## 1 Introduction  
Histologic and, more recently, immunohistochemical evaluation of resected tissue by anatomic pathologists, are the essential basis of surgical pathology diagnostics. Variously stained histology slices are routinely used by pathologists to assess tissue samples from various anatomical sites and determine tissue structure, the presence or extent of a disease, as well as the host reaction that describes the disease process. However, as the field continues to move forward, new technologies in imaging, protein, and nucleic acid analysis will enhance these traditional assessment techniques to allow more precise and actionable diagnoses [1]. This phenomenon has been dramatically exemplified by the integration of molecular features into diagnostic criteria. Similarly, rich data reflecting the biology underlying various pathologic processes are obtained by leveraging advances in imaging and machine learning in order to analyze histopathology slides to elucidate imagingfeatures in a quantitative and reproducible manner. These structural correlates of biological processes, particularly in the context of molecular insight when available, may lead to improved ability to tailor therapy based on biological markers.  
Non-rigid registration of consecutive 2D histologic slices with different stains is considered to be an important step in enabling more advanced computational analyses towards understanding tissue properties (biomechanical or architectural, cell subtyping, cellular networks). Furthermore, the use of thicker slices was found to improve the 2D registration by avoiding major distortions, thereby facilitating the combination of information from the slices to construct a meaningful picture for subsequent analyses [2].  
Various approaches have been proposed for 2D non-rigid registration of histology slides of the same anatomical site, such as B-splines and common information extraction [3], or multiresolution supervised registration [4], on the basis of the _elastix_ toolbox [5]. Both these examples [3; 4] have reported relatively accurate results in a decent amount of time, but none of them were fully automatic and their evaluation datasets were very small, i.e., 8 pairs of lung histology slides with few different stains [3] and 10 histology slide pairs stained with hematoxylin and eosin (H&E) and anti-PD-L1 antibody (CD274) [4]. [PERSON] et al. [6] used a comparatively larger multi-stain 2D histologic dataset (Figure 1) to evaluate 11 image registration methods, including intensity-based (_elastix_[5], ANTs [7; 8], NiftyReg [9], bUnwarp [10], Multistep [11], DeepHistReg [12]), integral projection-based [13], homography-based [14], feature-based (OpenCV [15], TrakEM2 [16]), hybrid of feature and intensity-based (DROP [17], feature-based + Elastix [18], register virtual stack slices [10]), as well as segmentation-based (ASSAR [19], SegReg [20]) approaches. Some of these approaches were developed during the automatic non rigid histological image registration (ANHIR) challenge and some were developed after the challenge concluded. According to that evaluation study [6], the method with the optimal accuracy and robustness for elastic registration was ANTs [7; 8], but at the cost of a very long runtime. An unsupervised registration approach for H&E slides has also been developed on the basis of deep learning features [21; 22; 23; 24], reporting relatively good performance with very low runtime. Although such approaches could be applied for computer-assisted interventions [25], they are limited by their need for very large datasets to be efficiently trained and their requirement for specialized hardware (i.e., a general-purpose graphical processing unit (GPGPU)) to achieve low runtime.