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"""Anomaly Map Generator for the PaDiM model implementation."""
# Copyright (C) 2020 Intel Corporation
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing,
# software distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions
# and limitations under the License.
from typing import List, Tuple, Union
import torch
import torch.nn.functional as F
from kornia.filters import gaussian_blur2d
from omegaconf import ListConfig
from torch import Tensor
class AnomalyMapGenerator:
"""Generate Anomaly Heatmap.
Args:
image_size (Union[ListConfig, Tuple]): Size of the input image. The anomaly map is upsampled to this dimension.
sigma (int, optional): Standard deviation for Gaussian Kernel. Defaults to 4.
"""
def __init__(self, image_size: Union[ListConfig, Tuple], sigma: int = 4):
self.image_size = image_size if isinstance(image_size, tuple) else tuple(image_size)
self.sigma = sigma
@staticmethod
def compute_distance(embedding: Tensor, stats: List[Tensor]) -> Tensor:
"""Compute anomaly score to the patch in position(i,j) of a test image.
Ref: Equation (2), Section III-C of the paper.
Args:
embedding (Tensor): Embedding Vector
stats (List[Tensor]): Mean and Covariance Matrix of the multivariate Gaussian distribution
Returns:
Anomaly score of a test image via mahalanobis distance.
"""
batch, channel, height, width = embedding.shape
embedding = embedding.reshape(batch, channel, height * width)
# calculate mahalanobis distances
mean, inv_covariance = stats
delta = (embedding - mean).permute(2, 0, 1)
distances = (torch.matmul(delta, inv_covariance) * delta).sum(2).permute(1, 0)
distances = distances.reshape(batch, height, width)
distances = torch.sqrt(distances)
return distances
def up_sample(self, distance: Tensor) -> Tensor:
"""Up sample anomaly score to match the input image size.
Args:
distance (Tensor): Anomaly score computed via the mahalanobis distance.
Returns:
Resized distance matrix matching the input image size
"""
score_map = F.interpolate(
distance.unsqueeze(1),
size=self.image_size,
mode="bilinear",
align_corners=False,
)
return score_map
def smooth_anomaly_map(self, anomaly_map: Tensor) -> Tensor:
"""Apply gaussian smoothing to the anomaly map.
Args:
anomaly_map (Tensor): Anomaly score for the test image(s).
Returns:
Filtered anomaly scores
"""
kernel_size = 2 * int(4.0 * self.sigma + 0.5) + 1
sigma = torch.as_tensor(self.sigma).to(anomaly_map.device)
anomaly_map = gaussian_blur2d(anomaly_map, (kernel_size, kernel_size), sigma=(sigma, sigma))
return anomaly_map
def compute_anomaly_map(self, embedding: Tensor, mean: Tensor, inv_covariance: Tensor) -> Tensor:
"""Compute anomaly score.
Scores are calculated based on embedding vector, mean and inv_covariance of the multivariate gaussian
distribution.
Args:
embedding (Tensor): Embedding vector extracted from the test set.
mean (Tensor): Mean of the multivariate gaussian distribution
inv_covariance (Tensor): Inverse Covariance matrix of the multivariate gaussian distribution.
Returns:
Output anomaly score.
"""
score_map = self.compute_distance(
embedding=embedding,
stats=[mean.to(embedding.device), inv_covariance.to(embedding.device)],
)
up_sampled_score_map = self.up_sample(score_map)
smoothed_anomaly_map = self.smooth_anomaly_map(up_sampled_score_map)
return smoothed_anomaly_map
def __call__(self, **kwds):
"""Returns anomaly_map.
Expects `embedding`, `mean` and `covariance` keywords to be passed explicitly.
Example:
>>> anomaly_map_generator = AnomalyMapGenerator(image_size=input_size)
>>> output = anomaly_map_generator(embedding=embedding, mean=mean, covariance=covariance)
Raises:
ValueError: `embedding`. `mean` or `covariance` keys are not found
Returns:
torch.Tensor: anomaly map
"""
if not ("embedding" in kwds and "mean" in kwds and "inv_covariance" in kwds):
raise ValueError(f"Expected keys `embedding`, `mean` and `covariance`. Found {kwds.keys()}")
embedding: Tensor = kwds["embedding"]
mean: Tensor = kwds["mean"]
inv_covariance: Tensor = kwds["inv_covariance"]
return self.compute_anomaly_map(embedding, mean, inv_covariance)
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