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Related Concept Videos

Calibration Curves: Correlation Coefficient01:10

Calibration Curves: Correlation Coefficient

In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the direction of association between two variables. The correlation coefficient value ranges from −1 to +1. A value of +1 indicates a perfect positive linear correlation, −1 denotes a perfect negative correlation, and 0 implies no correlation between the two variables. A positive correlation value establishes that as one variable increases, the other increases, and...
Correlation and Regression00:53

Correlation and Regression

In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a negative...
Coefficient of Correlation01:12

Coefficient of Correlation

The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is.
What the VALUE of r tells us:
The value of r is always between –1 and +1: –1 ≤ r ≤ 1.
The size of the correlation r indicates the strength of the linear...
Correlations02:20

Correlations

Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between...
Correlation01:09

Correlation

In statistics, two variables are said to be correlated if the values of one variable are associated with the other variable. Depending on the relationship between two variables, correlation can be of three types– positive correlation, negative correlation, and zero correlation.
Two variables, for example, a and b, are said to be positively correlated if both variables move in the same direction. In other words, a positive correlation exists between two variables, a and b, if:
Calculating and Interpreting the Linear Correlation Coefficient01:11

Calculating and Interpreting the Linear Correlation Coefficient

The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable, x, and the dependent variable, y. Hence, it is also known as the Pearson product-moment correlation coefficient. It can be calculated using the following equation:

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Performance measures for correlation filters.

B V Kumar, L Hassebrook

    Applied Optics
    |June 23, 2010
    PubMed
    Summary
    This summary is machine-generated.

    Fractional power filters (FPFs) offer a framework for comparing correlation filter designs. The phase-only filter (POF) demonstrates a balance between noise tolerance and sharp peaks, optimizing performance.

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    Area of Science:

    • Optical Engineering
    • Signal Processing
    • Image Analysis

    Background:

    • Evaluating correlation filter designs requires standardized performance metrics.
    • Existing filters like matched, phase-only, and inverse filters have distinct characteristics.
    • Understanding trade-offs between criteria such as signal-to-noise ratio and peak sharpness is crucial.

    Purpose of the Study:

    • To introduce a comprehensive set of performance criteria for comparing correlation filters.
    • To introduce and analyze a new family of filters: fractional power filters (FPFs).
    • To illustrate the trade-offs between various performance criteria using FPFs.

    Main Methods:

    • Defined key performance metrics: signal-to-noise ratio, peak sharpness, peak location, light efficiency, discriminability, and distortion invariance.
    • Introduced fractional power filters (FPFs) as a generalized filter family.
    • Analyzed classical filters (matched, phase-only, inverse) as special cases of FPFs.

    Main Results:

    • Demonstrated trade-offs between different performance criteria using FPFs.
    • Showcased that the phase-only filter (POF) is a special case of FPFs.
    • Empirical examples indicate the POF offers a favorable balance between noise tolerance and peak sharpness.

    Conclusions:

    • FPFs provide a unified approach to understanding and comparing correlation filter performance.
    • The phase-only filter (POF) emerges as a practical choice for applications requiring good noise tolerance and sharp correlation peaks.
    • Further research into FPFs can lead to optimized filter designs for specific applications.