## Abstract

The multi-seed region growing (MSRG) algorithm from previous work is extended to extract elongated segments from breast Magnetic Resonance Imaging (MRI) stacks. A model is created to adjust the MSRG parameters such that the elongated segments may reveal vessels that can support clinicians in their diagnosis of diseases or provide them with useful information before surgery during e. g. a neoadjuvant therapy. The model is a pipeline of tasks and contains user-defined parameters that influence the segmentation result. A crucial task of the model relies on a skeletonization-like algorithm that collects useful information about the segments’ thickness, length, etc. Length, thickness, and gradient information of the pixel intensity along the segment helps to determine whether the extracted segments have a tubular structure, which is assumed to be the case for vessels. In this work, we show how the results are derived and that the MSRG algorithm is capable of extracting vessel-like segments even from noisy MR images.

## Zusammenfassung

Wir bauen auf der bestehende Arbeit des Multi-Seed Region-Growing (MSRG) Algorithmus auf und erweitern ihn um damit längliche Segmente aus Brust-MR (Magnet Resonanz) Bildern zu extrahieren. Ein Modell wird von uns erstellt, das dazu dient die Eingabe-Parameter des MSRG so einzustellen, dass die länglichen Segmente potentielle Blutgefäße in der Brust darstellen um u. a. Chirurgen vor einem operativen Eingriff bei der Vorbereitung zu unterstützen. Das Modell stellt eine Aneinanderreihung von Aufgaben dar, die das Ergebnis beeinflussen sollen. Eine essentielle Aufgabe besteht darin Informationen wie Breite, Länge der Segmente und Gradient der Intensität der einzelnen Pixel entlang eines Segments zu erfassen. Mit dieser a priori Information werden Segmente extrahiert, die auf eine zylindrische Struktur hinweisen, da dies auf die zu detektierenden Blutgefäße zutrifft. In dieser Arbeit wird gezeigt, dass der MSRG Algorithmus in der Lage ist, auch bei erhöhtem Bildrauschen Segmente, die auf potentielle Gefäße hinweisen, extrahieren zu können.

## 1 Introduction

Seeded Region Growing (SRG) by Adams and Bischof [1] is an effective and well-known image segmentation algorithm. SRG grows one or more regions, initially called seeds, that can be single-pixel-sized or a set of adjacent pixels. The algorithm grows these distinct regions due to some homogeneous criterion until all pixels are assigned a region. The number of iterations equals the number of pixels, i. e. the algorithm halts when all pixels are partitioned.

In previous work, we presented a fast multi-seed region growing (MSRG) algorithm [2] that employs independent seeds, which can grow fully in parallel without a rendezvous before every pixel has been visited. Also, the mean intensity of a region is neglected (other than with SRG) and growth is promoted where two directly neighboring pixels meet the condition of some homogeneous criterion only.

In many region growing algorithms, *k* seeds typically grow *k* regions, and selecting a proper set of seed positions is a non-trivial task and crucial to the outcome. In our approach, we use one or more seeds but positions are homogeneously dispersed in pixel space and the number of seeds does not necessarily equal the number of extracted regions.

Detection of blood vessels is a challenging task in Magnetic Resonance Imaging (MRI) due to noise and low resolution, and particularly in breast MRI, connective and fat tissues sometimes resemble elongated structures similar to blood vessels [3].

Although region growing is known for its weakness in noisy environments, the proposed novel algorithm is capable of extracting homogeneous regions even in images exhibiting noise artefacts. We make the assumption that breast vessels have turbular structure and process spatial information of adjacent MR images of given MR image stacks to distinguish elongated fat tissue and blurry-edged structures like the breast contour from allegedly segmented vessels.

While the algorithm is still in active development, it has shown promising results on which we rely on in this current contribution. The algorithm generates a finite two-dimensional solution space of extracted homogeneous regions from a given input image. We extend the previous work with a skeletonization-like algorithm that is capable of filtering elongated segments from this solution space that may help to detect vessel-like structures in breast MRI. Information about location, size and morphology of vessels may provide clinicians with useful information before surgery during e. g. a neoadjuvant therapy.

In Section 2, the algorithm of the previous work is explained in detail. The subsequent section will describe the skeletonization-like algorithm and show the results of allegedly extracted vessels. We evaluate the results intrinsically: The proposed method is applied to two noise exhibiting input MRI stacks from the same patient (and same breast), that are acquired during two sessions to show the likelihood of the occurrence of artefacts. As research shows [3], [4], blood vessels in breast MRI are determined subjectively by radiologists, which is considered as the gold standard. In [3], authors claim to be the first who perform 3D blood vessel segmentation in breast MRI. They employ a Hessian method to enhance tubular structures.

## 2 Previous work

The following algorithm is described for *n*-bit grayscale images in *u* and height *v* with

as schematically depicted in red (*k* seeds as follows: Let *q*. Initially, the queue is filled with the seed only, which is a single pixel only. An iteration *i* is initiated by polling a bucket

At the end of an iteration, each result is added to the queue as

### 2.1 Heuristic

Additionally, the number of newly assigned pixels *i*. A map *k* seeds and every *i*. Finally, when the queue is empty, i. e. every pixel was visited,

Then, all *k* binary maps are added up elementwise to

The following pseudo code in Algorithm 1 gives an additional overview of the algorithm for a single seed.

Other than described above, with slight adaption, it is not necessary to visit every pixel. The iteration can halt when the number of non-visited pixels becomes smaller than

Growth is depicted in Fig. 2 and Fig. 3 for two arbitrary seed positions. Figure 2 shows a cumulative histogram of the pixel assimilation process and highlights the iteration for each seed where the largest peak is detected and Fig. 3 shows the corresponding growing process.

### 2.2 Preprocessing

The algorithm’s result is influenced by an input image and the selected grid size so far. However, it is desired to dynamically ‘scan’ for multiple acceptable solutions. Image quantization is used as a preprocessing step to decrease the image’s bit depth, which has shown to be very useful to find practical solutions. Scaling parameter *g* as shown in Fig. 4 until a suitable solution is found. We want to refer to [6], where image quantization is investigated when applied as a preprocessing step for dimensionality reduction in image classification pipelines.

## 3 Filter

In this section we initially detail an algorithm that filters elongated segments from the result set of the multi-seed region growing (MSRG) algorithm. Furthermore, in the second subsection, a model is depicted to show how these two algorithms interact to obtain vessel-like structures from an input breast MRI stack. The stack is defined as follows: Let

### 3.1 Algorithm

Elongated vessel-like segments are filtered out from the set of segments derived by the MSRG. We apply a skeletonization-like algorithm *C* is an arbitrary RGB image and *g*, *u*, *v* the other MSRG input parameters as described in the previous section. Result

Initially, we select a random pixel *A* and 8-adjacently flood-fill until every pixel has been ‘filled’. Let *A*. Each iteration, we prioritize from the set of potential new pixels

This rule leads to a fast method such that the segment is flood-filled nearly homogeneously along an elongated segment as shown in Fig. 6 right. Each iteration and until every pixel has been examined, we derive an updated set of

### 3.2 Model

We generate with the MSRG a one-dimensional solution space: The seed grid size *w* and image height *h* and results in a binary map

To keep the computation time low, we do not iterate over all possible values of the image quantization factor *g*. We limit the range from

The model is schematically depicted in Fig. 5. The results are binary images with elongated structures that potentially reveal vessels. Formally, we generate a result stack (see Fig. 5 right) for all

where

where ∧ and ∨ denote element-wise binary operators. Finally, as a post processing step, we set

where *t* is a user-defined threshold.

With this technique, it is possible to differ the contours of the skin from elongated segments that are within the region of interest. We assume that the color gradient more likely varies along the cross section as shown in Fig. 7. This can be detected by the algorithm of the previous subsection by statistical analysis of

## 4 Results and evaluation

We apply the proposed method of the previous section to two different breast MRI stacks that were acquired from the same patient (and same breast) during two sessions. Several weeks elapsed between these two sessions. Algorithm parameters are set for both stacks equally as follows:

Due to the breast varying in shapes in different postures, it is very challenging to detect common features, however, this method might be used for automatic image registration.

## 5 Conclusions

With our proposed filter and combined with the MSRG algorithm from the previous work, it seems possible to assist clinicians in detecting vessel-like segments. The employed algorithm filtered elongated structures from the solution space of the MSRG algorithm. The results seem promising, however, they could not be evaluated for the correct detection of vessels without medical expertise. Instead, the proposed method was applied to two input MRI stacks from the same patient (and same breast), that were acquired during two sessions. The evaluation showed how barely the results deviate from each other. Although vessels will be positioned slightly differently between two sessions due to shaping the breast dependent on the actual posture in the MRI scanner, this method seemingly extracted similar elongated segments for both input MRI stacks. This suggests the assumption that the extracted segments are not artefacts. Since noise is a common problem in MRI, our approach may help to circumvent this issue.

Based on user experience, the solution space of the MSRG algorithm was searched through. Due to the complexity and computation time, it is impractical to search through the whole solution space. It is required to adjust the MSRG parameters accordingly, however, the MSRG algorithm is not guaranteed to be complete.

Further investigations are required for more efficient search strategies. Future work may focus much more on the automatic adjustment of the MSRG algorithm parameters via state of the art machine learning approaches.

**Funding source: **Linz Center of Mechatronics

**Funding statement: **This work has been supported by the LCM K2 Center within the framework of the Austrian COMET-K2 Programme.

## About the authors

Marco Gierlinger will complete his bachelor’s degree in computer science in 2021. Subsequently, a master’s degree in electrical engineering will be started. Currently, he works as student assistant at Johannes Kepler University at Institute for Measurement Technology.

Dinah Brandner received her BSc degree in Mechatronics from the Johannes Kepler University Linz, Austria in 2019 and is currently enrolled there in the master’s program in Mechatronics specializing in Measurement Technology and Signal Processing. In July 2020 she finished her master’s thesis with the title ‘Sound Field Simulation in Breast Cancer Research’. Part of the work was done during her research stay as a Visiting Student Researcher at the Ferrara Lab as part of the Radiology Department of Stanford University, Palo Alto, USA while working on Quantitative Ultrasound (QUS) imaging using numerical simulations and experimental studies.

Bernhard G. Zagar has been the head of the Institute for Measurement Technology of the Johannes Kepler University Linz since 2001. He has been working in this field and specializing in digital signal and image processing, sensors, laser-optical systems and magnetic tomography.

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**Received:**2021-02-13

**Accepted:**2021-07-30

**Published Online:**2021-07-14

**Published in Print:**2021-08-27

© 2021 Gierlinger et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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