binary tree predictive coding

Binary Tree Predictive Coding for Efficient Image Compression

Introduction: Image compression plays a crucial role in digital communication and storage, aiming to reduce the size of image data without compromising visual quality. One effective approach is predictive coding, where information about previously encoded pixels is used to predict the values of subsequent pixels, thus achieving compression by encoding the prediction errors rather than the original pixel values.

Binary Tree Predictive Coding: A Pyramidical Approach

Binary Tree Predictive Coding (BTPC) is a novel predictive coding scheme that employs a hierarchical structure to efficiently predict and encode image data. It utilizes a pyramid of increasingly dense meshes to organize the pixels, starting with a sparse mesh of subsampled pixels on a widely spaced square lattice. Each subsequent mesh is created by placing pixels at the centers of the squares (or diamonds) formed by the preceding mesh, effectively doubling the number of pixels with each level. This pyramid structure allows for efficient prediction by utilizing information from coarser levels to predict finer details.

Prediction and Error Coding:

The key to BTPC's efficiency lies in its non-linear adaptive interpolation for prediction. Instead of relying on simple linear interpolation, BTPC employs a more sophisticated approach that adapts to the local image characteristics. This adaptive nature significantly improves prediction accuracy, especially in regions with complex details and textures.

The difference between the predicted pixel value and the actual pixel value, known as the prediction error, is then quantized and encoded. BTPC utilizes a binary tree to efficiently represent the quantized errors. This tree structure allows for effective coding of zero values, which are prevalent in prediction errors, leading to further compression gains.

Entropy Coding:

After the binary tree encoding, the resulting codewords are subjected to entropy coding to further minimize the bitrate. Entropy coding techniques like Huffman coding or arithmetic coding exploit the statistical properties of the encoded data to represent frequently occurring symbols with shorter codewords, leading to overall compression.

Advantages of BTPC:

• High Compression Efficiency: The hierarchical structure and adaptive interpolation in BTPC lead to highly accurate predictions, resulting in low prediction errors and significant data compression.
• Adaptive Prediction: The non-linear adaptive interpolation adapts to local image characteristics, leading to better predictions and improved compression efficiency.
• Efficient Zero-Run Coding: The binary tree structure effectively handles zero values in the prediction errors, contributing to further compression gains.

Applications and Future Directions:

BTPC has the potential to be applied in various image compression applications, including:

• Image storage: BTPC can be used to reduce the storage space required for images, making it suitable for archival purposes and multimedia databases.
• Image transmission: BTPC's high compression efficiency allows for faster transmission of images over limited bandwidth networks.
• Real-time image processing: BTPC's computational efficiency makes it suitable for real-time applications like video conferencing and image editing.

Future research directions in BTPC include exploring further optimization techniques for the binary tree encoding, developing more robust adaptive interpolation algorithms, and investigating its application in multi-resolution image coding.

Conclusion:

BTPC presents a novel and promising approach to image compression, utilizing a hierarchical pyramid structure, adaptive interpolation, and efficient binary tree coding to achieve high compression efficiency. Its ability to adapt to complex image content and effectively exploit data redundancy makes it a valuable tool for various image compression applications, paving the way for future advances in the field.