though this is not your case here).

在估计 S 之后，对第二个图像应用图像扭曲，整个 image 2 。变换将改变像素位置，但不会改变它们的外观。不可避免地， image 2 的一些变换区域将位于图像1 的网格之外，您可以决定

After estimating S, apply image warping on the second image to get the transformed grid (pixel) coordinates of the entire image 2. The transform will change pixel locations but not their appearance. Unavoidably some of the transformed regions of image 2 will lie outside the grid of image 1, and you can decide on the values for those null locations (e.g. 0, NaN etc.).

有关详细信息：R. Szeliski，图像对齐和拼接：A教程（第4.3节几何注册）

For more details: R. Szeliski, "Image Alignment and Stitching: A Tutorial" (Section 4.3 "Geometric Registration")

在OpenCV中，请参阅：几何图像转换，例如 cv :: getRotationMatrix2D cv :: getAffineTransform 和 cv :: warpAffine。请注意，您应该估计和应用相似变换（仿射的特殊情况），以保留角度和形状。

In OpenCV see: Geometric Image Transformations, e.g. cv::getRotationMatrix2D cv::getAffineTransform and cv::warpAffine. Note though that you should estimate and apply a similarity transform (special case of an affine) in order to preserve angles and shapes.

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