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Steerable Pyramid Transform Enables Robust Left Ventricle Quantification

Xiangyang Zhu, Kede Ma, Wufeng Xue

TL;DR

This work addresses the vulnerability of deep learning–based left ventricle quantification to input perturbations in CMR. It introduces a fixed front-end steerable pyramid transform to provide orientation- and scale-aware representations aligned with LV anatomy, discarding the highpass residual to promote robust learning. The method combines SPT with a CNN-LSTM pipeline to predict eleven LV indices, with a regularized loss to encourage robust, diverse features. On Cardiac-DIG data, the approach achieves competitive accuracy while substantially improving robustness to spatial transformations, distortions, and adversarial attacks; ablation studies confirm the benefit of multi-scale/orientation sharing.

Abstract

Predicting cardiac indices has long been a focal point in the medical imaging community. While various deep learning models have demonstrated success in quantifying cardiac indices, they remain susceptible to mild input perturbations, e.g., spatial transformations, image distortions, and adversarial attacks. This vulnerability undermines confidence in using learning-based automated systems for diagnosing cardiovascular diseases. In this work, we describe a simple yet effective method to learn robust models for left ventricle (LV) quantification, encompassing cavity and myocardium areas, directional dimensions, and regional wall thicknesses. Our success hinges on employing the biologically inspired steerable pyramid transform (SPT) for fixed front-end processing, which offers three main benefits. First, the basis functions of SPT align with the anatomical structure of LV and the geometric features of the measured indices. Second, SPT facilitates weight sharing across different orientations as a form of parameter regularization and naturally captures the scale variations of LV. Third, the residual highpass subband can be conveniently discarded, promoting robust feature learning. Extensive experiments on the Cardiac-Dig benchmark show that our SPT-augmented model not only achieves reasonable prediction accuracy compared to state-of-the-art methods, but also exhibits significantly improved robustness against input perturbations.

Steerable Pyramid Transform Enables Robust Left Ventricle Quantification

TL;DR

This work addresses the vulnerability of deep learning–based left ventricle quantification to input perturbations in CMR. It introduces a fixed front-end steerable pyramid transform to provide orientation- and scale-aware representations aligned with LV anatomy, discarding the highpass residual to promote robust learning. The method combines SPT with a CNN-LSTM pipeline to predict eleven LV indices, with a regularized loss to encourage robust, diverse features. On Cardiac-DIG data, the approach achieves competitive accuracy while substantially improving robustness to spatial transformations, distortions, and adversarial attacks; ablation studies confirm the benefit of multi-scale/orientation sharing.

Abstract

Predicting cardiac indices has long been a focal point in the medical imaging community. While various deep learning models have demonstrated success in quantifying cardiac indices, they remain susceptible to mild input perturbations, e.g., spatial transformations, image distortions, and adversarial attacks. This vulnerability undermines confidence in using learning-based automated systems for diagnosing cardiovascular diseases. In this work, we describe a simple yet effective method to learn robust models for left ventricle (LV) quantification, encompassing cavity and myocardium areas, directional dimensions, and regional wall thicknesses. Our success hinges on employing the biologically inspired steerable pyramid transform (SPT) for fixed front-end processing, which offers three main benefits. First, the basis functions of SPT align with the anatomical structure of LV and the geometric features of the measured indices. Second, SPT facilitates weight sharing across different orientations as a form of parameter regularization and naturally captures the scale variations of LV. Third, the residual highpass subband can be conveniently discarded, promoting robust feature learning. Extensive experiments on the Cardiac-Dig benchmark show that our SPT-augmented model not only achieves reasonable prediction accuracy compared to state-of-the-art methods, but also exhibits significantly improved robustness against input perturbations.
Paper Structure (13 sections, 7 equations, 10 figures, 2 tables)

This paper contains 13 sections, 7 equations, 10 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Steerable Pyramid Transform
  3. Proposed Method
  4. SPT Decomposition
  5. LV Quantification
  6. Loss Function
  7. Robustness Evaluation
  8. Experiments
  9. Experimental Setup
  10. Accuracy Results
  11. Robustness Results
  12. Ablation Studies
  13. Conclusion

Figures (10)

  • Figure 1: Adopted LV quantification setting. (a) Two example sequences of CMR slices with different shapes, brightness, and contrast. (b) LV myocardium area ($A_1$) and cavity area ($A_2$). (c) Three directional dimensions of the cavity ($D_{1} \sim D_{3}$). (d) Six regional wall thicknesses ($T_{1} \sim T_{6}$).
  • Figure 2: The block diagram of SPT (including both analysis and synthesis transforms), reproduced from Simoncelli1995Thesteerable. The pyramid is recursively constructed by inserting a copy of the shaded portion of the diagram at the location of the solid circle Simoncelli1995Thesteerable.
  • Figure 3: SPT of a CMR image. Left: CMR image $\bm x$ and its residual highpass subband. Right: Subbands oriented at $30\degree$, $90\degree$, and $150\degree$ and the residual lowpass subband.
  • Figure 4: The system diagram of our SPT-augmented method for LV quantification.
  • Figure 5: Top: Regional walls of the mid-cavity LV myocardium by the $17$-segment model Cerqueira2002Standardized. Bottom: the corresponding subbands of SPT in the Fourier domain.
  • ...and 5 more figures