3DGS初始化：从SfM稀疏点云到高斯分布

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

# 设置中文字体
plt.rcParams["font.family"] = ["SimHei", "WenQuanYi Micro Hei", "Heiti TC"]

class SfMPointCloud:
    """
    模拟SfM点云数据
    """
    def __init__(self, num_points=100):
        # 生成随机3D点
        self.points = np.random.rand(num_points, 3) * 10 - 5  # 范围[-5, 5]
        
        # 为每个点生成随机颜色(RGB)
        self.colors = np.random.rand(num_points, 3)
        
    def get_points(self):
        return self.points
        
    def get_colors(self):
        return self.colors

class Gaussian3D:
    """
    3D高斯分布类
    """
    def __init__(self, position, covariance, color, alpha=0.1):
        self.position = position      # 位置 (x, y, z)
        self.covariance = covariance  # 协方差矩阵 (3x3)
        self.color = color            # 颜色 (R, G, B)
        self.alpha = alpha            # 透明度
        
    def __str__(self):
        return f"Gaussian3D(position={self.position}, color={self.color}, alpha={self.alpha})"

class GaussianSplattingInitializer:
    """
    3DGS初始化器
    """
    def __init__(self, point_cloud, initial_sigma=0.1):
        self.point_cloud = point_cloud
        self.initial_sigma = initial_sigma
        self.gaussians = []
        
    def initialize(self):
        """
        执行3DGS初始化
        """
        points = self.point_cloud.get_points()
        colors = self.point_cloud.get_colors()
        
        # 创建单位协方差矩阵
        covariance = np.eye(3) * self.initial_sigma**2
        
        # 为每个点创建高斯分布
        for i in range(len(points)):
            position = points[i]
            color = colors[i]
            
            # 创建3D高斯分布
            gaussian = Gaussian3D(position, covariance, color)
            self.gaussians.append(gaussian)
            
        return self.gaussians
        
    def visualize(self):
        """
        可视化点云和初始化的高斯分布
        """
        points = self.point_cloud.get_points()
        colors = self.point_cloud.get_colors()
        
        fig = plt.figure(figsize=(12, 5))
        
        # 绘制原始点云
        ax1 = fig.add_subplot(121, projection='3d')
        ax1.scatter(points[:, 0], points[:, 1], points[:, 2], c=colors, s=20)
        ax1.set_title('SfM点云')
        ax1.set_xlabel('X')
        ax1.set_ylabel('Y')
        ax1.set_zlabel('Z')
        
        # 绘制高斯分布中心点（与点云相同）
        ax2 = fig.add_subplot(122, projection='3d')
        ax2.scatter(points[:, 0], points[:, 1], points[:, 2], c=colors, s=20)
        ax2.set_title('3DGS初始化（高斯分布中心）')
        ax2.set_xlabel('X')
        ax2.set_ylabel('Y')
        ax2.set_zlabel('Z')
        
        plt.tight_layout()
        plt.show()

# 主程序
def main():
    # 1. 创建模拟的SfM点云
    sfm_cloud = SfMPointCloud(num_points=50)
    
    # 2. 初始化3DGS
    initializer = GaussianSplattingInitializer(sfm_cloud, initial_sigma=0.2)
    gaussians = initializer.initialize()
    
    # 3. 打印前5个高斯分布信息
    print("前5个初始化的3D高斯分布：")
    for i in range(min(5, len(gaussians))):
        print(f"  {i+1}. {gaussians[i]}")
    
    # 4. 可视化结果
    initializer.visualize()

if __name__ == "__main__":
    main()