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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...
Downsampling01:20

Downsampling

When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
Boundary Conditions: Lossless Lines01:21

Boundary Conditions: Lossless Lines

Consider a single-phase, two-wire, lossless transmission line terminated by an impedance at the receiving end and a source with Thevenin voltage and impedance at the sending end. The line, with length, has a surge impedance and wave velocity determined by the line's inductance and capacitance.
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...
Upsampling01:22

Upsampling

Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
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...

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Related Experiment Video

Updated: Jun 13, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

Globally optimized linear windowed tone mapping.

Qi Shan1, Jiaya Jia, Michael S Brown

  • 1Department of Computer Science and Engineering, University of Washington, Seattle, WA 98195-2350, USA. shanqi@cs.washington.edu

IEEE Transactions on Visualization and Computer Graphics
|May 15, 2010
PubMed
Summary
This summary is machine-generated.

This study presents a novel tone mapping operator for high dynamic range (HDR) images. The method uses local linear adjustments to preserve image details and structure, and can also synthesize HDR images from low dynamic range (LDR) sources.

Related Experiment Videos

Last Updated: Jun 13, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

Area of Science:

  • Computer Vision
  • Image Processing
  • Computer Graphics

Background:

  • Tone mapping is crucial for displaying High Dynamic Range (HDR) images on standard displays.
  • Existing methods often struggle with preserving local details and handling abrupt radiance changes.

Purpose of the Study:

  • Introduce a new tone mapping operator for HDR images.
  • Preserve image structures and details, even in challenging HDR content.
  • Enable the synthesis of HDR images from Low Dynamic Range (LDR) images.

Main Methods:

  • A novel tone mapping operator employing local linear adjustments on overlapping image windows.
  • Global optimization framework satisfying local constraints defined by a guidance map.
  • Guidance map suppresses local contrast while preserving details.

Main Results:

  • Effective preservation of image structures in HDR images with abrupt or smooth transitions.
  • Successful suppression of local high contrast while maintaining fine details.
  • Demonstrated capability to synthesize HDR images from LDR inputs.

Conclusions:

  • The proposed tone mapping operator effectively handles challenging HDR content.
  • The method offers a robust approach for detail preservation and contrast enhancement.
  • The operator provides a dual benefit of tone mapping and HDR image synthesis.