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Convolution Properties II

Convolution Properties II

The important convolution properties include width, area, differentiation, and integration properties.
The width property indicates that if the durations of input signals are T1 and T2, then the width of the output response equals the sum of both durations, irrespective of the shapes of the two functions. For instance, convolving two rectangular pulses with durations of 2 seconds and 1 second results in a function with a width of 3 seconds.
The area property asserts that the area under the...

Convolution Properties I

Convolution Properties I

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Support reactions in three dimensions help maintain the stability and equilibrium of various structures and systems. These reactions prevent the system from translating and rotating, ensuring the design can withstand external forces and perform its intended function efficiently and safely. Some of the supports providing support reactions in three dimensions are discussed below:
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Relative Velocity in One Dimension

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The understanding of the concept of reference frames is essential to discuss relative motion in one or more dimensions. When we say that an object has a certain velocity, we must state the velocity with respect to a given reference frame. In most examples, this reference frame has been Earth. For instance, if a statement reads that a person is sitting in a train moving at 10 m/s east, then it implies that the person on the train is moving relative to the surface of Earth at this velocity,...

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Relative velocity is the velocity of an object as observed from a particular reference frame, or the velocity of one reference frame with respect to another reference frame. The concept of relative velocity can be used to describe motion in two dimensions. Consider a particle P and two reference frames S and S′. The position of the origin of S′ as measured in S is , the position of P as measured in S′ is , and the position of P as measured in S is , which can be evaluated by utilizing...

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Significant Dimension Reduction of 3D Brain MRI using 3D Convolutional Autoencoders.

Hayato Arai, Yusuke Chayama, Hitoshi Iyatomi

Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual International Conference

|November 17, 2018

Summary

This study introduces a new method using 3D convolutional autoencoders (3D-CAE) to reduce the dimensions of brain MRI data. This technique effectively compresses voxel information for content-based image retrieval (CBIR) in clinical neuroradiology.

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Area of Science:

Medical Imaging
Artificial Intelligence
Radiology

Background:

Content-based image retrieval (CBIR) is valuable for image database searching but faces challenges in clinical neuroradiology.
High-dimensional voxel data in 3D brain MRI overwhelms current CBIR methods, hindering clinical application.
Effective dimension reduction is critical for successful CBIR in medical imaging.

Purpose of the Study:

To develop and evaluate a novel dimension reduction technique for 3D brain MRI data.
To enable the application of CBIR in clinical neuroradiology by overcoming data complexity.
To preserve clinically relevant features during data compression.

Main Methods:

A novel dimension compression method utilizing 3D convolutional autoencoders (3D-CAE) was proposed.
The 3D-CAE method was applied to the Alzheimer's Disease Neuroimaging Initiative 2 (ADNI2) 3D brain MRI dataset.
The technique compressed approximately 5 million voxel data points into 150 dimensions.

Main Results:

The proposed 3D-CAE method successfully compressed high-dimensional 3D brain MRI data.
Clinically relevant neuroradiological features were preserved after dimension reduction.
The root-mean-square error (RMSE) per voxel was reduced to 8.4%.

Conclusions:

The 3D-CAE method offers effective dimension reduction for 3D brain MRI data.
This approach shows promise for enabling content-based image retrieval in clinical neuroradiology.
Preserving key features while compressing data is feasible for medical imaging applications.