3D Morphable Model Method
来源:互联网 发布:企业网络搭建方案文档 编辑:程序博客网 时间:2024/04/28 10:48
This note is a brief summary of the 3DMM paper A Morphable Model For The Synthesis Of 3D Faces.
Note: I have no idea why there is a “|” following each math environment and “\bold” has no effect, for clarity, see the original version 3D Morphable Model Method.
Prerequisite
- 3D head lase scans
- full correspondence of faces (the method for acquiring this condition is described in the last section of the note.)
Model Construction
The model construction process consists of two steps: compute correspondence and construct model. Notice that these are steps for TRAINING, when the model is constructed, we can apply this model to new faces and scans through matching algorithm.
concept of morphable face model
A face has two major properties: geometry represented as shape-vector
Notice that this representation is based on exemplar faces, we actually use the PCA form in next section to perform reconstruction.
model representation
The construction process can be described as a PCA procedure, i.e., use principle components(eigenvectors of convariance matrices of shape and texture) to represent the model:
in equation(1),
To quantify the results in terms of the plausibility of being faces, the author fits a multivariate normal distribution to the data set of 200 faces, then the probability for coefficients
In addition, we can divide the faces into independent subregions that are morphed independently. In this paper, the author defines four subregions, by which the complete 3D face is generated by computing linear combinations for each segment simultaneously and blending them at the borders according to algorithm [1].
face attributes
To map facial attributes(gender, fullness of faces, darkness of eyebrows, double chins, hooked and concave noses) defined by hand-labeled set of example faces to the parameter space of the morphable model, first define shape and texture vectors that will manipulate a specific attribute:
where
Application– Matching 3DMMs to images and 3D scans
Matching a morphable model to images is to optimize the coefficients of the 3D model(
From parameters
are rendered using perspective projection and the Phong illumination model. To estimate the maximum posterior probability of
The optimazation of this cost function is the process of obtain the optimal parameters
If we neglect correlations between some of the variables, the right-hand side is
In which,
In the process of optimization, we need to inference
The above are the procedure to map a 3D morphable model to images, in order to apply to scans, we just need to replace
in which
Building morphable model without correspondence
All process stated above are based on the assumption that all exemplar faces are in full correspondence. This section will describe two algorithms for computing correspondence.
3D corresponding using optic flow
Optic flow is first proposed to estimate corresponding points in images
Bootstrapping the model
Since optic flow does not incorporate any constraints on the set of solutions, it fails on some of the more unusual faces in the database. The modified bootstrapping method improve correspondence iteratively.
The process if as follows:
1. use optic flow to compute preliminary correspondences between faces and a reference face.
2. compute morphable models based on the correspondences and average faces as new reference face.
3. match the models to 3D scans, now we have original scans and approximated scans.
4. compute the correspondences between the two scans using optic flow.
5. iterate above steps.
Reference
[1] P.J. Burt and E.H. Adelson. Merging images through pattern decomposition. In Applications of Digital Image Processing VIII, number 575, pages 173–181. SPIE The International Society for Optical Engeneering, 1985.
[2] Blanz,V.,&Vetter,T.(2003).Face recognition based on fitting a 3d morphable model. Pattern Analysis and Machine Intelligence, IEEE Transactions on, 25(9), 1063–1074.
[3] T. Vetter and V. Blanz. Estimating coloured 3d face models from single images:An example based approach. In Burkhardt and Neumann, editors, ComputerVision – ECCV’98 Vol. II, Freiburg, Germany, 1998. Springer, Lecture Notes in Computer Science 1407.
- 3D Morphable Model Method
- A Morphable Model For The Synthesis of 3D Faces
- 文献笔记:《Fitting a 3D Morphable Model to Edges: A Comparison Between Hard and Soft Correspondences》读后感~
- 3D model study
- Load 3D Model in OpenGL
- Model 貼圖呈現 - 3D模型匯出
- sgu - 519 - 3D City Model
- 3D Model & 图片类网站
- Model Class Method Instance Variables
- 3D技术深入剖析 Shader Model 3.0特色揭密
- 三维浏览软件-JT2GO / 3D Model Viewer JT2GO
- WPF 3D model - Sphere, Cone, and Cylinder
- Export 3D model to JSON in Blender on Fedora
- Make3D Convert your image into 3d model
- SGU - 519 - 3D City Model (模拟)
- CF:3D City Model(小思维)
- Template-Based 3D Model Fitting Using Dual-Domain Relaxation
- WPF 3D Hit Test method VisualTreeHelper.HitTest()
- QT中如何让控件跟随随窗口大小变化
- listview滑动,变换动画
- 基于LAMP的网站搭建介绍
- 版本更新
- HTML5学习02-元素、属性和格式化
- 3D Morphable Model Method
- 10张图带你深入理解Docker容器和镜像
- redis本地测试环境安装windows
- Integer.valueOf()方法 java
- 路线更改事件 $ROUTECHANGESTART 与 $LOCATIONCHANGESTART
- Effective C++第四章-设计与声明-1
- 专业名词解释
- 通过OpenCV修改图片某一像素的数值 Python实现
- MFC pictur控件下显示Mat图片