AMAT: Medial Axis Transform for Natural Images (1703.08628v2)

Abstract: We introduce Appearance-MAT (AMAT), a generalization of the medial axis transform for natural images, that is framed as a weighted geometric set cover problem. We make the following contributions: i) we extend previous medial point detection methods for color images, by associating each medial point with a local scale; ii) inspired by the invertibility property of the binary MAT, we also associate each medial point with a local encoding that allows us to invert the AMAT, reconstructing the input image; iii) we describe a clustering scheme that takes advantage of the additional scale and appearance information to group individual points into medial branches, providing a shape decomposition of the underlying image regions. In our experiments, we show state-of-the-art performance in medial point detection on Berkeley Medial AXes (BMAX500), a new dataset of medial axes based on the BSDS500 database, and good generalization on the SK506 and WH-SYMMAX datasets. We also measure the quality of reconstructed images from BMAX500, obtained by inverting their computed AMAT. Our approach delivers significantly better reconstruction quality with respect to three baselines, using just 10% of the image pixels. Our code and annotations are available at https://github.com/tsogkas/amat .

• The paper introduces a novel extension of the classical MAT to color images by computing medial points with intrinsic scale and appearance information.
• It formulates the approach as a weighted geometric set cover problem to balance sparse representation with high-quality image reconstruction.
• The framework outperforms benchmarks with precision of 0.52, F-measure of 0.57, PSNR of 22.74 dB, and SSIM of 0.74 while using only 10% of the original pixels.

An Evaluation of Appearance-MAT for Natural Image Analysis

The paper "AMAT: Medial Axis Transform for Natural Images" introduces a novel computational framework, Appearance-MAT (AMAT), aimed at extending the concept of the Medial Axis Transform (MAT) across the domain of natural images. Developed as a weighted geometric set cover (WGSC) problem, the AMAT framework innovatively encapsulates the representation of natural image symmetries by associating medial points with both local scale and appearance information.

Key Contributions

The researchers present several critical contributions in their work:

1. Generalization of MAT: The paper extends the classical MAT, traditionally applied to binary shapes, by adapting it to color images, crucially associating each medial point with an intrinsic local scale parameter.
2. Invertibility and Reconstruction: Inspired by the invertibility of the binary MAT, AMAT provides the ability to reconstruct images from their medial axis representation by incorporating a local appearance encoding for each medial point.
3. Clustering Scheme: A novel clustering approach efficiently organizes individual medial points into coherent medial branches, facilitating a meaningful shape decomposition of the image regions involved.

Methodological Insight

The AMAT framework is elegantly formulated through a weighted geometric set cover interpretation, providing an efficient mechanism to achieve a sparse yet informative representation of natural images. This geometric interpretation inherently balances representation sparseness against reconstruction accuracy, using a scale cost parameter to favor larger medial disk selections where feasible. The algorithm circumvents traditional learning-based approaches, favoring a bottom-up, parameter-free methodology that necessitates no prior object-level assumptions.

Numerical Performance and Comparative Analysis

The authors leverage BMAX500 (a new dataset derived from BSDS500), SK506, and WH-SYMMAX datasets to experimentally validate the AMAT framework. Notable quantitative performance is documented with AMAT achieving superior results in medial point detection on BMAX500, demonstrating metrics such as a precision of 0.52 and an F-measure of 0.57. Moreover, AMAT significantly outperforms benchmarked baselines in image reconstruction tasks, highlighted by a PSNR of 22.74 dB and 0.74 SSIM, all while leveraging a sparse set of medial points representing merely 10% of the original pixels.

Practical and Theoretical Implications

Practically, AMAT's inherent compact and sparse representation holds considerable promise for applications requiring robust key point selection such as image registration, retrieval, and pose estimation. Theoretically, the introduction of the invertibility component transforms AMAT from a purely analytical tool into a functional reconstruction methodology, challenging current perceptions of image abstraction to include comprehensive decompositional capabilities without significant performance detriment.

Future Directions

The research opens pathways for further exploration, especially in enhancing the encoding functions to better capture textural elements, which, in their current simplicity, are limited. Furthermore, expanding AMAT's applicability through multi-scale hierarchical groupings and task-specific tuning of its framework presents intriguing possibilities for extending the range of image analysis tasks it can undertake effectively.

In conclusion, "AMAT: Medial Axis Transform for Natural Images" establishes a formidable basis for both academic inquiry and practical application within the scope of natural image processing. Its balance of innovation, theoretical depth, and associated empirical validation articulates a mature advance in computational imaging, positioned well for adaptive refinement and expanded utility.