# From out-of-distribution detection to quality control

Benjamin Lambert, Florence Forbes, Michel Dojat

► To cite this version:

Benjamin Lambert, Florence Forbes, Michel Dojat. From out-of-distribution detection to quality con- trol. Trustworthy AI in Medical Imaging, Elsevier, pp.101-126, 2025, 9780443237614. 10.1016/B978- 0-44-323761-4.00014-6. hal-04915422

HAL Id: hal-04915422

https://hal.science/hal-04915422v1

Submitted on 14 Feb 2025

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<figure><img src="image_1.png" /></figure>
# Chapter 1

# From Out-of-distribution detection to Quality Control

## ABSTRACT

Quality Control (QC) is an important step of any medical image analysis pipeline to impose safeguards against biased interpretation. Visual QC can be tedious and time-consuming when the volume of data is important and a branch of work has thus focused on providing automated QC algorithms. In the context of computerized image analysis, such algorithms can be categorized according to the domain on which they operate, namely input (i.e. image) or output (i.e. prediction). Input QC is akin to out-of-distribution detection, aiming at the detection of images that are unusual due for example to the presence of artifacts. Output QC, in contrast, focuses on detecting automated predictions that do not meet expectations. These two facets of QC are intertwined, as noisy images are likely to produce poor predictions. However, they are generally considered as separate problems in the literature and tackled with different methodologies and evaluation procedures. In this chapter, a taxonomy of QC methods is first proposed, oriented to input or output checking. Then, a general framework to jointly combine these two QC facets is proposed and illustrated on two tasks, namely binary segmentation of polyps in endoscopic images and multi-class tumor segmentation in multi-modal MRIs.

## KEYWORDS

AI Safety, Uncertainty, Out-of-Distribution, Segmentation, Interpretation, Medical imaging

## 1.1 INTRODUCTION

Quality Control (QC) is an essential step for medical image acquisition and analysis. The poor resolution, the presence of noise or artifacts can indeed greatly complicate the reading of the exam, leading to misdiagnosis, delayed treatment, and increased healthcare costs. Thus, many QC protocols have been proposed in the general context of radiology [111], or dedicated to specific imaging modalities, such as MRI [109], CT [101] and PET [43], or Diffusion Tensor Imaging [64]. These protocols consist of a set of rules that aims at ensuring the reliability of acquired images by the verification of the imaging device as well as the acquisition sequence parameters and processing steps.

On the other side, automated algorithms based on Machine Learning (ML) or Deep Learning (DL) are widely introduced as key elements in medical image
analysis pipelines [106]. For instance, they can automatize fastidious annotation
tasks, such as the manual delineation of lesions or anatomical regions. An
illustrative example is volBrain, an open-access tool for brain volumetry [69]
in T1-w MRI, accessible via an online platform¹, which has performed more
than 500,000 analyses from several thousands of different institutions at the
time of writing this article. It provides a precise parcellation of the brain into
more than one hundred classes, a process that would take days for a human to
perform. However, DL algorithms are not foolproof, and they are known to
perform poorly when the input data are *out-of-distribution* (OOD), meaning that
it is not drawn from the same distribution as the training data distribution [127,
70, 86, 128]. Modifications in the image acquisition protocol or device can
thus lead to unpredictable behaviors. Additionally, DL models are known to be
particularly sensitive to adversarial attacks, corresponding to subtle engineered
perturbations applied to the input image, which drastically modify the prediction
of the network [82, 6, 92]. Thus, when relying on predictive models within an
image analysis pipeline, it is desirable to perform QC not only on the input image
but also on the automated prediction to make sure that errors are not introduced
in the decision-making.

Visual QC, however, is a time-consuming process, prone to inter-rater vari-
ability [120], which becomes intractable when the quantity of data to control
becomes very large. Yet the tendency is towards an increasing volume of medical
images to process [123, 108]. This naturally leads to the replacement of manual
QC with automated QC tools.

Automatic QC methods can be categorized into two classes: methods that
operate in the input image domain, and methods that operate in the output
prediction domain. Another possible denomination is pre-analysis (input) and
post-analysis QC [31]. Input QC usually does not make any assumption regarding
the downstream task (e.g. registration, classification, or segmentation), and
focuses on detecting poor-quality images, generally by using rules defined by
human experts to control the objective quality of the data. In contrast, output QC
is defined with respect to a target task aiming at detecting poor predictions (e.g.
erroneous segmentation or registration). These two aspects are intertwined, as
a poor-quality image is more likely to produce a poor prediction, compared to a
noise-free one. However, this is not always the case. Indeed, DL models can be
trained with a data augmentation procedure to enhance their robustness, which
makes them able to correctly generalize to noisy data [104]. Thus, some noisy
images can be flagged as incorrect by an input QC algorithm, while leading
to a correct prediction. As an illustrative example, Figure 1.1 presents the
predictions of a brain tumor segmentation model trained on the BraTS 2023
dataset [73, 9]. The model was trained using a data augmentation strategy
including Gaussian noise. At test time, the model was able to process an image
corrupted with Gaussian noise with a performance similar to the corresponding
<figure><img src="image_2.png" /><figcaption>**FIGURE 1.1** Brain tumor segmentation for two variants of a T2w FLAIR MRI: the noise-free image (top row) and a noisy image obtained by applying Gaussian Noise (bottom row). The top row segmentation achieves a Dice score of 0.907. In the presence of noise, the segmentation remains valid (bottom row, Dice score of 0.904). The model has been trained using a data augmentation strategy including Gaussian noise, making it robust to this type of noise.</figcaption></figure>

noise-free image. In this setting, raising the alarm for the noisy input image may be considered a false alarm as the model is able to process it seamlessly.

Based on this simple example, it appears that QC can lead to two different conclusions depending on the domain considered (input or output). It can be considered that input and output QC are complementary tasks that can be combined to boost the informativeness of the global QC procedure. For instance, knowing that the image is poorly segmented (failed output QC) **and** out-of-distribution (failed input QC) gives insights regarding the source of errors. Alternatively, when the output QC indicates failures **and not** the input QC, the user may be confronted with images causing in-domain errors that could be included in the training set. However, these two QC facets are generally tackled in separate literature and few works have been proposed to merge the corresponding QC strategies.

In this chapter, an overview of existing methods for both input and output QC is first proposed. In the second part, a practical demonstration of the introduced paradigms is provided in the context of image segmentation.
<figure><img src="image_3.png" /><figcaption>**FIGURE 1.2** Pie chart of the studies according to the QC level: input (red), output (green), or both (blue). The corresponding number of papers is mentioned in parentheses. UAD: Unsupervised Anomaly Detection; UQ: Uncertainty Quantification; RCA: Reverse Classification Accuracy</figcaption></figure>

**1.2 A TAXONOMY OF QC METHODS FOR ML-BASED MEDICAL IMAGE ANALYSIS**

In this section, a review of existing methods for input and/or output QC in the context of medical imaging is presented. To this end, a systematic search was performed on October 2023 using Google Scholar and PubMed to identify papers on QC for medical imaging published from 2016 (included) to October 2023. The following keywords were employed: "Quality Control", "Deep Learning", and "Medical image". Papers were included if they explored automatic QC solutions applied to medical images, resulting in a list of 95 papers selected for reading and analysis. The collected papers were further classified according to the QC method as well as to the QC domain (input, output, or both). Within each category, the frequency of each proposed framework is further reported. The resulting taxonomy is presented in Figure 1.2. In the following of the section, each QC method class is briefly described.

**1.2.1 QC on the input image domain**

QC on the input image domain (40.0% of the reviewed papers) aims at detecting images that have a poor resolution or present artifacts that make them unqualified
for further processing. The corresponding methods are generally evaluated in
a binary classification scenario using a set of images labeled as poor or good-
quality samples.

1.2.1.1 *Supervised Input QC*

The most straightforward and widely-used approach to automatize input QC is to train a classifier (e.g. CNN or Transformer) to separate conform and non-conform images. This requires the building of a large dataset comprising annotated examples of each category. For instance, Bottani et al. [14] propose a CNN to reject poor-quality images from a large brain T1w MRI warehouse. Images were manually labeled into good, medium and bad quality images based on different characteristics: the presence of contrast agent, motion artifact or noise, and the quality of contrast. Additionally, their model was able to detect images that *were not* brain T1w MRI. Similarly, in the QC-Automator [97] framework, authors trained two different CNNs in a supervised fashion to detect artifacts in axial and sagittal slices respectively. The models were developed for diffusion MRIs and were able to distinguish between multi-band interleaving, ghosting, susceptibility, herringbone and chemical-shift artifacts. This supervised approach was also extensively explored for quality assessment of brain MRI [53, 3, 27, 65, 135], diffusion MRI [49, 37], prostate MRI [75] and cardiac MRI [132, 112, 130, 18, 131, 79, 65]. Esses et al. [26] trained a CNN to assess the diagnostic power of liver MRI, while different studies can be found in fetal MRI making use of supervised CNNs [98, 126, 56, 61, 29, 125]. While numerous applications can be found for MR imaging due to the heterogeneity of the data, similar strategies were also investigated for radiography [19, 110, 122, 24], computed tomography (CT) [88, 78], mammography [119] and PET imaging [85].

Instead of directly predicting the quality of the input image in a binary setting (accept or reject), which may lack interpretability in the decision, other methods have been proposed to mimic the process of a human rater performing visual QC. To do so, the classification models are trained to predict a set of relevant image metrics from which a decision (accept or reject) can be derived. An illustrative example is the work of Sun et al. [110], where an input QC model (CNN) is trained to predict QC indicators for knee radiography, namely, the anteroposterior/lateral overlap ratios and flexion angle. These indicators correspond to criteria that a human rater verifies to ensure the correct positioning of the knee in the image [76]. Similarly in the context of lumbar spine radiography, authors derive an automated QC protocol based on criteria defined in radiology textbooks. From the segmentation of the spine, they control the visibility and number of key anatomical features, allowing them to reject non-conform images.

However, such supervised approaches still require access to a sufficient num-
ber of noisy data for the training of the DL model and a time-consuming anno-
tation labeling by human experts. Thus, some supervised strategies proposed to
use data augmentation to inject artifacts in noise-free data, which allows to easily
construct large databases for automatic input QC. For example, the RegQCNET [102] was developed to detect affine registration errors in brain MRI using simulated spatial transformations for training. Another illustrative example is the work of Zhang et al. [132] for missing slice detection in cardiac MRI. As the training dataset contained only good-quality images, they proposed to remove slices to simulate acquisition problems.

### 1.2.1.2 Unsupervised Anomaly Detection for Input QC

The Unsupervised Anomaly Detection (UAD) framework corresponds to a set of methods aiming to detect outlier images without requiring a labeled training dataset.

A general UAD methodology is to detect outlier images as deviations from a reference distribution. A typical example of such paradigm for input QC corresponds to latent-space methods, illustrated in Figure 1.3. The principle is as follows: from a trained neural network, intermediate NN activations are collected for a set of in-distribution ( artifact-free) data. They are used to model the distribution of the activations of conforming images. The hypothesis is that activations corresponding to non-conform images should deviate from this distribution. At test time, the activations generated for the test sample are compared to the in-distribution distribution by computing a distance metric. A popular choice is the Mahalanobis Distance (MD), widely used for medical image analysis [36, 17, 58] or the L2 distance [22].

Alternatively, self-supervision techniques can be derived to perform QC and can be seen as a form of UAD as they do not require explicit QC labels. Briefly, self-supervision involves training a discriminative model to perform a supervised task (e.g. segmentation or classification) jointly with a fully unsupervised surrogate task (e.g. edge detection) for which the target can directly be derived from the input image, without expert annotation. The rationale is that the performance of this proxy task should be poor when confronted with non-conform input images, allowing for their detection. In Gonzalez et al. [35], authors investigate two self-supervision tasks, namely edge detection and contrastive learning, in order to detect outlier data in the context of cardiac segmentation. Contrastive learning was also further explored by Zuo et al. [136] for artifact detection in brain MRI.

### 1.2.1.3 Uncertainty-based Input QC

Uncertainty Quantification is increasingly being explored in AI-based medical image processing to detect model misfunctions due to instance to noisy data or learning pitfalls [57]. Traditionally, uncertainty is divided into two categories: aleatoric uncertainty, which is linked to the inherent and irreducible randomness in the input data, and epistemic uncertainty which stems from the lack of knowledge of the predictive model concerning a given input.

In particular, epistemic uncertainty is expected to be high for images that
<figure><img src="image_4.png" /><figcaption>**FIGURE 1.3** Illustration of the latent-space approach for out-of-distribution detection.</figcaption></figure>

are different from the ones encountered during training [50]. Thus, monitoring model uncertainty could theoretically be used to detect out-of-distribution samples. This idea was explored in [71] where authors used Monte Carlo dropout [30] to estimate the uncertainty of a brain tumor segmentation model. They further used this uncertainty score to detect bad-quality MRI scans. However, uncertainty is rarely used to perform input QC and only one occurrence of this approach was identified when preparing this review.

### 1.2.2 QC on the output prediction domain

Evaluating the quality of a prediction is trivial when ground truth data is available. However, the task is much more challenging when no references are available. Automatic QC on the output domain aims at detecting predictions that do not meet a predefined level of quality. For segmentation tasks, one can think of a Dice threshold under which predictions should be disqualified. The metric and threshold are dependent of course on the underlying predictive task and its overall difficulty. Numerous studies have focused on this task (52.6% of the review papers) and the associated frameworks are presented in the following Section.
1.2.2.1 Uncertainty-based Output QC

In contrast to input QC, uncertainty has been more successfully explored for
output QC. Pioneer work has been carried out by Roy et al. [95] who used Monte
Carlo (MC) dropout to obtain a set of plausible whole-brain segmentation masks
for each input image. From this set of images, they propose different metrics
that consider the level of agreement between the predictions: the average Dice
between samples, the coefficient of variation (CoV), the Intersection over Union
between the samples, and the average uncertainty (see Figure 1.4). They showed
that these estimators had an important correlation with the segmentation quality,
estimated using the Dice score. These scores, easily computable from a set of
segmentation masks, could then serve as proxies to estimate the performance
of a prediction without ground truth. This framework was further explored and
improved in several studies. From the outputs of a MC dropout model, several
other proxy metrics were proposed: the Predictive Dice Coefficient [41], the
Contour Quality metric [10], the Doubt score [47] or the mean uncertainty [81,
80]. Other variants replaced MC dropout by Test Time Augmentation [116,
117], Ensembling [52, 42, 94, 72, 5, 133], probabilistic models [87] or fuzzy
uncertainty [62, 63], which are alternative uncertainty approaches to generate
the set of plausible masks.

To further improve the output QC procedure, several works have explored
the use of these uncertainty metrics as features to train a ML model to directly
infer the prediction quality, in a regression setting. Ghosal et al. [34] and Hann
et al. [39, 38, 40] trained linear regression models to predict the Dice directly
from uncertainty estimates, for digital histopathology image segmentation and
cardiac MRI segmentation, respectively. Alternatively, Arega et al. [7] used
a Random Forest (RF) either in a binary classification approach (accept/reject
poor segmentation) or regression (predict the Dice score) from the outputs of
a MC dropout model. These approaches require building a training dataset
comprising automated predictions and associated quality to allow the training
of the auxiliary ML model. Such a concept is closely related to the Supervised
Output QC approach presented in the next section.

1.2.2.2 Supervised Output QC

As for its input counterpart, supervised output QC is extremely popular. A
straightforward idea for supervised output QC is to build a CNN model that
takes as input both the image and automated prediction and infers the quality of
the prediction, for example by estimating the Dice score [28], or by predicting
a QC label (for example, high-quality or poor segmentation) [59]. Additionally
to the input image and prediction, studies also incorporated uncertainty maps
as input to the output QC model to enhance the Dice prediction [23, 20], while
Galdran et al. [33] used the segmentation only as input to a CNN. As an
alternative to training directly from the images, Jungo et al. [46] extracted
radiomics from uncertainty maps in the context of brain tumor segmentation,
<figure><img src="image_5.png" /><figcaption>**FIGURE 1.4** Illustration of output QC based on the generation of various plausible segmentation masks using an uncertainty framework.</figcaption></figure>

and further trained a RF model to predict Dice scores. A similar approach is adopted by extracting a set of features from the segmentation, followed by the training of a Support Vector Machine to predict the Dice score [51]. Lastly, another approach is to extract a set of meaningful statistical and geometrical features from the segmentations and use them to train a ML classifier to detect failed analyses [2, 103, 25].

While these previous works focus on estimating the overall quality of the segmentation, other studies instead proposed to detect local errors within the segmentation [129, 99]. It is worth mentioning that while most supervised output QC studies are proposed for segmentation tasks, similar techniques can be employed to detect poor image registrations [102, 11].

However, building such a supervised output QC module requires access to an auxiliary database for which automated predictions are available. Additionally, to correctly train the model the dataset should contain a sufficient amount of poor predictions, which however are scarce when fortunately the predictive model has good performances. A potential way to alleviate this is to artificially degrade segmentation masks to mimic segmentation errors during training [33].

### 1.2.2.3 Unsupervised Anomaly Detection for Output QC

Output QC can be tackled in an unsupervised fashion, without explicitly training a model to distinguish between high-quality and poor predictions using annotated data. For instance, Hui et al. [44] proposed an outlier approach to output QC, by first modeling the features of valid delineations using a parametric distribution.
Then, poor segmentations are detected as outliers to this historic distribution. Alternatively, Audelan et al. [8] proposed an unsupervised Bayesian framework to provide a surrogate segmentation that smoothly follows the visible boundaries of the target ROI (e.g. lesion). The Dice coefficient between the surrogate and automated segmentation is then used as a proxy score for the real Dice. Finally, Luo et al. [66] propose to compute variograms to automatically detect erroneous ground truth landmarks in annotated image registration datasets.

Another popular unsupervised approach is the reconstruction paradigm. The concept is simple: an autoencoder is trained to reconstruct its input using conform data only. At test time, when confronted with non-conform inputs, the autoencoder is supposed to produce large reconstruction errors, allowing to detect the outlier. One idea is to mask the input image using the predicted segmentation, and train an autoencoder to recover the original input from the masked one [134, 121]. Alternatively, the autoencoder can be used to reconstruct the segmentation mask [32]. The hypothesis is that incorrect segmentations should yield to masked images that are difficult to reconstruct. Alternatively, a conditional Generative Adversarial Network (GAN) can be trained to reconstruct the image from its automated segmentation [15]. The differences between the original and synthesized images can then be used to detect segmentation errors. Alternatively, a variational autoencoder is used in [118] to learn a manifold of valid pairs of inputs and outputs, by learning to reconstruct the inputs. At test time, the predicted segmentation is projected to the learned manifold, yielding to a surrogate segmentation. A quality score can then be computed by comparing the original segmentation and the surrogate one. A similar idea is pursued in the CRISP framework making use of contrastive learning to learn a manifold of valid input-segmentation pairs [45]. Finally, Nourzadeh et al. [77] used autoencoders trained to reconstruct the posterior probabilities of an ensemble on classification models to detect errors in organ delineations.

### 1.2.2.4 Reverse Classification Accuracy

Reverse Classification Accuracy (RCA) was first proposed by Valindria et al. [114] and further extended in follow-up studies [90, 89, 91]. The RCA strategy requires a labeled reference database comprising images and ground truth segmentation. Then, for a pair composed of a test image and a prediction whose quality we wish to evaluate, RCA proposes to build a classifier using only the test pair as training data. To do so, the automated segmentation is considered as a pseudo ground truth. The assumption is that if the automated segmentation is of good quality, the trained classifier should be able to segment at least one reference image with high performance. In contrast, if the segmentation is poor, the trained classifier should fail on all reference images. To estimate a quality score, the trained classifier is applied to all images of the reference set to obtain automated segmentation, and a metric (e.g. Dice) is computed using the available reference ground truth. Then, the highest score is used as a proxy estimation
of the true quality. In the original RCA paper, several RCA classifiers have been
explored, including Atlas Forests, Deep Learning, and registration [114]. The
latter was found to outperform competing approaches. Registration was then
further used for RCA [91, 90]. Interestingly, RCA does not require access to a
database comprising good and poor segmentation. The only assumption is that
training and test data are similar.

1.2.3 Combining Input and Output QC

In Sections 1.2.1 and 1.2.2, the previously proposed frameworks to perform
input and output QC were introduced. The following step is to examine whether
potential gains could be obtained by addressing input and output QC in a unified
way. Few works can be found in the literature in this direction (only 7.4% of
the reviewed papers). A straightforward choice is to combine two different QC
techniques, one for the input image and one for the prediction. For instance,
Machado et al. [67] leverage a supervised CNN for input QC and RCA for
prediction quality estimation. Ruijsink et al. [96] detect outlier images using a
CNN, while the adequacy of the prediction is estimated using a Support Vector
Machine classifier. Alternatively, Comballa et al. [21] rely on the uncertainty
quantification paradigm which can be interestingly used to estimate both the
confidence in the prediction and to detect outlier images, in the context of
dermoscopic image classification.

To go further in associating input and output QC, the pioneering work of Shaw
et al. [105] defined MRI quality with respect to the model's ability to provide
correct output. Thus, if an image presents an artifact that does not prevent the
correct functioning of the model, it should still be considered valid. They further
proposed to enhance a segmentation model with a heteroscedastic uncertainty
quantification module. It allows the quantification of the noise present in the
input images (e.g. motion, blurring, or ghosting artifacts), and the uncertainty
score was found to correlate strongly with the Dice coefficient, thus bridging the
gap between input and output QC.

The concept of defining non-conform images with respect to the performance
of the downstream task is also explored in three recent studies focusing on
image segmentation [115, 124, 60, 140]. Instead of defining OOD inputs as images
presenting artifacts or missing attributes, they propose to cast OOD images as
cases for which the associated segmentation is poor. This redefinition of OOD
allows to take into account the generalization capability of the network, which
can be robust to certain types of noise, as illustrated in Figure 1.1. On the other
hand, it will also be considered as OOD, a conform (noise-free) image when
poorly segmented by the model. Vasiliuk et al. [115] further proposed a new
metric to evaluate the performance of an OOD detector in this setting, called the
Expected Performance Drop (EPD). The principle is to determine the expected
performance on clean data used as a target performance. Then, the OOD detector
is used to reject samples expected to yield to poor predictions (OOD samples) at
test time. Finally, EPD computes the difference between the target performance and the empiric performance on the remaining test data points. The metric can be minimized by rejecting poorly segmented samples, while correctly segmenting the remaining ones.

For output QC, Lennartz et al. [60] proposed a proxy score called *Segmentation Distortion*, computed from the latent space of a trained segmentation model, which exhibits a strong correlation with the Dice coefficient. Authors compared their metric with MD (introduced in Section 1.2.1.2). They show that MD, which has been designed for input QC, performs poorly at predicting the segmentation quality (output QC). On the other hand, Segmentation Distortion is successful at output QC but performs poorly at detecting shifts in the acquisition device (input QC), while MD performs extremely well. Authors conclude that OOD detection is more suitable for critical applications where strong protection against silent failures is required. However, this may also consider as OOD images that are well processed by the model. Alternatively, output QC is most preferred when the goal is to identify cases that should be reviewed by a human expert.

In the following of this chapter, based on these previous studies, a general framework to encompass both input and output QC is illustrated to enhance QC decision-making.

## 1.3 PRACTICAL DEMONSTRATION OF A UNIFIED INPUT-OUTPUT QC FOR MEDICAL IMAGE SEGMENTATION

### 1.3.1 Ensemble-based input and output QC scores

In this section, a practical application of the different tools presented for input and output QC is proposed. The aim of the following experiments is to serve as a concrete illustration of how QC can be implemented to monitor simultaneously the conformity of the input image and its associated prediction. Here, the focus is on medical image segmentation due to its preponderance in the automatized QC literature.

For this proof-of-concept, the emphasis is on QC methods that are i) easy to implement, ii) do not require the training of a dedicated model dedicated to QC, and iii) do not require the building of a labeled dataset of good/bad quality for inputs and outputs, which is cumbersome to obtain for most applications. Instead, QC metrics are seamlessly obtained from an ensemble of DL segmentation models. More formally, let's consider an ensemble of K encoder-decoder segmentation models (e.g. the U-Net [93]). From this ensemble, two QC estimates are computed: the *Globally Normalized Mahalanobis Distance* (GNMD) [17] for input QC, and the *Ensemble Dice Agreement* for output QC, respectively. Both scores are introduced below.
### 1.3.1.1 Input QC using the Globally Normalized Mahalanobis Distance

The GNMD score is a latent-space approach for input QC [17]. In practice, the GNMD score can be computed from the latent space of a single trained model. The final input-level QC score will correspond to the average score across the K models.

We consider the k-th model of the ensemble, composed of L convolution layers $C_1, ..., C_N$. To compute the GNMD for layer $C_i$ with $M_i$ filters, the initial step is to model the output of the layer by a multivariate Gaussian distribution with mean $\mu_i \in \mathbb{R}^{M_i}$ and covariance matrix $\Sigma_i \in \mathbb{R}^{M_i \times M_i}$. To do so, the feature maps $\phi_{C_i}(x)$ are collected at layer $C_i$ on a set of in-distribution (noise-free) images $S$. The resulting maps are then reduced over the spatial dimensions:

$$ \{A^i(x) : x \in S\} \quad \text{with} \quad A^i(x) = \frac{1}{H} \frac{1}{W} \sum_{h=1}^{H} \sum_{w=1}^{W} \phi_{C_i}(x)(h, w) \quad (1.1) $$

From this set of reduced activations, the layer mean $\mu_i$, layer variance $\sigma_i$, and covariance matrix $\Sigma_i$ are estimated. Then, for a test image $x_T$, the MD for layer $C_i$ is obtained using:

$$ \begin{aligned} \tilde{A}^i(x_T) &= (A^i(x_T) - \mu_i)/\sigma_i \\ \Sigma_i &= \text{Cov}(\tilde{A}^i(x_T)) \\ \text{MD}^i(x_T) &= \sqrt{\tilde{A}^i(x_T)^T \Sigma_i^{-1} \tilde{A}^i(x_T)} \end{aligned} $$

To obtain the GNMD for the k-th model, this process is repeated for each convolution layer, independently. As MD scales with the number of filters $M$, the layer scores are aggregated using a weighted average:

$$ \text{GNMD}_k(x_T) = \frac{1}{L} \sum_{i=1}^{L} \frac{1}{M_i} \text{MD}^i(x_T) \quad (1.2) $$

In the proposed setting, the GNMD is computed for each model of the ensemble, separately. Then the ensemble's GNMD is taken as the average of the individual GNMDs. It is supposed to yield high values for images that are out-of-distribution, as their representations in the latent space of the models are expected to deviate from the learned in-distribution distribution.

### 1.3.1.2 Output QC using the Ensemble Prediction Agreement

The inter-predictions agreement is a popular proxy metric to estimate the quality of a segmentation, from a set of plausible masks [39, 132, 40, 42]. In the proposed setting, the masks are provided by the ensemble of segmentation models. Each model produces a prediction mask $S_k$, $k \in [1, ..., K]$. The first step is to compute the majority vote segmentation MV that will be used as the
final ensemble prediction. Then, the overlap between each mask and the majority vote is measured using Dice(S<sub>k</sub>, MV). The final output QC estimate, named Ensemble Predictions Agreement (EPA), corresponds to:

$$EPA = \frac{1}{K} \sum_{i=1}^{K} \text{Dice}(S_k, MV) \qquad (1.3)$$

The hypothesis is that if the segmentation is of good quality, the individual segmentations should be stable between the ensemble's members, hence the EPA should be high. In contrast, if the segmentation deviates significantly from one model to the other, it is likely that the prediction is uncertain, and its overall quality should be rather low. To get a score that grows with the degree of nonconformity, 1 - EPA is used in practice as the output QC score.

### 1.3.2 Defining thresholds for input and output QC

The selected input and output QC scores produce continuous values, however, for practical QC it is desired to have binary decisions: either accept or reject. Thus, it is necessary to define thresholds on the scores above which the sample (image or prediction) will be flagged for review. To determine these thresholds, the predictions and QC scores are gathered on a clean validation labeled dataset, representative of conforming inputs and outputs. Following the intuition that non-conform inputs and outputs should be rare events [115], the thresholds for the GNMD and EPA metrics are set as the 95-th percentiles of the validation QC scores.

### 1.3.3 Stratification of the Prediction space

The prediction space is referred to as the positioning of the test pair (image, prediction) according to their unified QC protocol. More specifically, 4 cases are possible using the proposed protocol (see Figure 1.5), listed below in increasing priority:

* **Region A - Input QC ✓ and Output QC ✓**: optimum operating regime; corresponding to the ideal setting where the image is close to the training distribution and the output prediction is estimated as accurate. It is expected that this subgroup contains the high-quality predictions of the model.

* **Region B - Input QC ✗ and Output QC ✓**: Robust operating regime; corresponding to images that may contain an anomaly ( artifact), but for which the output QC is successful. This could represent images that the model is able to process even though their quality is not perfect.

* **Region C - Input QC ✓ and Output QC ✗**: Dysfunctional regime, corresponding to images that have passed the input QC, but for which the prediction is unsure (high EPA). This could represent images that are conform in terms of quality but are still poorly segmented. The reviewing priority for this
<figure><img src="image_6.png" /><figcaption>**FIGURE 1.5** Proposed stratification of the prediction space using input and output QC estimates.</figcaption></figure>

subgroup is high.

* **Region D - Input QC × and Output QC ×:** Divergent regime, corresponding to the worst-case scenario where both input and output QC failed. This could represent out-of-distribution images for which the prediction is highly sub-optimal. This subgroup should be reviewed with top priority.

### 1.3.4 Experiments

The general unified input-output QC protocol is illustrated on two tasks: binary segmentation of polyps in endoscopic images and multi-class tumor segmentation in multi-model brain MRI. For each setting, a synthetic and a real scenario are investigated, causing degradations to the input images, and/or an expected degradation on the output performance.

#### 1.3.4.1 *Task 1: binary polyp segmentation in 2D endoscopic images*

For this task, a training dataset is built composed of data collected from different sources: Kvasir [84] (1000 images), ETIS-LaribPolyp [107] (196 images), CVC-ColonDB [13] (380 images) and CVC-ClinicDB [12] (612 images). This results in a set of 2188 endoscopic images with associated binary polyp mask, from which a random split is performed in 60% for training (1312 images), 20% for validation (438 images) and 20% (438 images) for in-distribution test, referred
<figure><img src="image_7.png" /><figcaption>**FIGURE 1.6** Samples from 2D endoscopic images. Top row: *Test ID*, initial samples. Bottom row: *Synthetic Degradation*, associated downgraded versions.</figcaption></figure>

to as *Test ID* in the following. All images are resized to a resolution of 768×512.

Two degraded datasets are then explored to test the QC protocol on poor-quality samples (poor inputs and/or poor predictions). The first dataset, *Synthetic Degradation*, is an augmented version of *Test ID*. More precisely, the albumen-tation library [16] is employed to artificially downgrade the quality of the images by applying the following operators: *Downscale*, *ImageCompression* and *ISONoise*.

The second scenario explores *domain-shifts* using the PolypGen dataset [4]. This dataset comprises endoscopy images from 6 different centers, exhibiting a heterogeneous population and acquired with different endoscopic systems.

### 1.3.4.2 Task 2: multi-class tumor segmentation in multi-modal 3D brain MRI

For this task, the large-scale BraTS 2023 dataset [9, 73] is employed to train models that take as inputs 4 MRI sequences (T1w, T2w, T1w with contrast agent, and T2w FLAIR) and segment tumor tissues into 3 classes: necrotic tissue, edematous and enhancing tumor. The open source adult population dataset comprises 1133 patients, randomly split into 60% for training (679 images), 20% for validation (227 images), and 20% for in-distribution testing (227 images) (referred to *Test ID* in the following).

Then, a *Synthetic Degradation* dataset specially tailored for MRI data is created. More specifically, the TorchIO library [83] is employed to downgrade the quality of *Test ID*. The following operators are applied: *RandomAnisotropy* (in each of the 3 axes), and *RandomMotion*. Illustrations of this process are provided in Figure 1.7.

Additionally, the BraTS 2023 dataset also includes various auxiliary datasets to explore domain-shift robustness. To mimic shifts in the population demogra-phy, the BraTS-Africa dataset [1] is employed, comprising 60 cases exhibiting
<figure><img src="image_8.png" /><figcaption>FIGURE 1.7 Samples from the tumor test datasets. Top row: axial views of a patient from Test ID, bottom row: axial views of the corresponding degraded patient in Synthetic Degradation.</figcaption></figure>

lower MRI quality and more advanced stages of the disease as well as the BraTS-Pediatric dataset [48] comprising 99 cases. To mimic shifts in the observed pathology, the BraTS 2023 Metastasis dataset [74] is used (238 cases) as well as 250 cases from the BraTS 2023 Intracranial Meningioma dataset [54]. These last two datasets contain patients with a type of brain tumor unseen during training, as the Adult dataset only includes glioblastoma. All images are provided pre-processed, including brain extraction and registration of the MRI sequences to a common anatomical template.

### 1.3.4.3 Evaluation Metrics

To evaluate the quality of a segmentation $\hat{Y}$ with respect to a ground truth annotation $Y$, two metrics are used. First, the Dice coefficient, which is a popular volumetric overlap score in medical image segmentation defined as:

$$Dice(\hat{Y}, Y) = \frac{2 \times (\hat{Y} \cap Y)}{\hat{Y} \cup Y} \qquad (1.4)$$

However, the Dice score is known to be biased toward large segmented volumes [68]. Thus, the Surface Dice (SD) is also used to measure the overlap of two surfaces instead of the overlap of two volumes. SD computes the proportion of the segmentation boundary correctly identified. A point of boundary is considered as correct if the closest distance to the ground truth boundary is
smaller than or equal to a user-level tolerance threshold, defining the acceptable
deviation in pixels (or voxels). SD is defined as:

$$
SD(\hat{Y}, Y) = \frac{|\mathcal{D}'_Y| + |\mathcal{D}'_{\hat{Y}}|}{|\mathcal{D}_Y| + |\mathcal{D}_{\hat{Y}}|} \quad (1.5)
$$

where $\mathcal{D}_Y$ and $\mathcal{D}_{\hat{Y}}$ are the sets of nearest neighbors from the predicted
boundary towards the reference and vice versa. $\mathcal{D}'_Y$ and $\mathcal{D}'_{\hat{Y}}$ are the subsets of
distances that are smaller than or equal to the tolerance threshold $\tau$:

$$
\mathcal{D}'_Y = \{d \in \mathcal{D}_Y | d \le \tau\} \qquad (1.6)
$$

For the standard Dice and SD, the metric is computed for each foreground
class independently (thus excluding the background class), and the final score is
the average of the classes scores. For SD, a tolerance threshold of 3 pixels/voxels
is set.

1.3.4.4 Implementation Details

For both tasks, a segmentation ensemble is obtained by aggregating 5 U-Nets
independently trained with the same conditions. The implementation of the
base network is obtained from the Monai library<fnref n="2" />. Models are trained using
a combination of the Dice loss and cross-entropy loss until the Dice score on
the validation dataset seizes to improve for 20 epochs. The Adam optimizer is
employed with a learning rate of 2 × 10⁻⁴, with a batch size of 8 for the polyp
models and a batch size of 1 for brain tumors.

1.3.5 Results

Tables 1.1 and 1.2 present the segmentation metrics on each test dataset and on each of the 4 identified QC regions, for polyps and brain tumors, respectively. Additionally, Figure 1.8 presents the result of the stratification of test datapoints according to their input and output QC estimates. Three visualizations of the same scatter plot are provided: one showing the source dataset of each test point, and the two others that show the true quality of the predictions estimated using Dice and SD scores, respectively.

First, in terms of segmentation performance, both the polyp and brain tumor
ensemble achieve high segmentation quality on in-distribution data (Test ID).
Then, for the perturbed datasets exhibiting degraded image quality (Synthetic
Degradation, BraTS Africa), domain shifts (PolypGen), population shift (BraTS
Pediatric), or target shifts (Brats Metastases and Meningioma), the quality of
the predictions degrades. For the polyp models, it can be observed that this

<footnote n="2">2. https://docs.monai.io/en/stable/_modules/monai/networks/nets/basic_unet.html</footnote>
<table><caption>**TABLE 1.1** Ensemble segmentation performance on each test dataset for polyp segmentation in endoscopy images. A: Optimal regime, B: Robust regime, C: Dysfunctional regime, D: Divergent regime.</caption><thead><tr><th>Dataset</th><th>N samples</th><th>Dice</th><th>Surface Dice</th></tr></thead><tbody><tr><td>Test ID</td><td>438</td><td>0.87 ± 0.15</td><td>0.64 ± 0.25</td></tr><tr><td>Synthetic Degradation</td><td>438</td><td>0.78 ± 0.22</td><td>0.48 ± 0.68</td></tr><tr><td>PolypGen-Center 1</td><td>251</td><td>0.80 ± 0.21</td><td>0.50 ± 0.26</td></tr><tr><td>PolypGen-Center 2</td><td>270</td><td>0.74 ± 0.26</td><td>0.49 ± 0.29</td></tr><tr><td>PolypGen-Center 3</td><td>456</td><td>0.84 ± 0.17</td><td>0.61 ± 0.24</td></tr><tr><td>PolypGen-Center 4</td><td>146</td><td>0.56 ± 0.30</td><td>0.29 ± 0.22</td></tr><tr><td>PolypGen-Center 5</td><td>206</td><td>0.53 ± 0.34</td><td>0.32 ± 0.26</td></tr><tr><td>PolypGen-Center 6</td><td>83</td><td>0.76 ± 0.27</td><td>0.52 ± 0.27</td></tr><tr><td>Total</td><td>2288</td><td>-</td><td>-</td></tr></tbody></table><table><thead><tr><th>QC Region</th><th>N samples</th><th>Dice</th><th>Surface Dice</th></tr></thead><tbody><tr><td>A</td><td>1333 (58.26%)</td><td>0.88 ± 0.13</td><td>0.63 ± 0.23</td></tr><tr><td>B</td><td>358 (15.65%)</td><td>0.80 ± 0.23</td><td>0.54 ± 0.27</td></tr><tr><td>C</td><td>225 (9.83%)</td><td>0.60 ± 0.23</td><td>0.28 ± 0.18</td></tr><tr><td>D</td><td>372 (16.26%)</td><td>0.46 ± 0.29</td><td>0.22 ± 0.18</td></tr></tbody></table>

<table><caption>**TABLE 1.2** Ensemble segmentation performance on each test dataset for tumor segmentation in brain MRI.A: Optimal regime, B: Robust regime, C: Dysfunctional regime, D: Divergent regime.</caption><thead><tr><th>Dataset</th><th>N samples</th><th>Dice</th><th>Surface Dice</th></tr></thead><tbody><tr><td>Test ID</td><td>227</td><td>0.84 ± 0.13</td><td>0.91 ± 0.14</td></tr><tr><td>Synthetic Degradation</td><td>227</td><td>0.78 ± 0.13</td><td>0.89 ± 0.15</td></tr><tr><td>BraTS-Africa</td><td>60</td><td>0.74 ± 0.19</td><td>0.81 ± 0.20</td></tr><tr><td>BraTS-Pediatric</td><td>99</td><td>0.39 ± 0.23</td><td>0.41 ± 0.25</td></tr><tr><td>BraTS-Metastases</td><td>238</td><td>0.55 ± 0.29</td><td>0.64 ± 0.33</td></tr><tr><td>BraTS-Meningioma</td><td>250</td><td>0.66 ± 0.34</td><td>0.54 ± 0.31</td></tr><tr><td>Total</td><td>1101</td><td>-</td><td>-</td></tr></tbody></table><table><thead><tr><th>QC Region</th><th>N samples</th><th>Dice</th><th>Surface Dice</th></tr></thead><tbody><tr><td>A</td><td>736 (66.85%)</td><td>0.78 ± 0.17</td><td>0.84 ± 0.19</td></tr><tr><td>B</td><td>85 (7.72%)</td><td>0.70 ± 0.18</td><td>0.76 ± 0.23</td></tr><tr><td>C</td><td>204 (18.53%)</td><td>0.45 ± 0.35</td><td>0.38 ± 0.29</td></tr><tr><td>D</td><td>76 (6.90%)</td><td>0.32 ± 0.33</td><td>0.28 ± 0.27</td></tr></tbody></table>

degradation is very heterogeneous depending on the source center. For instance, data from center 3 is segmented with a performance close to the one achieved on Test ID data, while data from center 5 is very poorly segmented. Similarly, for the brain models, the performance on BraTS Africa remains acceptable while the performance collapses on pediatric data.

For both experiments, the general input/output QC strategy allows a stratification of the predictions in 4 different sub-regions (A, B, C and D in Figure 1.8). Predictions in Region A (Optimal operation regime, success of input and output
QC) contain the best quality predictions, with an average performance close to the one achieved on Test ID. Then, B, C, and D regions exhibit performances that are increasingly decreasing, with D containing the worst segmentation.

Interestingly, even though conform in-distribution data are under-represented in our evaluation protocol (438 / 2288 samples for polyps, and 227 / 1101 for brain tumors), the majority of samples are still located in Region A (58.26% of samples for polyps, and 66.26% for brain tumors). This indicates that the segmentation models are able to generalize to some extent to noisy data. The dysfunctional (C) and divergent regimes (D) contain together approximately one-quarter of the data points (26.10% for polyps and 25.43% for brain tumors). This correspond to cases that should be absolutely reviewed by the user.

<figure><img src="image_9.png" /><figcaption>**FIGURE 1.8** Stratification of the polyp (top row) and brain tumor (bottom row) prediction spaces in 4 regions according to the input QC scores (x-axis) and output QC scores (y-axis). Left: prediction distribution according to the source dataset. Center and Right: prediction distribution according to the Dice and Surface Dice scores, respectively. The vertical blue dashed line indicates the threshold for the GNMD values, and the horizontal purple dashed line is the threshold for the EPA scores.</figcaption></figure>

1.4 CONCLUSION

In this chapter, the different techniques proposed in the literature to tackle QC
in the context of ML-based medical image analysis have been discussed. While
most proposed methods have been proposed to either tackle input QC or output
QC, there is a growing interest regarding the merging of both notions. In this
direction, Uncertainty Quantification appears as a natural paradigm, allowing the
assessment of both data (aleatoric) and model (epistemic) uncertainty. The most
popular uncertainty approaches, including Monte Carlo Dropout [30] and Deep
Ensemble [55], are easy to implement and are thus a scalable and general solution
for QC. However, in practice, it appears that uncertainty is mostly investigated
for output QC. This can be explained by the fact that uncertainty estimates
have been shown to be poorly calibrated on non-conform inputs, thus they are
generally not reliable for input QC [100, 113]. Other techniques address QC
more directly, such as the supervised techniques, which were widely investigated
for both input and output QC. Their increased performance is at the cost of a
dedicated training stage making use of a dataset comprising examples of both
poor and good-quality input and/or predictions.

After reviewing the main paradigms for QC, a practical illustration of a
unified input/output QC strategy was detailed. This method relies on 2 features:
one for estimating the conformity of the input data and one for estimating the
quality of the output segmentation. Both metrics are easily obtained from an
ensemble of DL models and do not require the training of auxiliary models
dedicated to QC. By jointly considering input and output QC, it is possible to
stratify the space of predictions into 4 sub-regions. First, the optimal regime
contains the best quality predictions. Second, the robust regime which contains
samples that the model is able to process smoothly, despite they are far from the
training distribution. Third, the dysfunctional regime corresponds to images that
are considered as conform, yet the quality of the prediction is doubtful. Finally,
the divergent regime corresponds to the case where both input and QC failed and
thus encompass the worst quality predictions. The corresponding experiments
on medical image segmentation serve as a demonstration of the usefulness of
a unified QC strategy, providing additional information to the user and helping
prioritize the cases to review.
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