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Related Concept Videos

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Linear Approximations01:23

Linear Approximations

For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...
Linearization and Approximation01:26

Linearization and Approximation

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
Parallel-axis Theorem01:06

Parallel-axis Theorem

The parallel-axis theorem provides a convenient and quick method of finding the moment of inertia of an object about an axis parallel to the axis passing through its center of mass. Consider a thin rod as an example. There is a striking similarity between the process of finding the moment of inertia of a thin rod about an axis through its middle, where the center of mass lies, and about an axis through its end using the conventional method. In the conventional method, the concept of linear mass...
Application of Linearization and Approximation01:29

Application of Linearization and Approximation

A drone flying through complex terrain often relies on more than one sensing method to estimate small changes in altitude. Along with direct measurements, air pressure provides a useful indirect indicator of vertical movement. Atmospheric pressure decreases as altitude increases, and this relationship is commonly described using an exponential model. Although accurate, converting pressure measurements into altitude values requires calculations that are too complex to perform repeatedly during...

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Updated: Jun 21, 2026

Harmonic Nanoparticles for Regenerative Research
09:23

Harmonic Nanoparticles for Regenerative Research

Published on: May 1, 2014

Exploiting inherent parallelisms for accelerating linear Hough transform.

S Suchitra Sathyanarayana1, R K Satzoda, T Srikanthan

  • 1Center for High Performance Embedded Systems, Nanyang Technological University, Singapore.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|July 10, 2009
PubMed
Summary
This summary is machine-generated.

The Additive Hough transform (AHT) accelerates image processing by dividing images into grids, achieving a 1000x speedup. This parallel computation method significantly reduces processing time and area utilization for real-time applications.

Related Experiment Videos

Last Updated: Jun 21, 2026

Harmonic Nanoparticles for Regenerative Research
09:23

Harmonic Nanoparticles for Regenerative Research

Published on: May 1, 2014

Area of Science:

  • Computer Engineering
  • Image Processing
  • Hardware Acceleration

Background:

  • Real-time image processing relies on efficient Hough transform (HT) architectures.
  • Existing linear HT methods process edge maps serially, leading to high computation times (O(m^2) cycles).

Purpose of the Study:

  • To introduce a novel parallel computation method, the Additive Hough transform (AHT), for accelerating HT.
  • To propose an efficient hardware implementation of AHT using look-up tables (LUTs) and adder arrays.
  • To analyze the performance and area-time trade-offs of the proposed AHT architecture.

Main Methods:

  • Image division into a k x k grid for parallel processing.
  • Implementation using a condensed LUT and two-operand adder arrays per angle.
  • Incorporation of a hierarchical addition step for global accumulation.
  • Area-time trade-off analysis and performance comparison with existing architectures.

Main Results:

  • AHT reduces computation time by a factor of k^2.
  • LUT size reduction by up to 50% improves area utilization.
  • Achieved a 1000x speedup compared to existing architectures for various image sizes.
  • Demonstrated at least 43% lower area-time product compared to other reported implementations.
  • The hierarchical addition step maintains performance and area-time superiority.

Conclusions:

  • The proposed Additive Hough transform (AHT) offers significant speedup and reduced area utilization for hardware-accelerated Hough transforms.
  • AHT provides a superior area-time product and performance, making it suitable for real-time image processing.
  • The AHT method is effective for both square and rectangular images.