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Equivariant Filters for Efficient Tracking in 3D Imaging.

Daniel Moyer¹, Esra Abaci Turk², P Ellen Grant²

¹CSAIL, Massachusetts Institute of Technology, Cambridge, MA, USA.

Medical Image Computing and Computer-Assisted Intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention

|June 22, 2026

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We developed a novel 3D object tracking method using equivariant filters for efficient and accurate real-time tracking. This approach preserves spatial transformations, outperforming previous convolutional methods in medical imaging applications.

Area of Science:

Medical image analysis
Computer vision
Neuroimaging

Background:

Traditional 3D object tracking methods often rely on flattening convolutional features or using fully connected layers, which can be computationally expensive and may lose spatial information.
Existing approaches struggle to maintain the integrity of transformations (e.g., rotations, translations) between input and output data.

Purpose of the Study:

To introduce a novel object tracking method for 3D images with fixed computational cost and state-of-the-art performance.
To develop an architecture that preserves spatial transformations using equivariant filters, suitable for low-latency applications like real-time tracking.

Main Methods:

Proposed an architecture that utilizes equivariant filters, avoiding feature flattening and fully connected layers.

Keywords:

Equivariant Convolution Fetal MRI Tracking

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Preserves transformations between inputs and outputs, allowing rotations/translations of inputs to directly affect outputs.

Derives transformation parameters in closed form from filter outputs.

Main Results:

Achieved state-of-the-art performance in 3D object tracking with a fixed computational cost.
Demonstrated the model's efficacy on synthetically augmented adult brain MRI data.
Validated the method on fetal brain MRI, the primary intended application.

Conclusions:

The proposed equivariant filter-based method offers an efficient and high-performance solution for 3D object tracking.
The architecture's ability to preserve transformations makes it ideal for real-time applications, particularly in medical imaging.
This technique shows significant promise for applications like fetal brain MRI analysis.