Convolutional Feature Noise Reduction for 2D Cardiac MR Image Segmentation

TL;DR

The paper addresses noise contamination in convolutional features used for 2D cardiac MR image segmentation by introducing the Convolutional Feature Filter (CFF), a lightweight, trainable 1×1 convolution with sigmoid gating that acts as a low-amplitude pass filter to suppress noise in feature-signal matrices. It couples this filtering with an entropy-based framework (global cross-entropy and local information entropy) to quantify improvements in information content, evaluating across single-domain cardiac datasets (ACDC, M&Ms) and a non-medical VOCH dataset. Empirical results show that CFFs reduce feature-noise (lower ΔH), improve Dice scores, and decrease Hausdorff distances, including better generalization to unseen domains in multi-domain settings and even in non-medical data, while maintaining modest parameter increases. The work argues for a unified, entropy-guided view of feature fusion and suggests CFFs as a generally applicable, low-overhead tool for improving segmentation performance by stabilizing the entire feature system. Limitations include validation across more diverse distributions and tasks, with future work aimed at broader applicability and standardizing entropy-based metrics for feature analysis.

Abstract

Noise reduction constitutes a crucial operation within Digital Signal Processing. Regrettably, it frequently remains neglected when dealing with the processing of convolutional features in segmentation networks. This oversight could trigger the butterfly effect, impairing the subsequent outcomes within the entire feature system. To complete this void, we consider convolutional features following Gaussian distributions as feature signal matrices and then present a simple and effective feature filter in this study. The proposed filter is fundamentally a low-amplitude pass filter primarily aimed at minimizing noise in feature signal inputs and is named Convolutional Feature Filter (CFF). We conducted experiments on two established 2D segmentation networks and two public cardiac MR image datasets to validate the effectiveness of the CFF, and the experimental findings demonstrated a decrease in noise within the feature signal matrices. To enable a numerical observation and analysis of this reduction, we developed a binarization equation to calculate the information entropy of feature signals.

Figures (10)

• Figure 1: An illustration for feature signal matrices, where $f$, $d$, H, W, and C correspond to a feature signal matrix, a filtered feature signal matrix, Height, Width, and Channel, respectively. The first row elucidates the rationale behind treating a 3D signal matrix as a 2D channel-based signal matrix, while the second row demonstrates the filtering process for a single-pixel signal and one signal matrix.
• Figure 2: Several examples of convolution feature signals with different channel numbers, where the x- and y-axes denote the channel number and amplitude, respectively. These feature signals are selected from the center of feature signal matrices when inputting a random CMRI to $Ne{u_u}$ for the single-domain cardiac segmentation task. The steel-blue dashed lines represent the original feature signals containing the high-peak noise. The orange-red lines depict the filtering results of those steel-blue lines, where the noise has been reduced.
• Figure 3: Comparing validation results (validation loss) of global entropy across different segmentation tasks. Semi-translucent and opaque lines represent all results and their averages, respectively. The opaque lines with different colors indicate the different network results, whereas the opaque lines with the same color but dashed and full denote the results of the original network and this network after appending CFFs. (a) Single-domain Cardiac segmentation. (b) Object segmentation.
• Figure 4: Comparing the average information entropy on VaC across different networks. The steel-blue and orange-red lines represent $HF$ and $HD$, respectively. The x- and y-axes represent the number of elements within an information entropy set and the corresponding information entropy values, respectively. (a) Results of $Ne{u_f}$. (b) Results of $Ne{u_u}$.
• Figure 5: Heat maps of the information entropy variation on VaC across different networks at different times, where the blue color goes light while the information entropy decrease, and vice versa. (a) $\Delta H$ for $Ne{u_f}$ ($\Delta {H_f}$). (b) $\Delta H$ for $Ne{u_u}$ ($\Delta {H_u}$).

Theorems & Definitions (1)

• Theorem 1