Three-dimensional Convolution
Three-dimensional Convolution - Related Videos
01:17
Convolution Properties II
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2024
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...
01:20
Convolution Properties I
0 Views •
2024
Convolution computations can be simplified by utilizing their inherent properties. The commutative property reveals that the input and the impulse response of an LTI (Linear Time-Invariant) system can be interchanged without affecting the output: The associative property suggests that the merged convolution of three functions remains unchanged regardless of the sequence of convolution. For instance, for three functions x(t), h(t), and g(t) is written as, When two LTI systems with impulse...
01:24
Convolution: Math, Graphics, and Discrete Signals
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2024
In any LTI (Linear Time-Invariant) system, the convolution of two signals is denoted using a convolution operator, assuming all initial conditions are zero. The convolution integral can be divided into two parts: the zero-input or natural response and the zero-state or forced response, with t0 indicating the initial time. To simplify the convolution integral, it is assumed that both the input signal and impulse response are zero for negative time values. The graphical convolution process...
03:40
Dimensional Analysis
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2020
Dimensional analysis, also known as the factor label method, is a versatile approach for mathematical operations. The main principle behind this approach is: the units of quantities must be subjected to the same mathematical operations as their associated numbers. This method can be applied to computations ranging from simple unit conversions to more complex and multi-step calculations involving several different quantities and their units. Conversion Factors and Dimensional Analysis The unit...
07:31
Two-Dimensional Gel Electrophoresis
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2023
Two-dimensional gel electrophoresis (2DGE) is a technique that can resolve thousands of biomolecules from a mixture. This technique involves two distinct separation methods that have been coupled together: isoelectric focusing (IEF) and sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE). This physically separates compounds across two axes of a gel by their isoelectric points (an electrochemical property) and their molecular weights. The procedure in this video covers the main...
FAQs
Learned weights determine how strongly different voxel patterns contribute to each output value. As the kernel moves through the volume, it multiplies local voxel values by these weights and combines the results. Repeating this operation creates feature maps that emphasize informative structures, including boundaries, textures, or anatomical patterns, rather than treating every voxel relationship as equally important.
Neighboring slices provide connected spatial information that may be missed when images are considered independently. By operating across three spatial dimensions, the method can represent relationships within the volume and preserve the broader structure of an anatomical feature. This is particularly relevant when a pattern extends across multiple slices in computed tomography or magnetic resonance imaging data.
A kernel can respond to local arrangements of voxel values that correspond to boundaries, textures, or anatomical structures. Its response depends on both the values in the neighborhood and the learned weights applied to them. Consequently, the resulting feature maps provide intermediate representations that a medical imaging model can use when analyzing more complex volumetric patterns.
The process begins with a volumetric scan, such as computed tomography or magnetic resonance imaging data. A small three-dimensional kernel is moved across the spatial dimensions, and each position produces a combined value from local voxels and learned weights. Repeating this operation generates feature maps that retain information about patterns throughout the scan’s full three-dimensional structure.
Models using this technique can support several image-analysis tasks, including segmentation, lesion detection, and classification. They can also contribute to treatment planning by extracting volumetric patterns from medical scans. The specific task determines how the generated feature representations are used, while the three-dimensional analysis helps preserve relationships between neighboring slices and structures across the volume.
Treatment planning can require information about the location, boundaries, and structure of anatomy or abnormalities within a volume. Feature maps generated from three-dimensional scan data can represent these spatial patterns for downstream model tasks. By retaining relationships across neighboring slices, the approach can provide volumetric information that supports planning alongside applications such as segmentation, lesion detection, and classification.