IMAGE PROCESSING USING GRAPHS

 

Article By,
Vidyashree H R
Assistant Professor
Department of Mathematics
NCMS.

Image processing and graph theory are two distinct fields, but they can be interconnected in various ways. Graph theory can be applied to analyze and process images by representing image data as graphs.

Graph theory plays a very significant role in image processing, particularly in image segmentation. Image segmentation is a process of separating a digital image into its integral regions or segments which is useful in the analysis of an image. The various applications of image segmentation are remote sensing, biometrics, satellite image detection, face recognition, vehicle number plate detection, optical character recognition (OCR), medical image analysis and many others. In graph theory, the term cut-vertex is useful in finding the graph cut. Similarly bi-partite graph is useful in finding the normalized cut.

Here’s a brief overview of how image processing and graph theory can be connected:

    Pixel Graphs: In an image, each pixel can be considered as a node in a graph, and the relationships between neighbouring pixels can be represented as edges. This graph can be used for various purposes like image segmentation.

     Object Recognition: Graph theory can be used to represent and analyze relationships between objects or regions of interest within an image. For example, you can create a graph where nodes represent objects and edges represent spatial relationships, helping in object recognition tasks.

    Skeletonization: Skeletonizing an image involves finding its main structural components. Graph theory can be used to represent and extract the skeleton of an image by identifying critical points and connecting them with edges.

     Image Filtering: Graph-based filters can be applied to images to enhance or suppress certain features. Graph Laplacian filters, for instance, can be used to denoise images while preserving important structures.

    Image Registration: In medical imaging or remote sensing, graph theory can help align images taken at different times or from different sensors by modelling the transformation as a graph optimization problem.

    Texture Analysis: Representing textures as graphs allows for texture classification and discrimination based on the statistical properties of the graph structure.

    Morphological Operations: Graph-based morphological operations can be used for tasks like erosion, dilation and closing in images.

    Conclusion: Graph theory provides a versatile framework for modelling and analyzing the structure and relationships within images. It’s often used in conjunction with other image-processing techniques to extract meaningful information and features from images for various applications, including computer vision and image analysis.