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Related Concept Videos

Uncertainty in Measurement: Reading Instruments02:46

Uncertainty in Measurement: Reading Instruments

Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such measurements result in exact numbers. By counting the eggs in a carton, for instance, one can determine exactly how many eggs are there in the carton. Similarly, the numbers of defined quantities are also exact. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Quantities...
Variability: Analysis01:11

Variability: Analysis

Measures of variability are statistical metrics that reveal the dispersion pattern within a dataset. They are pivotal in biostatistics, providing insights into the heterogeneity within health and biological data. Variability signifies the degree to which data points diverge from one another, helping researchers understand the potential range of values and associated uncertainty within the data.
The range is a simple measure of variability, indicating the difference between the highest and...
Variance01:15

Variance

The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.The standard deviation measures the spread in the same units as the data.
Coefficient of Variation01:10

Coefficient of Variation

The coefficient of variation measures the dispersion of the data points or distribution around the mean. Using the coefficient of variation, we can compare two data series with drastically different means or different units of measurement. The coefficient of variation for a sample and a population is expressed as a percentage of the ratio of standard deviation to the mean.
The coefficient of variation is a practical statistical tool in finance. It allows investors to assess the volatility or...
Imaging Biological Samples with Optical Microscopy01:18

Imaging Biological Samples with Optical Microscopy

Optical microscopy uses optic principles to provide detailed images of samples. Antonie van Leeuwenhoek designed the first compound optical microscope in the 17th century to visualize blood cells, bacteria, and yeast cells. In 1830, Joseph Jackson Lister created an essentially modern light microscope. The 20th century saw the development of microscopes with enhanced magnification and resolution.
In optical microscopy, the specimen to be viewed is placed on a glass slide and clipped on the stage...
What is Variation?01:14

What is Variation?

Apart from the measures of central tendency, distribution, outliers, and the changing characteristics of data with time, an important characteristic of any data set is its variation or spread. In some data sets, the data values are concentrated closely near the mean; in others, the data values are more widely spread out from the mean.
The range, standard deviation, standard error, and variance are the different measures of variation.
Range: The range is the difference between its maximum and...

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Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating
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Published on: October 11, 2016

Variance measurements by a coherent optical method, with application to image processing.

E Garcia, H Stark, R C Barker

    Applied Optics
    |February 2, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a novel procedure for measuring local variance in spatial random scenes, crucial for accurate image analysis. The method enhances automatic image processing through the generation of specialized spatial masks.

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    Area of Science:

    • Optics
    • Image Processing
    • Spatial Statistics

    Background:

    • Accurate measurement of local variance in spatial random scenes is essential for quantitative image analysis.
    • Understanding the relationship between optical parameters and second-order statistics is key for reliable variance estimation.
    • Existing methods may lack the precision or stability required for complex scene analysis.

    Purpose of the Study:

    • To develop and validate a procedure for measuring point-to-point local variance in spatial random scenes.
    • To establish the necessary relations between second-order statistics and optical configuration parameters for accurate variance estimation.
    • To create a modified procedure for generating spatial masks for automatic image processing applications.

    Main Methods:

    • Developing a procedure to measure local variance in spatial random scenes.
    • Establishing theoretical relations between second-order statistics of random processes and optical configuration parameters.
    • Experimental verification using calibrated random checkerboard and overlapping circular grain models.
    • Modifying the procedure to generate spatial masks for image segmentation.

    Main Results:

    • The proposed procedure provides accurate and stable estimates of local variance.
    • Experimental validation confirmed the effectiveness of the procedure with known random models.
    • A modified procedure successfully generated spatial masks for object isolation in image processing.
    • Demonstrated the utility of synthesized masks as binary spatial gates for selective object detection.

    Conclusions:

    • The developed procedure offers a robust method for quantifying local variance in spatial random scenes.
    • The established relations enable precise control over optical parameters for improved variance estimation.
    • The generated spatial masks significantly enhance automatic image processing capabilities by enabling targeted object selection.