Original: Robust quad-tree based registration on whole slide images
Revised: Robust Quad-Tree based Registration on Whole Slide Images

Original: Editor:
Revised: Editor

Original: Abstract
Revised: Abstract

Original: The registration of whole slide images (WSIs) provides the basis for many subsequent processing steps in digital pathology.
Revised: The registration of whole slide images (WSIs) provides the basis for many subsequent processing steps in digital pathology.

Original: For instance, the registration of immunohistochemistry (IHC) and hematoxylin & eosin (H&E)-stained WSIs is usually the ﬁrst step in guiding
Revised: For instance, the registration of immunohistochemistry (IHC) and hematoxylin & eosin (H&E)-stained WSIs is usually the ﬁrst step in guiding

Original: IHC diagnostic procedures.
Revised: IHC diagnostic procedures.

Original: Still, many registration methods operate poorly on WSIs.
Revised: Still, many registration methods operate poorly on WSIs.

Original: Reasons for this include the WSI size, ﬂuctuating image quality or elastic tissue deformations.
Revised: Reasons for this include the WSI size, ﬂuctuating image quality or elastic tissue deformations.

Original: Multiple prior methods are further specialised towards a speciﬁc image modality, such as histology or cytology, or rely on a speciﬁc preparation protocol.
Revised: Multiple prior methods are further specialised towards a speciﬁc image modality, such as histology or cytology, or rely on a speciﬁc preparation protocol.

Original: To minimise these effects, we developed a robust WSI registration, which diﬀers from previous methods by the following new aspect: We introduce a multi-scale approach based on a quad-tree (QT), with several termination criteria that makes the algorithm particularly insensitive to tissue artefacts and that further allows to estimate a piece-wise aﬃne transformation.
Revised: To minimise these ef- fects, we developed a robust WSI registration, which diﬀers from previous methods by the following new aspect: We introduce a multi-scale approach based on a quad-tree (QT), with several termination criteria that makes the algorithm particularly insensitive to tissue artefacts and that further allows to estimate a piece-wise aﬃne transformation.

Original: We validated our method on ﬁve scanner systems and 60 WSIs with diﬀerent stainings.
Revised: We validated our method on ﬁve scanner systems and 60 WSIs with diﬀerent stainings.

Original: Our results outperformed any publicly available WSI registration method.
Revised: Our results outperformed any publicly available WSI registration method.

Original: The QT code, WSI landmarks and tools used to create the validation dataset are made publicly available.
Revised: The QT code, WSI landmarks and tools used to create the validation dataset are made publicly available.

Original: 1. Introduction
Revised: 1. Introduction

Original: Digital pathology has experienced an unprecedented growth in recent years due to the availability of scanners with Food and Drug Administration (FDA) clearance, progress in software applications as well as an increasing acceptance by pathologists (Aeﬀner et al., 2019).
Revised: Digital pathology has experienced an unprecedented growth in recent years due to the availability of scanners with Food and Drug Administration (FDA) clearance, progress in software applications as well as an increasing acceptance by pathologists (Aeﬀner et al., 2019).

Original: The open challenges in digital pathology include scanner independence for automatic analysis algorithms as well as the simultaneous assessment of multiple stainings.
Revised: The open challenges in digital pathology include scanner independence for automatic analysis algorithms as well as the simultaneous assessment of multiple stainings.

Original: For the ﬁrst case, datasets where the same slide is digitised by multiple scanners play an essential role.
Revised: For the ﬁrst case, datasets where the same slide is digitised by multiple scanners play an essential role.

Original: To avoid an extremely time-consuming re-annotation and instead transfer the labels from one scanner to the next, ﬁne-grained alignment of the WSIs is essential.
Revised: To avoid an extremely time-consuming re-annotation and instead transfer the labels from one scanner to the next, ﬁne-grained alignment of the WSIs is essential.

Original: In the second case, standard H&E datasets are often complemented by specialised IHC reactions that allow for a more detailed assessment of diﬀerent pathologies (see Sec. 2.1).
Revised: In the second case, standard H&E datasets are often complemented by specialised IHC reactions that allow for a more detailed assessment of diﬀerent pathologies (see Sec. 2.1).

Original: Aligning the diﬀerent visualisations allows both to transfer annotations from one staining to another and to jointly visualise the same image region in both WSIs, supporting a faster assessment by the pathologist.
Revised: Aligning the diﬀerent visualisations allows both to transfer annotations from one staining to another and to jointly visualise the same image region in both WSIs, supporting a faster assessment by the pathologist.

Original: For these purposes, robust WSIs registration techniques are required.
Revised: For these purposes, robust WSIs registration techniques are required.

Original: Proprietary WSI formats by diﬀerent scanner vendors, diﬀering magniﬁcation factors, multi-resolution pyramid image storage, background representation and focus algorithms make WSI registration a challenging task.
Revised: Proprietary WSI formats by diﬀerent scanner vendors, diﬀering magniﬁcation factors, multi-resolution pyramid image storage, background representation and focus algorithms make WSI registration a challenging task.

Original: Apart from these technical aspects, the samples themselves can contain artefacts like tissue detachment, deformation, folding or tearing, which poses additional challenges for any registration method.
Revised: Apart from these technical aspects, the samples themselves can contain artefacts like tissue detachment, deformation, folding or tearing, which poses additional challenges for any registration method.

Original: Registration plays a signiﬁcant role for many medical image processing tasks across diﬀerent imaging modalities (Song et al., 2017).
Revised: Registration plays a signiﬁcant role for many medical image processing tasks across diﬀerent imaging modalities (Song et al., 2017).

Original: Two main classes of registration approaches are intensity- and keypoint-based methods.
Revised: Two main classes of registration approaches are intensity- and keypoint-based methods.

Original: Intensity-based methods attempt to minimise the intensity gradient between a moving (source) and a ﬁxed (target) image (Jiang et al., 2019);
Revised: Intensity-based methods attempt to minimise the intensity gradient between a moving (source) and a ﬁxed (target) image (Jiang et al., 2019);

Original: In contrast, keypoint-based strategies use keypoint extractors like Oriented FAST and
Revised: In contrast, keypoint-based strategies use keypoint extractors like Oriented FAST and

Original: Rotated BRIEF (ORB) (Rublee et al., 2011) or Scale Invariant Feature Transform (SIFT) (Lowe, 2004) and then match and align corresponding keypoints in multiple images.
Revised: Rotated BRIEF (ORB) (Rublee et al., 2011) or Scale Invariant Feature Transform (SIFT) (Lowe, 2004) and then match and align corresponding keypoints in multiple images.

Original: In both cases, the extracted information is used to calculate a linear transformation (translation, rotation, skewing, scaling) or a non-linear transformation that compensates for non-linear distortions between the source and target WSI.
Revised: In both cases, the extracted information is used to calculate a linear transformation (translation, rotation, skewing, scaling) or a non-linear transformation that compensates for non-linear distortions between the source and target WSI.

Original: An example of a rigid transformation is the registration of the same WSI scanned with multiple scanners, while a non-rigid registration is needed for registration of consecutive slides with or without diﬀerent stains.
Revised: An example of a rigid transformation is the registration of the same WSI scanned with multiple scanners, while a non-rigid registration is needed for registration of consecutive slides with or without diﬀerent stains.

Original: In addition to the methods of classical image processing, deep learning-based methods can also be applied for registration tasks (Lee et al., 2019) as a whole or parts thereof.
Revised: In addition to the methods of classical image processing, deep learning-based methods can also be applied for registration tasks (Lee et al., 2019) as a whole or parts thereof.

Original: In the recent Automatic Non-Rigid Histological Image Registration (ANHIR) benchmark challenge (Borovec et al., 2020), several algorithms have been proposed for non-linear registration; however, the submitted approaches do not naively support WSIs and depend upon down-sampled images (down to 2%) and therefore would require considerable modiﬁcations to operate on full WSIs.
Revised: In the recent Automatic Non-Rigid Histological Image Registration (ANHIR) benchmark challenge (Borovec et al., 2020), several algorithms have been proposed for non-linear registration; however, the submitted approaches do not naively support WSIs and depend upon down-sampled images (down to 2%) and therefore would require considerable modiﬁcations to operate on full WSIs.

Original: A further limitation of the ANHIR dataset is the use of the same source and target scanner, which neglects particular challenges like diﬀerent scanned areas, magniﬁcations and resolution levels.
Revised: A further limitation of the ANHIR dataset is the use of the same source and target scanner, which neglects particular challenges like diﬀerent scanned areas, magniﬁcations and resolution levels.

Original: Furthermore, pathological registration methods often require a form of tissue pre-segmentation (Levy et al., 2020; Jiang et al., 2019; Rossetti et al., 2017) or background knowledge about anatomical structures present in the images (Schwier et al., 2013).
Revised: Furthermore, pathological registration methods often require a form of tissue pre-segmentation (Levy et al., 2020; Jiang et al., 2019; Rossetti et al., 2017) or background knowledge about anatomical structures present in the images (Schwier et al., 2013).

Original: For cytology WSIs, which where not included in the
Revised: For cytology WSIs, which where not included in the

Original: ANHIR dataset, these approaches are not applicable, since they - unlike tissue-based WSIs - do not contain contiguous areas for segmentation.
Revised: ANHIR dataset, these approaches are not applicable, since they - unlike tissue-based WSIs - do not contain contiguous areas for segmentation.

Original: Additionally, the down-sampling of
Revised: Additionally, the down-sampling of

Original: WSIs could lead to the disappearance of small space structures like cells and therefore prevent a successful registration.
Revised: WSIs could lead to the disappearance of small space structures like cells and therefore prevent a successful registration.

Original: Out of the mentioned methods, only Jiang et al.
Revised: Out of the mentioned methods, only Jiang et al.

Original: (2019) provide publicly accessible source code and are able to deal with WSI images directly, but the approach is limited to a translation-based registration that ignores rotation or scaling diﬀerences.
Revised: (2019) provide publicly accessible source code and are able to deal with WSI images directly, but the approach is limited to a translation-based registration that ignores rotation or scaling diﬀerences.

Original: In this paper, we therefore propose a general and conﬁgurable approach based on a quadtree (QT) (Bardera et al., 2006) that supports a robust and fast piece-wise aﬃne (rigid + scaling) registration between full-scale WSI for many application ﬁelds out of the box.
Revised: In this paper, we therefore propose a general and conﬁgurable approach based on a quadtree (QT) (Bardera et al., 2006) that supports a robust and fast piece-wise aﬃne (rigid + scaling) registration between full-scale WSI for many application ﬁelds out of the box.

Original: No additional preconditions like a pre-segmentation or a speciﬁc anatomical structure have to be fulﬁlled.
Revised: No additional preconditions like a pre-segmentation or a speciﬁc anatomical structure have to be fulﬁlled.

Original: We validate our method with manually positioned landmarks on 60 WSIs from four diﬀerent ﬁelds of application across diﬀerent scanners and compare the results with the open-source WSI-registration method by Jiang et al.
Revised: We validate our method with manually positioned landmarks on 60 WSIs from four diﬀerent ﬁelds of application across diﬀerent scanners and compare the results with the open-source WSI-registration method by Jiang et al.

Original: and the publicly available methods from the ANHIR challenge on down-sampled sub-images.
Revised: and the publicly available methods from the ANHIR challenge on down-sampled sub-images.

Original: To ensure the reproducibility of our results, we publish the code for our method as Pip Python package 1 together with the evaluation code 2  .
Revised: To ensure the reproducibility of our results, we publish the code for our method as Pip Python package 1 together with the evaluation code 2 and implementation 3 .

Original: The WSIs can be provided by the corresponding author upon reasonable request.
Revised: The WSIs can be provided by the corresponding author upon reasonable request.

Original: https://pypi.org/*** 2.

Original: https://github.com/***/***

Original: [Figure]

Original: 2. Materials
Revised: 2. Materials

Original: For our experiments, we compiled four WSI datasets which cover a broad range of WSI registration tasks.
Revised: For our experiments, we compiled four WSI datasets which cover a broad range of WSI registration tasks.

Original: Two datasets address registration of the same slide digitised with four diﬀerent scanners and contain ﬁve H&E-stained tissue slides and ﬁve Prussian Blue pulmonary hemorrhage cytology WSIs, respectively.
Revised: Two datasets address registration of the same slide digitised with four diﬀerent scanners and contain ﬁve H&E-stained tissue slides and ﬁve Prussian Blue pulmonary hemorrhage cytology WSIs, respectively.

Original: The other two datasets allow to assess the performance between diﬀerent stains, namely H&E and IHC.
Revised: The other two datasets allow to assess the performance between diﬀerent stains, namely H&E and IHC.

Original: First, the same ﬁve tissue slides were stained and digitised, then destained, IHC-stained and again digitised with the same scanner.
Revised: First, the same ﬁve tissue slides were stained and digitised, then destained, IHC-stained and again digitised with the same scanner.

Original: Secondly, ﬁve H&E and ﬁve consecutive IHC slides were digitised with two diﬀerent scanners.
Revised: Secondly, ﬁve H&E and ﬁve consecutive IHC slides were digitised with two diﬀerent scanners.

Original: The datasets and the ground truth generation are described in more detail in the following sections.
Revised: The datasets and the ground truth generation are described in more detail in the following sections.

Original: 2.1 Datasets
Revised: 2.1 Datasets

Original: Multi scanner cytology dataset (MSC):
Revised: Multi scanner cytology dataset (MSC):

Original: For the cytology WSI dataset, we used ﬁve equine bronchoalveolar lavage ﬂuid samples.
Revised: For the cytology WSI dataset, we used ﬁve equine bronchoalveolar lavage ﬂuid samples.

Original: The samples were prepared by cytocentrifugation and stained with Prussian Blue.
Revised: The samples were prepared by cytocentrifuga- [Figure] tion and stained with Prussian Blue.

Original: Digitisation of the glass slide was performed using four diﬀerent linear scanners.
Revised: Digitisation of the glass slide was performed using four diﬀerent linear scanners.

Original: The Aperio ScanScope CS2 (WSI resolution 0 .
Revised: The Aperio ScanScope CS2 (WSI resolution 0 .

Original: 2533 µmpx ),
Revised: µm px ),

Original: Hamamatsu NanoZoomer S210 (WSI resolution 0 .
Revised: Hamamatsu NanoZoomer S210 (WSI resolution 0 .

Original: 2533 µmpx ) and the Hamamatsu NanoZoomer 2.0-HT (WSI resolution 0 .
Revised: 2533 µmpx ) and the Hamamatsu NanoZoomer 2.0-HT (WSI resolution 0 .

Original: 2533 µmpx )
Revised: 2533 µmpx )

Original: each with a magniﬁcation of 400 × and the ZEISS Axio
Revised: each with a magniﬁcation of 400 × and the ZEISS Axio

Original: Scan.
Revised: Scan.

Original: Z1 at a magniﬁcation of 200 × (WSI resolution 0 .
Revised: Z1 at a magniﬁcation of 200 × (WSI resolution 0 .

Original: 221 µmpx ).
Revised: 221 µmpx ).

Original: The digitisation process resulted in 20 WSI and in the following we will refer to this dataset as MSC.
Revised: The digitisation process resulted in 20 WSI and in the following we will refer to this dataset as MSC.

Original: Multi scanner tissue dataset (MST):
Revised: Multi scanner tissue dataset (MST):

Original: For the H&E tissue dataset, we used slides from canine cutaneous mast cell tumours, also digitised with the same four scanners as the MSC dataset.
Revised: For the H&E tissue dataset, we used slides from canine cutaneous mast cell tumours, also digitised with the same four scanners as the MSC dataset.

Original: We will refer to this dataset as MST.
Revised: We will refer to this dataset as MST.

Original: In-situ proteomic single scanner dataset (ISC):
Revised: In-situ proteomic single scanner dataset (ISC):

Original: In pathological diagnostics, IHCstaining is used to visualise expression patterns of so-called marker proteins that are expressed only by certain cell or tissue types.
Revised: In pathological diagnostics, IHCstaining is used to visualise expression patterns of so-called marker proteins that are expressed only by certain cell or tissue types.

Original: This allows to detect structures that cannot be discriminated by H&E morphology alone.
Revised: This allows to detect structures that cannot be discriminated by H&E morphology alone.

Original: D2-40 is such a marker protein, speciﬁcally expressed by cell linings of lymphatic vessels.
Revised: D2-40 is such a marker protein, speciﬁcally expressed by cell linings of lymphatic vessels.

Original: These thin-walled vessels are especially relevant in cancer metastasis as they become invaded by tumor cells, which thus spread to lymph nodes and other organs.
Revised: These thin-walled vessels are especially relevant in cancer metastasis as they become invaded by tumor cells, which thus spread to lymph nodes and other organs.

Original: To include this diagnostically highly relevant information, we ﬁrst H&E-stained ﬁve colorectal cancer tissue samples from ﬁve diﬀerent patients to obtain morphological information.
Revised: To include this diagnostically highly relevant information, we ﬁrst H&E-stained ﬁve colorectal cancer tissue samples from ﬁve diﬀerent patients to obtain morphological information.

Original: After digitisation with a Roche Ventana iScan HT scanner with 200 × magniﬁcation (WSI resolution 0 .
Revised: After digitisation with a Roche Ventana iScan HT scanner with 200 × magniﬁcation (WSI resolution 0 .

Original: 25 µmpx ), the cover slips were removed and the sections unstained, washed, subjected to IHC for the lymphatic vessel marker D2-40 and digitised again.
Revised: 25 µmpx ), the cover slips were removed and the sections unstained, washed, subjected to IHC for the lymphatic vessel marker D2-40 and digitised again.

Original: The resulting dataset of paired morphological and in-situ D2-40 expression data is referred to as ISC dataset.
Revised: The resulting dataset of paired morphological and in-situ D2-40 expression data is referred to as ISC dataset.

Original: Multi-slide multi scanner dataset (MSSC):
Revised: Multi-slide multi scanner dataset (MSSC):

Original: The procedure of staining, destaining and IHC-restaining of the same slide has potential disadvantages like physical trauma to the slide tissue and a reduced ﬁnal staining quality.
Revised: The procedure of staining, destaining and IHC-restaining of the same slide has potential disadvantages like physical trauma to the slide tissue and a reduced ﬁnal staining quality.

Original: An alternative is the use of two consecutive slides where one slide is IHC-stained and the second slide is H&E-stained.
Revised: An alternative is the use of two consecutive slides where one slide is IHC-stained and the second slide is H&E-stained.

Original: We prepared this dataset from the same samples and in analogy to ISC, and reference it as MSSC.
Revised: We prepared this dataset from the same samples and in analogy to ISC, and reference it as MSSC.

Original: 2.2 Ground truth generation
Revised: 2.2 Ground truth generation

Original: To validate the registration accuracy, we placed a 5x5 rectangular grid of landmarks on each WSI such that it covers as much tissue as possible (see Fig. 1) using the online annotation software EXACT (Marzahl et al., 2021).
Revised: To validate the registration accuracy, we placed a 5x5 rectangular grid of landmarks on each WSI such that it covers as much tissue as possible (see Fig. 1) using the online annotation software EXACT (Marzahl et al., 2021).

Original: We manually reﬁned the position of each landmark on the highest resolution level such that they are positioned on the same cell or prominent tissue landmarks near-by in corresponding WSIs.
Revised: We manually reﬁned the position of each landmark on the highest resolution level such that they are positioned on the same cell or prominent tissue landmarks near-by in corresponding WSIs.

Original: This landmark pattern allows us to measure the pixel-level deviation at 25 locations on the WSI and to quantify any macroscopic elastic deformation.
Revised: This landmark pattern allows us to measure the pixel-level deviation at 25 locations on the WSI and to quantify any macroscopic elastic deformation.

Original: In total, we created and manually checked 1500 registration points on 60 WSIs.
Revised: In total, we created and manually checked 1500 registration points on 60 WSIs.

Original: The landmarks are sized according to representative registration target structures for the individual datasets, e.g. mitotic ﬁgures for MST, hemosiderophages for MSC and lymphatic vessels for ISC and MSSC.
Revised: The landmarks are sized according to representative registration target structures for the individual datasets, e.g. mitotic ﬁgures for MST, hemosiderophages for MSC and lymphatic vessels for ISC and MSSC.

Original: Thereby, it can be determined whether the registration results are accurate enough to be used as ground truth for object detection algorithms.
Revised: Thereby, it can be determined whether the registration results are accurate enough to be used as ground truth for object detection algorithms.

Original: 3. Methods
Revised: 3. Methods

Original: The goal of any image registration method is to ﬁnd a transformation T between a moving source image I and a ﬁxed target image I (cid:48) .
Revised: The goal of any image registration method is to ﬁnd a transformation T between a moving source image I and a ﬁxed target image I (cid:48) .

Original: For the datasets MSC and MST the same slides were digitised with multiple scanners; thus, we assume that an aﬃne transformation is suitable to estimate the registration.
Revised: For the datasets MSC and MST the same slides were digitised with multiple scanners; thus, we assume that an aﬃne transformation is suitable to estimate the registration.

Original: For the ISC and MSSC dataset, a non-rigid registration is required to handle tissue distortions introduced by the use of sequential tissue slides or the process of de- and re-staining.
Revised: For the ISC and MSSC dataset, a non-rigid registration is required to handle tissue distortions introduced by the use of sequential tissue slides or the process of de- and re-staining.

Original: To handle both use cases, we construct our registration pipeline as follows:
Revised: To handle both use cases, we construct our registration pipeline as follows:

Original: Based on a QT backbone, we recursively divide the WSI into image segments with successively higher resolution levels.
Revised: Based on a QT backbone, we recursively divide the WSI into image segments with successively higher resolution levels.

Original: For each segment, we estimate a transformation matrix based on matching keypoints in both images.
Revised: For each segment, we estimate a transformation matrix based on matching keypoints in both images.

Original: We thereby reﬁne the estimate from the previous QT level until a previously deﬁned termination criterion is reached.
Revised: We thereby reﬁne the estimate from the previous QT level until a previously deﬁned termination criterion is reached.

Original: This results in a piece-wise aﬃne approximation of any non-linear deformation. 
Revised: This results in a piece-wise aﬃne approximation of any non-linear deformation. Q T - L Q T - L Q T - L

Original:  As keypoint detector, we use the low-level extractor SIFT.
Revised: Q T - L Q T - L Q T - L As keypoint detector, we use the low-level extractor SIFT.

Original: In the following section, we will describe our method in detail.
Revised: In the following section, we will describe our method in detail.

Original: 3.1 Quad tree-based registration approach
Revised: 3.1 Quad tree-based registration approach

Original: QTs are characterised by their recursive deﬁnition, where each segment on the previous level is divided into four sub-segments that have twice the spacial resolution but cover only a quarter of the spacial extent (see Fig. 2).
Revised: QTs are characterised by their recursive deﬁnition, where each segment on the previous level is divided into four sub-segments that have twice the spacial resolution but cover only a quarter of the spacial extent (see Fig. 2).

Original: Their hierarchical structure makes them ideal candidates to approximate WSIs with their pyramidal approach of saving images at multiple magniﬁcation levels.
Revised: Their hierarchical structure makes them ideal candidates to approximate WSIs with their pyramidal approach of saving images at multiple magniﬁcation levels.

Original: Using this data structure as the backbone, our registration algorithm is recursively applied for each level of the QT and can be described as follows:
Revised: Using this data structure as the backbone, our registration algorithm is recursively applied for each level of the QT and can be described as follows:

Original: First, we extract a source and a target region of interest (RoI) from the source/target WSI.
Revised: First, we extract a source and a target region of interest (RoI) from the source/target WSI.

Original: On QT level 0, this RoI is simply the complete WSI, whereas it consists of a subsegment in subsequent levels of the QT.
Revised: On QT level 0, this RoI is simply the complete WSI, whereas it consists of a sub-segment in subsequent levels of the QT.

Original: In the second step, keypoints and their respective feature vectors are extracted from source and target RoIs using SIFT.
Revised: In the second step, keypoints and their respective feature vectors are extracted from source and target RoIs using SIFT.

Original: Then, corresponding keypoints in both RoIs are determined using k-nearest neighbours (k=2) on the feature vectors.
Revised: Then, corresponding keypoints in both RoIs are determined using k-nearest neighbours (k=2) on the feature vectors.

Original: To avoid that outliers impact the estimation negatively, the point pairs are ﬁltered as described by Lowe (2004).
Revised: To avoid that outliers impact the estimation negatively, the point pairs are ﬁltered as described by Lowe (2004).

Original: For a total number of n successfully matched keypoints, (cid:126)x i ∈ R 2 , i ∈ [1 , n ] will refer to the pixel coordinates of a keypoint i in the source image, and (cid:126)x (cid:48) i ∈
Revised: For a total number of n successfully matched keypoints, (cid:126)x i ∈ R 2 , i ∈ [1 , n ] will refer to the pixel coordinates of a keypoint i in the source image, and (cid:126)x (cid:48) i ∈

Original: R 2 to the position of the matched keypoint in the target image.
Revised: R 2 to the position of the matched keypoint in the target image.

Original: In the next step, we compute the transformation matrix T ∈ R 2 × 3 with eight degrees of freedom by computing the homography matrix (OPENCV implementation) with RANSAC (Fischler and Bolles, 1981) ﬁltering or CoherentPoint Drift (Myronenko and
Revised: In the next step, we compute the transformation matrix T ∈ R 2 × 3 with eight degrees of freedom by computing the homography matrix (OPENCV implementation) with RANSAC (Fischler and Bolles, 1981) ﬁltering or Coherent

Original:  Song, 2010) depending which resulted in a lower error between matched keypoints.
Revised: Point Drift (Myronenko and Song, 2010) depending which resulted in a lower error between matched keypoints.

Original: This keypoint matching error (KME) E is the mean Euclidean distance between the transformed source keypoints T ( (cid:126)x i ) and the target keypoints (cid:126)x (cid:48)
Revised: This keypoint matching error (KME) E is the mean Euclidean distance between the transformed source keypoints T ( (cid:126)x i ) and the target keypoints (cid:126)x (cid:48)

Original: i and is deﬁned as
Revised: i and is deﬁned as

Original: [Equation]
Revised: [Equation]

Original: Q T - L

Original: Q T - L

Original: Q T - L

Original: Q T - L Q T - L Q T - L The ﬁnal step is the evaluation of the QT termination criteria.
Revised: The ﬁnal step is the evaluation of the QT termination criteria.

Original: The implementation allows to deﬁne ﬂexible stopping criteria based on maximum QT depth, run-time, a userdeﬁned threshold for the KME or when the KME increases compared to the previous level.
Revised: The implementation allows to deﬁne ﬂexible stopping criteria based on maximum QT depth, run-time, a user-deﬁned threshold for the KME or when the KME increases compared to the previous level.

Original: To keep the evaluation consistent, a maximum QT level of 2 was used as the stopping criterion for the results presented here.
Revised: To keep the evaluation consistent, a maximum QT level of 2 was used as the stopping criterion for the results presented here.

Original: If the termination criterion is not fulﬁlled, the source RoI is divided into four equal parts.
Revised: If the termination criterion is not fulﬁlled, the source RoI is divided into four equal parts.

Original: The calculated T is applied to each of the 16 corner points to estimate the corresponding RoIs on the target slide and the next QT level with the source and target RoI is initialised recursively.
Revised: The calculated T is applied to each of the 16 corner points to estimate the corresponding RoIs on the target slide and the next QT level with the source and target RoI is initialised recursively.

Original: To calculate the position of a given point in the source image after registration, the ﬁnal transformation matrix associated with the last QT level is used to transform the point to the target coordinate system.[Table]
Revised: To calculate the position of a given point in the source image after registration, the ﬁnal transformation matrix associated with the last QT level is used to transform the point to the target coordinate system.

Original: method has a native WSI support.

Original: 4. Results
Revised: 4. Results

Original: We evaluate our registration results by calculating the mean target registration error (TRE) in pixels (analogous to Eq. 1) between the ground truth landmarks and the transformed landmarks.
Revised: We evaluate our registration results by calculating the mean target registration error (TRE) in pixels (analogous to Eq. 1) between the ground truth landmarks and the transformed landmarks.

Original: For comparability between scanners with diﬀerent microns per pixel (MPP) values, all values are converted to microns.
Revised: For comparability between scanners with diﬀerent microns per pixel (MPP) values, all values are converted to microns.

Original: Furthermore, we calculate the mean Intersection over Union (IoU) over all landmarks to quantify if the registration algorithm is accurate enough for cell-level registration.
Revised: Furthermore, we calculate the mean Intersection over Union (IoU) over all landmarks to quantify if the registration algorithm is accurate enough for cell-level registration.

Original: For comparison, we use the open-source implementation of
Revised: For comparison, we use the open-source implementation of

Original: Jiang et al.
Revised: Jiang et al.

Original: (2019), which we will refer to as ReStain.
Revised: (2019), which we will refer to as ReStain.

Original: Because the provided implementation has no compensation for diﬀerent MPP values, we re-scaled all target WSIs according to the MPP values read out from the meta data provided by the scanner.
Revised: Because the provided implementation has no compensation for diﬀerent MPP values, we re-scaled all target WSIs according to the MPP values read out from the meta data provided by the scanner.

Original: Furthermore, we use the publicly available methods from the the ANHIR challenge (Borovec et al., 2020):
Revised: Furthermore, we use the publicly available methods from the the ANHIR challenge (Borovec et al., 2020):

Original: DROP, ANTs, Elastix, NiftyReg, bUnwarpJ which are provided as docker containers 3 .
Revised: DROP, ANTs, Elastix, NiftyReg, bUnwarpJ which are provided as docker containers 4 .

Original: The methods are described in detail in Borovec et al.
Revised: The methods are described in detail in Borovec et al.

Original: (2020) and
Revised: (2020) and

Original: due to their inability to handle full WSI we down-sampled all image to 4 k × 4 k as described in Borovec et al.
Revised: due to their inability to handle full WSI we down-sampled all image to 4 k × 4 k as described in Borovec et al.

Original: As additional reference, we calculate an aﬃne matrix between the source and corresponding target landmarks to estimate the error of a least-squares optimal aﬃne registration.
Revised: As additional reference, we calculate an aﬃne matrix between the source and corresponding target landmarks to estimate the error of a least-squares optimal aﬃne registration.

Original: We further report the initial mean Euclidean pixel distance without registration. 
Revised: We further report the initial mean Euclidean pixel distance without registration. [Table]

Revised: WSI support.

Original: 4.1 CMS and MST dataset
Revised: 4.1 CMS and MST dataset

Original: For the MSC and MST datasets, we use the Aperio scanner as source and the remaining three scanners as targets.
Revised: For the MSC and MST datasets, we use the Aperio scanner as source and the remaining three scanners as targets.

Original: The QT conﬁguration with the best results uses SIFT with 1024 keypoints and an RoI size of 1024 × 1024 pixels.
Revised: The QT conﬁguration with the best results uses SIFT with 1024 keypoints and an RoI size of 1024 × 1024 pixels.

Original: As shown in Table 1, each level of the QT reduces the pixel distance error between the ground truth landmarks and the transformed landmarks until, at level two, the QT results outperform the aﬃne landmark transformation.
Revised: As shown in Table 1, each level of the QT reduces the pixel distance error between the ground truth landmarks and the transformed landmarks until, at level two, the QT results outperform the aﬃne landmark transformation.

Original: We were unable to evaluate the ReStain approach on the MSC dataset due to the method’s dependence on an initial segmentation which we could not parameterise with the provided options.
Revised: We were unable to evaluate the ReStain approach on the MSC dataset due to the method’s dependence on an initial segmentation which we could not parameterise with the provided options.

Original: For the ISC and MSSC dataset, we use the IHC WSIs as registration source.
Revised: For the ISC and MSSC dataset, we use the IHC WSIs as registration source.

Original: For the
Revised: For the

Original: ISC dataset, we see equally high performance as for MSC and MST.
Revised: ISC dataset, we see equally high performance as for MSC and MST.

Original: In contrast, for the
Revised: In contrast, for the

Original: MSSC dataset the QT-based method is not able to match the error of the aﬃne landmark transformation.
Revised: MSSC dataset the QT-based method is not able to match the error of the aﬃne landmark transformation.

Original: We attribute this to the lack of matching (SIFT) keypoints since slides of sequential slices of tissue are registered: Compared to a mean of 268 matching keypoints on the ISC dataset, we only found a mean of 13 keypoints on the MSSC dataset.
Revised: We attribute this to the lack of matching (SIFT) keypoints since slides of sequential slices of tissue are registered: Compared to a mean of 268 matching keypoints on the ISC dataset, we only found a mean of 13 keypoints on the MSSC dataset.

Original: All quantitative results including the runtime can be found in Tab. 1.
Revised: All quantitative results including the runtime can be found in Tab. 1.

Original: 5. Discussion and Conclusion
Revised: 5. Discussion and Conclusion

Original: The registration of WSIs is a very challenging task due to their size and further diﬃculties like diﬀerent stainings, scanners and image artefacts.
Revised: The registration of WSIs is a very challenging task due to their size and further diﬃculties like diﬀerent stainings, scanners and image artefacts.

Original: We show that our method produces promising results on three out of four datasets and outperforms the reference method in all cases.
Revised: We show that our method produces promising results on three out of four datasets and outperforms the reference method in all cases.

Original: Furthermore, we oﬀer the ﬁrst registration method that is able to register cytology
Revised: Furthermore, we oﬀer the ﬁrst registration method that is able to register cytology

Original: WSIs as it does not require any kind of pre-segmentation.
Revised: WSIs as it does not require any kind of pre-segmentation.

Original: The importance of native WSIbased approaches is highlighted by both methods outperforming down-sampling strategies.
Revised: The importance of native WSIbased approaches is highlighted by both methods outperforming down-sampling strategies.

Original: With the proposed approach, the results achieved for the diﬀerent QT levels are considerably below the resolution level used in the respective RoI. We hypothesise that this is due to the large number of keypoints extracted in each RoI that allow for a sub-pixel accurate estimation of the transformation matrix.
Revised: With the proposed approach, the results achieved for the diﬀerent QT levels are considerably below the resolution level used in the respective RoI. We hypothesise that this is due to the large number of keypoints extracted in each RoI that allow for a sub-pixel accurate estimation of the transformation matrix.

Original: The fact that we are able to outperform an aﬃne transformation based on point correspondences can be attributed to, e.g. stitching artefacts.
Revised: The fact that we are able to outperform an aﬃne transformation based on point correspondences can be attributed to, e.g. stitching artefacts.

Original: One limitation of our work is highlighted when applied to consecutive tissue slices on which SIFT only ﬁnds a limited number of matching keypoints.
Revised: One limitation of our work is highlighted when applied to consecutive tissue slices on which SIFT only ﬁnds a limited number of matching keypoints.

Original: It is striking that all approaches performed abysmally on this data.
Revised: It is striking that all approaches performed abysmally on this data.

Original: We reason that the use of diﬀerent source and target scanners and heavy tissue artefacts particularly challenge registration.
Revised: We reason that the use of diﬀerent source and target scanners and heavy tissue artefacts particularly challenge registration.

Original: Still, this opens up the possibility of future improvements by implementing a speciﬁcally trained deep-learning-based keypoint detector as an alternative or to integrate intensitybased methods as well.
Revised: Still, this opens up the possibility of future improvements by implementing a speciﬁcally trained deep-learning-based keypoint detector as an alternative or to integrate intensitybased methods as well.

Original: In this paper, we showed that the proposed QT-based approach is accurate, eﬃcient and robust for WSI registration.
Revised: In this paper, we showed that the proposed QT-based approach is accurate, eﬃcient and robust for WSI registration.

Original: These properties are underlined by the fact that the proposed registration method is utilized in the context of a detection challenge.
Revised: These properties are underlined by the fact that the proposed registration method is utilized in the context of a detection challenge.

Original: Due to its ﬂexibility, we see a high potential to extend this method to further applications, e.g., as robust initialisation for fully elastic registration approaches.
Revised: Due to its ﬂexibility, we see a high potential to extend this method to further applications, e.g., as robust initialisation for fully elastic registration approaches.