3D高斯損失函式(2)新增BA最佳化和結構損失

MKT-porter發表於2024-06-28

在PyTorch中新增重投影誤差(Reprojection Error)作為損失函式通常用於計算機視覺任務,特別是涉及多檢視幾何(如立體視覺或多視角重建)的問題。重投影誤差衡量了3D點在投影到不同視角後的影像平面上的偏差。以下是如何在PyTorch中實現和使用重投影誤差作為損失函式的步驟:

定義重投影誤差函式:

重投影誤差通常是2D影像點的實際位置與透過投影矩陣計算得到的預測位置之間的距離。
實現損失函式:

使用PyTorch的操作來計算重投影誤差,並將其封裝在一個損失函式中。
假設你有以下變數:

points_3d: 原始的3D點,形狀為 (N, 3)
camera_matrix: 相機的內參矩陣,形狀為 (3, 3)
extrinsics: 相機的外參矩陣,形狀為 (3, 4)
points_2d: 實際2D影像點,形狀為 (N, 2)
以下是一個簡單的示例程式碼:

import torch
import torch.nn as nn
import torch.nn.functional as F

class ReprojectionLoss(nn.Module):
    def __init__(self):
        super(ReprojectionLoss, self).__init__()

    def forward(self, points_3d, points_2d, camera_matrix, extrinsics):
        # 新增一個列 [1] 到 3D 點的末尾 (N, 3) -> (N, 4)
        ones = torch.ones(points_3d.shape[0], 1, device=points_3d.device)
        points_3d_h = torch.cat([points_3d, ones], dim=1)  # (N, 4)

        # 計算投影點
        projected_points_2d_h = camera_matrix @ extrinsics @ points_3d_h.T  # (3, N)
        projected_points_2d = projected_points_2d_h[:2] / projected_points_2d_h[2]  # 歸一化 (2, N)
        projected_points_2d = projected_points_2d.T  # (N, 2)

        # 計算重投影誤差 (實際2D點和預測2D點之間的距離)
        reprojection_error = torch.norm(points_2d - projected_points_2d, dim=1)  # (N,)
        
        # 返回平均誤差作為損失
        return reprojection_error.mean()

# 示例資料
points_3d = torch.rand((10, 3), requires_grad=True)
points_2d = torch.rand((10, 2))
camera_matrix = torch.eye(3)
extrinsics = torch.cat([torch.eye(3), torch.zeros(3, 1)], dim=1)

# 例項化並計算損失
loss_fn = ReprojectionLoss()
loss = loss_fn(points_3d, points_2d, camera_matrix, extrinsics)
print("Loss:", loss.item())

# 使用最佳化器最小化損失
optimizer = torch.optim.Adam([points_3d], lr=0.01)
optimizer.zero_grad()
loss.backward()
optimizer.step()

  在這個示例中,我們定義了一個自定義的損失函式 ReprojectionLoss,計算了實際2D點和預測2D點之間的歐幾里得距離作為重投影誤差,並返回平均誤差作為損失。在訓練過程中,你可以使用這個損失函式來更新你的模型引數。、

可以將結構相似性指數(SSIM)損失與重投影誤差結合起來作為總損失函式。在此示例中,我們將兩者的權重設定為50%,即兩者各佔50%的權重。你可以使用PyTorch實現SSIM損失。

首先,我們需要實現或引入SSIM損失函式。然後,我們可以將兩個損失結合起來進行訓練。

實現SSIM損失函式
下面是一個簡單的SSIM損失實現:

import torch
import torch.nn.functional as F
import numpy as np

class SSIMLoss(nn.Module):
    def __init__(self, window_size=11, size_average=True):
        super(SSIMLoss, self).__init__()
        self.window_size = window_size
        self.size_average = size_average
        self.channel = 1
        self.window = self.create_window(window_size, self.channel)

    def create_window(self, window_size, channel):
        def gaussian(window_size, sigma):
            gauss = torch.Tensor(
                [np.exp(-(x - window_size // 2)**2 / float(2 * sigma**2)) for x in range(window_size)])
            return gauss / gauss.sum()

        _1D_window = gaussian(window_size, 1.5).unsqueeze(1)
        _2D_window = _1D_window.mm(_1D_window.t()).float().unsqueeze(0).unsqueeze(0)
        window = _2D_window.expand(channel, 1, window_size, window_size).contiguous()
        return window

    def _ssim(self, img1, img2, window, window_size, channel, size_average=True):
        mu1 = F.conv2d(img1, window, padding=window_size // 2, groups=channel)
        mu2 = F.conv2d(img2, window, padding=window_size // 2, groups=channel)

        mu1_sq = mu1.pow(2)
        mu2_sq = mu2.pow(2)
        mu1_mu2 = mu1 * mu2

        sigma1_sq = F.conv2d(img1 * img1, window, padding=window_size // 2, groups=channel) - mu1_sq
        sigma2_sq = F.conv2d(img2 * img2, window, padding=window_size // 2, groups=channel) - mu2_sq
        sigma12 = F.conv2d(img1 * img2, window, padding=window_size // 2, groups=channel) - mu1_mu2

        C1 = 0.01 ** 2
        C2 = 0.03 ** 2

        ssim_map = ((2 * mu1_mu2 + C1) * (2 * sigma12 + C2)) / ((mu1_sq + mu2_sq + C1) * (sigma1_sq + sigma2_sq + C2))

        if size_average:
            return ssim_map.mean()
        else:
            return ssim_map.mean(1).mean(1).mean(1)

    def forward(self, img1, img2):
        (_, channel, _, _) = img1.size()
        window = self.window.type_as(img1)

        return 1 - self._ssim(img1, img2, window, self.window_size, channel, self.size_average)

  

結合兩種損失函式
假設你有以下變數:

images_pred: 預測的影像
images_gt: 真實影像
我們可以將SSIM損失和重投影誤差結合起來:

import torch
import torch.nn as nn

class CombinedLoss(nn.Module):
    def __init__(self, reprojection_loss_weight=0.5, ssim_loss_weight=0.5):
        super(CombinedLoss, self).__init__()
        self.reprojection_loss_weight = reprojection_loss_weight
        self.ssim_loss_weight = ssim_loss_weight
        self.reprojection_loss_fn = ReprojectionLoss()
        self.ssim_loss_fn = SSIMLoss()

    def forward(self, points_3d, points_2d, camera_matrix, extrinsics, images_pred, images_gt):
        reprojection_loss = self.reprojection_loss_fn(points_3d, points_2d, camera_matrix, extrinsics)
        ssim_loss = self.ssim_loss_fn(images_pred, images_gt)

        combined_loss = (self.reprojection_loss_weight * reprojection_loss +
                         self.ssim_loss_weight * ssim_loss)
        return combined_loss

# 示例資料
points_3d = torch.rand((10, 3), requires_grad=True)
points_2d = torch.rand((10, 2))
camera_matrix = torch.eye(3)
extrinsics = torch.cat([torch.eye(3), torch.zeros(3, 1)], dim=1)
images_pred = torch.rand((1, 1, 256, 256), requires_grad=True)
images_gt = torch.rand((1, 1, 256, 256))

# 例項化並計算損失
combined_loss_fn = CombinedLoss()
loss = combined_loss_fn(points_3d, points_2d, camera_matrix, extrinsics, images_pred, images_gt)
print("Combined Loss:", loss.item())

# 使用最佳化器最小化損失
optimizer = torch.optim.Adam([points_3d, images_pred], lr=0.01)
optimizer.zero_grad()
loss.backward()
optimizer.step()

  在這個示例中,我們定義了一個 CombinedLoss 類,它結合了重投影誤差和SSIM損失。然後,我們使用這個組合損失函式來計算總損失,並用最佳化器最小化損失。你可以根據需要調整重投影誤差和SSIM損失的權重。

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