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Related Concept Videos

Common Leveling Mistakes and Errors01:17

Common Leveling Mistakes and Errors

A survey team is tasked with determining the elevation difference between points Point A and Point B, separated by uneven terrain. They use a leveling instrument and a leveling rod.Common MistakesMisreading the Rod: During a backsight reading at Point A, the instrumentman observes the rod partially obscured by tall grass. Instead of reading 1.135 m, they mistakenly record 1.735 m due to the misalignment of the crosshair with the wrong graduation. This error adds 0.600 m to all subsequent...
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...
Differential Leveling01:12

Differential Leveling

Differential leveling is a precise method in surveying used to determine the elevation difference between two points. Its primary goal is to establish accurate vertical measurements to create level surfaces or grade lines critical for designing and constructing infrastructures such as roads, bridges, and buildings.The procedure for differential leveling begins with setting up and leveling the instrument at a point where the benchmark can be seen. The level rod is held on the benchmark (BM), and...
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...
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Related Experiment Video

Updated: Jun 26, 2026

Enabling High Grayscale Resolution Displays and Accurate Response Time Measurements on Conventional Computers
06:50

Enabling High Grayscale Resolution Displays and Accurate Response Time Measurements on Conventional Computers

Published on: February 29, 2012

High-precision boundary length estimation by utilizing gray-level information.

Nataå A Sladoje1, Joakim Lindblad

  • 1Faculty of Engineering, University of Novi Sad, Novi Sad, Serbia. sladoje@uns.ns.ac.yu

IEEE Transactions on Pattern Analysis and Machine Intelligence
|December 27, 2008
PubMed
Summary

This study introduces a new method for accurately estimating object boundary length using pixel gray levels. The technique minimizes errors in digitized images, offering precise perimeter measurements for various shapes.

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Area of Science:

  • Image processing and computer vision.
  • Computational geometry and measurement science.

Background:

  • Accurate object boundary length estimation is crucial in image analysis.
  • Traditional methods often struggle with digitization errors and pixel quantization.

Purpose of the Study:

  • To develop a novel, accurate, and precise method for estimating object boundary length.
  • To account for gray levels at object boundaries in digitized images.
  • To minimize estimation errors in quantized pixel value scenarios.

Main Methods:

  • A novel perimeter estimation method utilizing gray level information at object boundaries.
  • Mathematical derivation of optimal estimates minimizing maximal error for quantized pixel values.
  • Implementation via pseudocode, emphasizing ease of implementation and parallelization.

Main Results:

  • Error-free perimeter measurements for straight boundaries with non-quantized pixels.
  • Optimal estimates derived for quantized pixel values, converging to correct values with increasing gray levels.
  • Successful evaluation on concave and convex shapes at varying resolutions.

Conclusions:

  • The presented method offers an accurate and precise approach to perimeter estimation.
  • The technique is robust to pixel quantization and easy to implement and parallelize.
  • Demonstrated applicability on real images, outperforming other local approaches.