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Self-similar random field models in discrete space.

Seungsin Lee¹, Raghuveer M Rao

¹Department of Electrical Engineering, Kate Gleason College of Engineering, Rochester Institute of Technology, Rochester, NY 14623-5603, USA. seungsin.lee@samsung.com

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society

|January 27, 2006

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This study introduces a more general definition for statistical self-similarity in random fields, enhancing image processing capabilities. The new framework allows for the synthesis of a broader range of discrete-space self-similar random fields and textures.

Area of Science:

Image Processing
Computer Vision
Statistical Modeling

Background:

Self-similar random fields are crucial for modeling natural patterns and textures in image processing.
Existing definitions of self-similarity in continuous 2-D space are restrictive, often extending 1-D definitions.
Current discrete-space methods lack a proper scaling framework, relying on ad hoc approaches.

Purpose of the Study:

To propose a more general and less restrictive definition of statistical self-similarity for continuous 2-D random fields.
To develop a novel formalism for discrete-space statistical self-similarity.
To enable the synthesis of a wider variety of discrete-space self-similar random fields and textures.

Main Methods:

Developed an alternative, more general definition for statistical self-similarity in continuous 2-D space.

Related Experiment Videos

Introduced a new scaling operator specifically designed for discrete images.

Formulated a new framework for discrete-space statistical self-similarity.

Main Results:

The proposed definition overcomes the limitations of current continuous-space approaches.
The new scaling operator provides a robust method for analyzing discrete images.
The developed framework facilitates the synthesis of a broader class of self-similar random fields and textures.

Conclusions:

The generalized definition and discrete-space formalism offer significant advancements in modeling and synthesizing self-similar textures.
This work provides a more comprehensive understanding and practical tool for researchers in image processing and computer vision.
The new methods expand the possibilities for generating realistic and diverse texture images.