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# 3D Morphable Face Models
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Advanced 3D face modeling capabilities using morphable models for face reconstruction, pose estimation, expression analysis, and realistic 3D face rendering. Built on the Basel Face Model (BFM) and other morphable model formats.
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## Capabilities
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### MorphabelModel Class
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Core 3D morphable face model for generating and manipulating 3D face geometry, texture, and expressions.
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```python { .api }
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class MorphabelModel:
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    def __init__(self, model_path, model_type='BFM'):
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        """
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        Initialize 3D morphable face model.
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        Parameters:
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        - model_path: str, path to morphable model file (.mat, .pkl, etc.)
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        - model_type: str, model type ('BFM', '3DMM', etc.)
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        """
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    def get_shape_para(self, type='random') -> np.ndarray:
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        """
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        Generate or retrieve shape parameters.
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        Parameters:
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        - type: str, parameter generation type ('random', 'zero', 'mean')
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        Returns:
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        np.ndarray: shape parameters vector
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        """
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    def get_exp_para(self, type='random') -> np.ndarray:
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        """
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        Generate or retrieve expression parameters.
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        Parameters:
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        - type: str, parameter generation type ('random', 'zero', 'mean')
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        Returns:
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        np.ndarray: expression parameters vector
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        """
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    def generate_vertices(self, shape_para, exp_para) -> np.ndarray:
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        """
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        Generate 3D face vertices from shape and expression parameters.
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        Parameters:
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        - shape_para: np.ndarray, shape parameters
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        - exp_para: np.ndarray, expression parameters
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        Returns:
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        np.ndarray: 3D vertices, shape (n_vertices, 3)
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        """
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    def get_tex_para(self, type='random') -> np.ndarray:
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        """
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        Generate or retrieve texture parameters.
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        Parameters:
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        - type: str, parameter generation type
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        Returns:
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        np.ndarray: texture parameters vector
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        """
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    def generate_colors(self, tex_para) -> np.ndarray:
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        """
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        Generate face colors/textures from texture parameters.
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        Parameters:
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        - tex_para: np.ndarray, texture parameters
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        Returns:
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        np.ndarray: vertex colors, shape (n_vertices, 3)
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        """
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    def rotate(self, vertices, angles) -> np.ndarray:
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        """
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        Rotate 3D face vertices.
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        Parameters:
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        - vertices: np.ndarray, 3D vertices to rotate
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        - angles: np.ndarray, rotation angles [pitch, yaw, roll] in radians
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        Returns:
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        np.ndarray: rotated vertices
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        """
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    def transform(self, vertices, s, angles, t3d) -> np.ndarray:
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        """
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        Apply full 3D transformation to vertices.
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        Parameters:
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        - vertices: np.ndarray, input vertices
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        - s: float, scaling factor
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        - angles: np.ndarray, rotation angles [pitch, yaw, roll]
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        - t3d: np.ndarray, 3D translation vector
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        Returns:
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        np.ndarray: transformed vertices
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        """
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    def transform_3ddfa(self, vertices, s, angles, t3d) -> np.ndarray:
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        """
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        Apply 3DDFA-style transformation to vertices.
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        Parameters: same as transform()
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        Returns:
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        np.ndarray: transformed vertices using 3DDFA convention
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        """
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    def fit(self, x, X_ind, max_iter=4, isShow=False) -> Tuple[np.ndarray, ...]:
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        """
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        Fit morphable model to 2D/3D landmarks.
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        Parameters:
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        - x: np.ndarray, target landmark coordinates
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        - X_ind: np.ndarray, indices of model vertices corresponding to landmarks
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        - max_iter: int, maximum fitting iterations
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        - isShow: bool, show fitting progress visualization
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        Returns:
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        tuple: (fitted_vertices, shape_params, exp_params, pose_params, ...)
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        """
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```
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### Model Attributes
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Key attributes of the morphable model providing model metadata and mesh information.
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```python { .api }
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# Model dimensions and parameters
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nver: float                    # Number of vertices in the model
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ntri: float                    # Number of triangles in the mesh
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n_shape_para: int             # Number of shape parameters (typically 199)
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n_exp_para: int               # Number of expression parameters (typically 29)
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n_tex_para: int               # Number of texture parameters (typically 199)
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# Mesh topology
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kpt_ind: np.ndarray           # Indices of keypoint vertices
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triangles: np.ndarray         # Triangle mesh connectivity
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full_triangles: np.ndarray    # Complete triangle mesh for rendering
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```
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### 3D Mesh Processing Modules
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Comprehensive 3D mesh processing capabilities for visualization and manipulation.
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```python { .api }
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# Mesh I/O operations
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def read_obj(filename) -> Tuple[np.ndarray, np.ndarray]: ...
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def write_obj(filename, vertices, triangles): ...
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# Mesh visualization
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def render_mesh(vertices, triangles, colors=None) -> np.ndarray: ...
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def plot_mesh(vertices, triangles): ...
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# 3D transformations
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def apply_transform(vertices, transform_matrix) -> np.ndarray: ...
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def compute_normal(vertices, triangles) -> np.ndarray: ...
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# Lighting calculations
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def phong_shading(vertices, normals, light_pos, light_color) -> np.ndarray: ...
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def lambert_shading(vertices, normals, light_dir) -> np.ndarray: ...
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```
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## Usage Examples
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### Basic 3D Face Generation
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```python
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from insightface.thirdparty.face3d.morphable_model import MorphabelModel
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import numpy as np
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# Load morphable model (requires BFM model file)
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model_path = 'path/to/BFM.mat'  # Basel Face Model file
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bfm = MorphabelModel(model_path, model_type='BFM')
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print(f"Model info:")
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print(f"  Vertices: {int(bfm.nver)}")
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print(f"  Triangles: {int(bfm.ntri)}")
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print(f"  Shape parameters: {bfm.n_shape_para}")
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print(f"  Expression parameters: {bfm.n_exp_para}")
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# Generate random face
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shape_params = bfm.get_shape_para('random')
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exp_params = bfm.get_exp_para('zero')  # Neutral expression
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# Generate 3D face vertices
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vertices = bfm.generate_vertices(shape_params, exp_params)
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print(f"Generated vertices shape: {vertices.shape}")
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# Generate face colors/texture
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tex_params = bfm.get_tex_para('random')
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colors = bfm.generate_colors(tex_params)
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print(f"Generated colors shape: {colors.shape}")
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```
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### 3D Face Pose Manipulation
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```python
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import numpy as np
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# Start with a neutral face
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shape_params = bfm.get_shape_para('mean')  # Average face shape
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exp_params = bfm.get_exp_para('zero')      # Neutral expression
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vertices = bfm.generate_vertices(shape_params, exp_params)
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# Apply different poses
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poses = [
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    {'name': 'frontal', 'angles': [0, 0, 0]},
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    {'name': 'left_profile', 'angles': [0, np.pi/3, 0]},
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    {'name': 'right_profile', 'angles': [0, -np.pi/3, 0]},
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    {'name': 'looking_up', 'angles': [np.pi/6, 0, 0]},
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    {'name': 'looking_down', 'angles': [-np.pi/6, 0, 0]}
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]
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posed_faces = {}
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for pose in poses:
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    # Apply rotation
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    rotated = bfm.rotate(vertices, pose['angles'])
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    # Apply full transformation with scaling and translation
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    s = 1.0  # No scaling
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    t3d = np.array([0, 0, 0])  # No translation
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    transformed = bfm.transform(rotated, s, pose['angles'], t3d)
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    posed_faces[pose['name']] = transformed
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print(f"Generated {len(posed_faces)} different poses")
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```
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### 3D Model Fitting to Landmarks
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```python
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# Fit model to detected facial landmarks
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from insightface.app import FaceAnalysis
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import cv2
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# Setup face analysis for landmark detection
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app = FaceAnalysis()
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app.prepare(ctx_id=0)
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# Load image and detect landmarks
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img = cv2.imread('face_image.jpg')
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faces = app.get(img)
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if faces:
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    face = faces[0]
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    # Use 3D landmarks if available
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    if hasattr(face, 'landmark_3d_68') and face.landmark_3d_68 is not None:
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        target_landmarks = face.landmark_3d_68
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        # Define corresponding model vertex indices
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        # (This would typically be predefined based on the model)
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        landmark_indices = np.array([
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            # Indices of BFM vertices that correspond to facial landmarks
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            # These need to be established based on the specific model
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            8163, 8174, 8213, 8194, 8227,  # Chin area
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            2435, 2452, 2463, 2441, 2456,  # Left eyebrow
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            # ... more landmark correspondences
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        ])
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        # Fit model to landmarks
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        fitted_results = bfm.fit(
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            x=target_landmarks,
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            X_ind=landmark_indices,
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            max_iter=10,
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            isShow=False
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        )
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        fitted_vertices, fitted_shape, fitted_exp, fitted_pose = fitted_results[:4]
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        print(f"Fitting completed:")
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        print(f"  Shape parameters: {fitted_shape.shape}")
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        print(f"  Expression parameters: {fitted_exp.shape}")
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        print(f"  Pose parameters: {fitted_pose.shape}")
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```
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### Expression Manipulation
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```python
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# Create faces with different expressions
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base_shape = bfm.get_shape_para('mean')
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# Define expression variations
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expressions = {
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    'neutral': bfm.get_exp_para('zero'),
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    'smile': bfm.get_exp_para('random') * 0.5,  # Scaled random expression
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    'surprise': np.zeros(bfm.n_exp_para),
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    'frown': np.zeros(bfm.n_exp_para)
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}
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# Manually adjust specific expression parameters if known
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# (These indices depend on the specific morphable model)
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expressions['smile'][12] = 2.0    # Smile-related parameter
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expressions['surprise'][5] = 1.5  # Eyebrow raise
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expressions['frown'][15] = -1.0   # Mouth corner down
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expression_faces = {}
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for exp_name, exp_params in expressions.items():
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    vertices = bfm.generate_vertices(base_shape, exp_params)
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    expression_faces[exp_name] = vertices
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print(f"Generated {len(expression_faces)} expression variations")
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```
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### 3D Face Rendering Pipeline
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```python
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from insightface.thirdparty.face3d.mesh import render, light
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def render_3d_face(vertices, triangles, colors, pose_angles, image_size=(256, 256)):
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    """Complete 3D face rendering pipeline."""
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    # Apply pose transformation
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    transformed_vertices = bfm.rotate(vertices, pose_angles)
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    # Set up lighting
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    light_positions = np.array([
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        [0, 0, 1],    # Front light
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        [-1, 1, 1],   # Left-top light
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        [1, 1, 1]     # Right-top light
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    ])
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    light_intensities = np.array([0.6, 0.3, 0.3])
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    # Compute normals for lighting
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    from insightface.thirdparty.face3d.mesh.transform import compute_normal
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    normals = compute_normal(transformed_vertices, triangles)
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    # Apply lighting
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    lit_colors = colors.copy()
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    for light_pos, intensity in zip(light_positions, light_intensities):
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        lighting = light.lambert_shading(normals, light_pos) * intensity
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        lit_colors = lit_colors * lighting[:, np.newaxis]
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    # Render to image
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    rendered_image = render.render_mesh(
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        transformed_vertices,
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        triangles,
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        lit_colors,
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        image_size
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    )
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    return rendered_image
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# Render faces with different poses and lighting
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shape_params = bfm.get_shape_para('mean')
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exp_params = bfm.get_exp_para('zero')
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tex_params = bfm.get_tex_para('mean')
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vertices = bfm.generate_vertices(shape_params, exp_params)
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colors = bfm.generate_colors(tex_params)
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# Render with different poses
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for angle in [0, np.pi/6, np.pi/3]:
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    pose = [0, angle, 0]  # Yaw rotation
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    rendered = render_3d_face(vertices, bfm.triangles, colors, pose)
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    # Save rendered image
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    cv2.imwrite(f'rendered_face_yaw_{int(np.degrees(angle))}.jpg', rendered)
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```
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### Face Morphing and Interpolation
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```python
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# Create morphing between two faces
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def morph_faces(shape1, exp1, shape2, exp2, n_steps=10):
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    """Create smooth morphing between two face configurations."""
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    morphed_faces = []
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    for i in range(n_steps):
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        alpha = i / (n_steps - 1)  # Interpolation weight
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        # Linear interpolation of parameters
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        morphed_shape = (1 - alpha) * shape1 + alpha * shape2
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        morphed_exp = (1 - alpha) * exp1 + alpha * exp2
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        # Generate intermediate face
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        vertices = bfm.generate_vertices(morphed_shape, morphed_exp)
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        morphed_faces.append(vertices)
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    return morphed_faces
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# Create two different faces
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face1_shape = bfm.get_shape_para('random')
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face1_exp = bfm.get_exp_para('zero')
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face2_shape = bfm.get_shape_para('random')
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face2_exp = bfm.get_exp_para('random')
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# Generate morphing sequence
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morph_sequence = morph_faces(face1_shape, face1_exp, face2_shape, face2_exp)
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print(f"Generated morphing sequence with {len(morph_sequence)} frames")
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# Save morphing frames
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for i, vertices in enumerate(morph_sequence):
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    # Render each frame (using rendering function from above)
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    colors = bfm.generate_colors(bfm.get_tex_para('mean'))
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    rendered = render_3d_face(vertices, bfm.triangles, colors, [0, 0, 0])
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    cv2.imwrite(f'morph_frame_{i:03d}.jpg', rendered)
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```
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### Advanced Model Analysis
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```python
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def analyze_morphable_model(bfm):
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    """Analyze morphable model properties and statistics."""
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    print("=== Morphable Model Analysis ===")
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    print(f"Model Dimensions:")
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    print(f"  Vertices: {int(bfm.nver)}")
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    print(f"  Triangles: {int(bfm.ntri)}")
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    print(f"  Keypoints: {len(bfm.kpt_ind)}")
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    print(f"\nParameter Dimensions:")
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    print(f"  Shape: {bfm.n_shape_para}")
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    print(f"  Expression: {bfm.n_exp_para}")
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    print(f"  Texture: {bfm.n_tex_para}")
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    # Analyze parameter ranges
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    test_shapes = [bfm.get_shape_para('random') for _ in range(100)]
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    shape_stats = np.array(test_shapes)
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    print(f"\nShape Parameter Statistics:")
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    print(f"  Mean range: [{shape_stats.mean(axis=0).min():.3f}, {shape_stats.mean(axis=0).max():.3f}]")
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    print(f"  Std range: [{shape_stats.std(axis=0).min():.3f}, {shape_stats.std(axis=0).max():.3f}]")
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    # Analyze mesh properties
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    mean_shape = bfm.get_shape_para('mean')
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    mean_exp = bfm.get_exp_para('zero')
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    mean_vertices = bfm.generate_vertices(mean_shape, mean_exp)
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    print(f"\nMesh Properties:")
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    print(f"  Vertex bounds: X[{mean_vertices[:, 0].min():.2f}, {mean_vertices[:, 0].max():.2f}]")
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    print(f"                 Y[{mean_vertices[:, 1].min():.2f}, {mean_vertices[:, 1].max():.2f}]")
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    print(f"                 Z[{mean_vertices[:, 2].min():.2f}, {mean_vertices[:, 2].max():.2f}]")
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# Run analysis
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analyze_morphable_model(bfm)
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```