Electron tomography (ET) is an important tool for investigating the internal organization of cells at a resolution of a few nanometers (McIntosh et al., 2005). To create a 3D volume, a series of micrographs are captured from the sample at various tilt angles and then reconstructed using tomographic algorithms (Fernandez, 2012). Prior to 3D reconstruction, it is necessary to align the micrographs with each other, correcting for any shifts, rotations, or distortions that may have occurred during electron imaging (Fernandez, 2012). The success of this calibration process relies on extracting features from the micrographs. Typically, gold beads are employed as fiducial markers, which are introduced into the sample during the preparation stage to facilitate feature extraction. Consequently, the detection of fiducial markers becomes a critical step in the entire electron micrograph processing pipeline. Fiducial markers in electron micrographs typically appear as circular or nearly circular areas, with sizes typically ranging from a few to tens of nanometers. Due to their small size relative to the entire field of view, detecting fiducial markers can be considered a specialized application of small object detection, ultimately influencing the quality of the alignment.

Small objects have certain characteristics that make them hard to be detected (Liu et al., 2021, Cao et al., 2019). Firstly, such small objects occupy only a small number of pixels in an image and lack salient features, making them difficult to distinguish from the other objects. Secondly, small objects are easily affected by the high noise contained in an image, which can result in low contrast of the small objects. Several studies have been conducted on small object detection in the image processing community (Tong et al., 2020, Li and Cao, 2020). Template matching is a fundamental technique, which has been widely studied and utilized in various situations since the early days (Amat et al., 2007, Trampert et al., 2015, Trampert et al., 2016, Cao et al., 2011, Modegi, 2008). Additionally, feature-based methods are also popular in the research of small object detection, such as Scale-Invariant Feature Transform (SIFT) (Lowe, 1999), Speeded-Up Robust Features (SURF) (Bay et al., 2008, Luo and Oubong, 2009), and Histogram of Oriented Gradients (HOG) (Dalal and Triggs, 2005, Zhang et al., 2010).

The fiducial markers in electron micrographs are similar to the small objects which makes their detection particularly challenging. Fiducial marker detection has been a topic of significant interest in electron micrograph processing. With the development of electron microscopy technologies (Wan and Briggs, 2016, Ruska and Jul, Jul 1987, Sorzano et al., 2010), the size of electron micrographs began to explode, which led to the need for a method for efficient fiducial marker detection. According to the specific features of fiducial markers, template matching is a widely adopted method in fiducial marker detection. Such algorithms detect the markers in the micrographs through the manually defined template and threshold (Amat et al., 2007, Trampert et al., 2015, Trampert et al., 2016, Cao et al., 2011). A concept of the average template is proposed to eliminate the uncertainty of fiducial marker detection using only one predefined template (Amat et al., 2007). Because the diameter of a fiducial marker is diverse in each dataset, users need to define the diameter in advance before using the algorithm. In order to simplify fiducial marker detection, automatic fiducial marker detection without manual settings is needed. A grid-based searching method is firstly proposed to generate the template automatically(Han et al., 2015). In addition to the template matching method, several noise-robust local information-based methods are proposed by taking advantage of the high-contrast features of the fiducial markers (Voss et al., 2009, Olivo-Marin, 2002, Izeddin et al., 2012, Cao et al., 2011, Püspöki et al., 2015).

In this article, we propose a novel method called MarkerDetector. The proposed MarkerDetector is an automatic detection algorithm. It is implemented with a wavelet-based template and filtering-based marker determination strategy, which can achieve fiducial marker detection with higher correctness. Extensive experiments are done on 8 different real electron micrographs datasets, which prove the superiority of MarkerDetector compared with previous methods. The main contributions of this work are summarized as follows:

A novel template generation algorithm is proposed. By combining wavelet transform and a shape-based criterion, a high-quality template will be derived.

A novel statistic-based filter strategy is proposed to improve the quality of the candidates by removing the candidates that have a low likelihood of being a fiducial marker.

A refined strategy is proposed to determine the accurate locations of fiducial markers.