Dynamical System Modeling and Stability Investigation�DSMSI-2025

May 08-10, 2025, Kyiv, Ukraine

Detection of potential obstacles in a field image using k-means and inertia drop tracking methods

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Presented by: Denys Zhuk, PhD student

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Authors:

Alla Dudnyk, Denys Zhuk, Nikolay Kiktev and Oleksiy Opryshko�National University of Life and Environmental Sciences of Ukraine�

Introduction

Machine vision technologies based on digital image processing can be divided into two main classes:

• Traditional computer vision methods - based on classical image processing algorithms. They include methods of filtering (Gaussian blurring), edge detection (Laplace operator, Canny), etc. These methods require considerable effort to choose the correct parameters and are not always effective in complex tasks.
• Machine learning and deep learning methods - use neural networks for image analysis (such as CNN, R-CNN). These models require large datasets for training and significant resources to work.

This work presents a research on the use of the classical approach to recognition based on k-means clustering

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Methodology

Dynamical System Modeling and Stability Investigation, DSMSI-2025

1. Image preprocessing

2. Clustering

3. Spatial cluster processing

1. Image preprocessing

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Point clouds at threshold values a) h=10; b) h=20; c) h=30; d) h=40

Laplace operator

2.1. Clustering

In the picture below we can see that most of the points are concentrated at the real obstacle location. It is assumed that when clustering by coordinates, the classes' centers should fall in the middle of a cloud with a large concentration of points. Thus, each such cloud is separated from the others into a single object.

The main disadvantage of the classical method is the manual setting of the clusters' amount, since to use this method for our issue, it should be calculated automatically

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Point clouds �after preprocessing

2.2. Inertia drop tracking method

Dynamical System Modeling and Stability Investigation, DSMSI-2025

2.2. Inertia drop tracking method

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Change in the ordinary and average relative inertia with increasing number of clusters, window size w=10

2.2. Inertia drop tracking� method

The overall algorithm consists of several stages:

1. Initialization: the initial number of clusters is set to 1 and the window size is given;
2. Clustering is performed by the selected number of clusters;
3. For the number of clusters k>1 the value of relative total inertia is calculated;
4. For k>w, if more than half of the relative inertia values from the window are higher than the average one, the optimal number of clusters is determined along the left edge of the window and the program exits the cycle, if not back to the step 2.

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Image processing algorithm using the inertia drop tracking method

3. Spatial cluster processing

From figure it can be concluded that the algorithm divided the points into a sufficient number of clusters so that each shell crater in the image is a separate cluster. It is also noticeable that some shell craters have split into separate objects, which can be corrected after the obstacle boundaries have been delineated by merging them if they are located nearby.

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Dynamical System Modeling and Stability Investigation, DSMSI-2025

Experimental image with marks of the identified cluster centers

The main problem with this method is a significant number of noise clusters that are not filtered out by the Laplace convolution throw threshold.

3. Spatial cluster processing

To filter out extraneous clusters, it is proposed to re-cluster by the number of points in the defined obstacle and filter out small objects as noise

Dynamical System Modeling and Stability Investigation, DSMSI-2025

The final result of obstacle detection

Bar chart of the distributing the number of points

Effect of window size on results

Dynamical System Modeling and Stability Investigation, DSMSI-2025

It is clear that the value of the determined optimal number of clusters can depend on the choice of window size. Using an experimental image, it was investigated how the value of the parameter w affects the final detection.

Table 1. Number of identified elements at each step of the algorithm

Applying the algorithm to other images

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Conclusion

The results of the research are as follows:

• The possibility of using classical image processing methods to recognize potential obstacles in the field image (based on Laplace convolution and k-means clustering) was tested.
• An inertia drop tracking method for optimizing the number of clusters is developed and the relevant algorithm is built.
• An experiment on the effect of the window size is conducted.
• The presented recognition algorithm is tested on other.

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Thank you for your attention