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归一化深度图约束nerf未归一化深度重建

class ScaleAndShiftInvariantLoss(nn.Module):
    """
    Scale and shift invariant loss as described in
    "Towards Robust Monocular Depth Estimation: Mixing Datasets for Zero-shot Cross-dataset Transfer"
    https://arxiv.org/pdf/1907.01341.pdf
    """

    def __init__(self, alpha: float = 0.5, scales: int = 4, reduction_type: Literal["image", "batch"] = "batch"):
        """
        Args:
            alpha: weight of the regularization term
            scales: number of scales to use
            reduction_type: either "batch" or "image"
        """
        super().__init__()
        self.__data_loss = MiDaSMSELoss(reduction_type=reduction_type)
        self.__regularization_loss = GradientLoss(scales=scales, reduction_type=reduction_type)
        self.__alpha = alpha

        self.__prediction_ssi = None

    def forward(
        self,
        prediction: Float[Tensor, "1 32 mult"],
        target: Float[Tensor, "1 32 mult"],
        mask: Bool[Tensor, "1 32 mult"],
    ) -> Float[Tensor, "0"]:
        """
        Args:
            prediction: predicted depth map (unnormalized)
            target: ground truth depth map (normalized)
            mask: mask of valid pixels
        Returns:
            scale and shift invariant loss
        """
        scale, shift = normalized_depth_scale_and_shift(prediction, target, mask)
        self.__prediction_ssi = scale.view(-1, 1, 1) * prediction + shift.view(-1, 1, 1)

        total = self.__data_loss(self.__prediction_ssi, target, mask)
        if self.__alpha > 0:
            total += self.__alpha * self.__regularization_loss(self.__prediction_ssi, target, mask)

        return total

    def __get_prediction_ssi(self):
        """
        scale and shift invariant prediction
        from https://arxiv.org/pdf/1907.01341.pdf equation 1
        """
        return self.__prediction_ssi

    prediction_ssi = property(__get_prediction_ssi)

scale，shift计算公式
出自MonoSDF

def normalized_depth_scale_and_shift(
    prediction: Float[Tensor, "1 32 mult"], target: Float[Tensor, "1 32 mult"], mask: Bool[Tensor, "1 32 mult"]
):
    """
    More info here: https://arxiv.org/pdf/2206.00665.pdf supplementary section A2 Depth Consistency Loss
    This function computes scale/shift required to normalizes predicted depth map,
    to allow for using normalized depth maps as input from monocular depth estimation networks.
    These networks are trained such that they predict normalized depth maps.

    Solves for scale/shift using a least squares approach with a closed form solution:
    Based on:
    https://github.com/autonomousvision/monosdf/blob/d9619e948bf3d85c6adec1a643f679e2e8e84d4b/code/model/loss.py#L7
    Args:
        prediction: predicted depth map
        target: ground truth depth map
        mask: mask of valid pixels
    Returns:
        scale and shift for depth prediction
    """
    # system matrix: A = [[a_00, a_01], [a_10, a_11]]
    a_00 = torch.sum(mask * prediction * prediction, (1, 2))
    a_01 = torch.sum(mask * prediction, (1, 2))
    a_11 = torch.sum(mask, (1, 2))

    # right hand side: b = [b_0, b_1]
    b_0 = torch.sum(mask * prediction * target, (1, 2))
    b_1 = torch.sum(mask * target, (1, 2))

    # solution: x = A^-1 . b = [[a_11, -a_01], [-a_10, a_00]] / (a_00 * a_11 - a_01 * a_10) . b
    scale = torch.zeros_like(b_0)
    shift = torch.zeros_like(b_1)

    det = a_00 * a_11 - a_01 * a_01
    valid = det.nonzero()

    scale[valid] = (a_11[valid] * b_0[valid] - a_01[valid] * b_1[valid]) / det[valid]
    shift[valid] = (-a_01[valid] * b_0[valid] + a_00[valid] * b_1[valid]) / det[valid]

    return scale, shift

MiDaSMSELoss

class MiDaSMSELoss(nn.Module):
    """
    data term from MiDaS paper
    """

    def __init__(self, reduction_type: Literal["image", "batch"] = "batch"):
        super().__init__()

        self.reduction_type: Literal["image", "batch"] = reduction_type
        # reduction here is different from the image/batch-based reduction. This is either "mean" or "sum"
        self.mse_loss = MSELoss(reduction="none")

    def forward(
        self,
        prediction: Float[Tensor, "1 32 mult"],
        target: Float[Tensor, "1 32 mult"],
        mask: Bool[Tensor, "1 32 mult"],
    ) -> Float[Tensor, "0"]:
        """
        Args:
            prediction: predicted depth map
            target: ground truth depth map
            mask: mask of valid pixels
        Returns:
            mse loss based on reduction function
        """
        summed_mask = torch.sum(mask, (1, 2))
        image_loss = torch.sum(self.mse_loss(prediction, target) * mask, (1, 2))
        # multiply by 2 magic number?
        image_loss = masked_reduction(image_loss, 2 * summed_mask, self.reduction_type)

        return image_loss

GradientLoss
出自于：https://arxiv.org/pdf/1907.01341.pdf

# losses based on https://github.com/autonomousvision/monosdf/blob/main/code/model/loss.py
class GradientLoss(nn.Module):
    """
    multiscale, scale-invariant gradient matching term to the disparity space.
    This term biases discontinuities to be sharp and to coincide with discontinuities in the ground truth
    More info here https://arxiv.org/pdf/1907.01341.pdf Equation 11
    """

    def __init__(self, scales: int = 4, reduction_type: Literal["image", "batch"] = "batch"):
        """
        Args:
            scales: number of scales to use
            reduction_type: either "batch" or "image"
        """
        super().__init__()
        self.reduction_type: Literal["image", "batch"] = reduction_type
        self.__scales = scales

    def forward(
        self,
        prediction: Float[Tensor, "1 32 mult"],
        target: Float[Tensor, "1 32 mult"],
        mask: Bool[Tensor, "1 32 mult"],
    ) -> Float[Tensor, "0"]:
        """
        Args:
            prediction: predicted depth map
            target: ground truth depth map
            mask: mask of valid pixels
        Returns:
            gradient loss based on reduction function
        """
        assert self.__scales >= 1
        total = 0.0

        for scale in range(self.__scales):
            step = pow(2, scale)

            grad_loss = self.gradient_loss(
                prediction[:, ::step, ::step],
                target[:, ::step, ::step],
                mask[:, ::step, ::step],
            )
            total += grad_loss

        assert isinstance(total, Tensor)
        return total

    def gradient_loss(
        self,
        prediction: Float[Tensor, "1 32 mult"],
        target: Float[Tensor, "1 32 mult"],
        mask: Bool[Tensor, "1 32 mult"],
    ) -> Float[Tensor, "0"]:
        """
        multiscale, scale-invariant gradient matching term to the disparity space.
        This term biases discontinuities to be sharp and to coincide with discontinuities in the ground truth
        More info here https://arxiv.org/pdf/1907.01341.pdf Equation 11
        Args:
            prediction: predicted depth map
            target: ground truth depth map
            reduction: reduction function, either reduction_batch_based or reduction_image_based
        Returns:
            gradient loss based on reduction function
        """
        summed_mask = torch.sum(mask, (1, 2))
        diff = prediction - target
        diff = torch.mul(mask, diff)

        grad_x = torch.abs(diff[:, :, 1:] - diff[:, :, :-1])
        mask_x = torch.mul(mask[:, :, 1:], mask[:, :, :-1])
        grad_x = torch.mul(mask_x, grad_x)

        grad_y = torch.abs(diff[:, 1:, :] - diff[:, :-1, :])
        mask_y = torch.mul(mask[:, 1:, :], mask[:, :-1, :])
        grad_y = torch.mul(mask_y, grad_y)

        image_loss = torch.sum(grad_x, (1, 2)) + torch.sum(grad_y, (1, 2))
        image_loss = masked_reduction(image_loss, summed_mask, self.reduction_type)

        return image_loss

self.depth_loss = ScaleAndShiftInvariantLoss(alpha=0.5, scales=1)