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Building kernels from binary strings for image matching.

Francesca Odone¹, Annalisa Barla, Alessandro Verri

¹Istituto Nazionale di Fisica della Materia and with DISI, Universita di Genova, 1-16146 Genova, Italy. odone@disi.unige.it

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

|February 11, 2005

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This study explores image kernels in statistical learning, showing histogram intersection is a Mercer's kernel. It also details modifications for Hausdorff distance kernels, improving trainable systems.

Area of Science:

Machine Learning
Computer Vision
Statistical Learning

Background:

Kernels are crucial for improving performance in statistical learning by measuring similarity between data points.
Effective kernels can capture domain knowledge and enhance problem-solving capabilities.
Image data presents unique challenges for kernel design due to its high dimensionality and complex structure.

Purpose of the Study:

To investigate and develop novel kernels specifically for image data within the statistical learning framework.
To theoretically analyze the properties of image kernels derived from binary string representations and bitwise operations.
To demonstrate the Mercer's kernel property for histogram intersection and modified Hausdorff distance measures applied to images.

Main Methods:

Related Experiment Videos

Representing image information content using binary strings.
Applying bitwise manipulations (logical operators) and convolution with nonbinary stencils to image data.
Theoretically proving that histogram intersection is a Mercer's kernel.
Determining modifications to Hausdorff distance-based similarity measures to satisfy Mercer's kernel conditions.
Explicitly deriving the mapping from the input space to the feature space for the proposed kernels.

Main Results:

Demonstrated that histogram intersection, when applied to image representations, is a valid Mercer's kernel.
Identified specific modifications to Hausdorff distance measures that render them Mercer's kernels for image data.
Provided explicit mappings to feature spaces for these image kernels.
Experimental results validated the effectiveness of the proposed kernels in trainable systems.

Conclusions:

The developed image kernels, based on histogram intersection and modified Hausdorff distance, offer a robust approach for statistical learning tasks involving image data.
Explicit feature space mappings facilitate the practical application of these kernels in machine learning models.
The findings contribute to advancing kernel methods in computer vision and statistical learning, enabling more effective trainable systems.