Find the Peak of a Curve Defined by Points

In summary, there is no definitive way to determine the peak of a curve based on discrete values. However, it is possible to construct a smooth curve through the given points and estimate a maximum value, with the highest value being 111 in this case. Additional information, such as the context of the curve, may help in accurately determining the peak. In this specific case, the peak is estimated to be around 4.3, based on constructing a smooth curve through the given points.
  • #1
davidco2
8
0
I have a curve defined by some points.
These points represent the pixel brightness on the image sensor

For example get these values:
5 14 60 111 100 37

Where is the brightness peak? Somewhere between pixel 4 and 5... ~4,3

Is there a method to determine this? Something with a name or do you have an idea?
 
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  • #2
There is no way to "determine" from, discrete values, where a curve might peak. Certainly, It would be possible to construct a smooth curve through those points which would have a maximum value of 111. Since there is no reason, here, to think there are values larger than 111, that would seem most reasonable to me. But it would be just as possible to construct a smooth function giving those values that would have a "peak" of any number you wished to give between, say, 5 and 14. Do you have any information in addition to what is given there?
 
  • #3
This is a cross-section of the laser line and if the center of the line is on 4.3 (numerating above pixels as 1-6) the peak would be over 111
If I draw a graph in Excel using these values and set curve to smooth, the peak is drawn somewhere around 4.3
 

1. What is the purpose of finding the peak of a curve defined by points?

The purpose of finding the peak of a curve defined by points is to determine the highest point or maximum value of a set of data points. This can be useful in various fields such as statistics, economics, and engineering, where identifying the peak value can provide important insights and aid in decision-making.

2. How do you find the peak of a curve defined by points?

To find the peak of a curve defined by points, you can use various methods such as graphical analysis, numerical methods, or curve fitting techniques. Graphical analysis involves plotting the points on a graph and visually identifying the highest point. Numerical methods use mathematical algorithms to calculate the peak value. Curve fitting techniques involve finding a curve that best fits the data points and determining the peak value from the resulting equation.

3. Can the peak of a curve defined by points be affected by outliers?

Yes, outliers can greatly affect the peak of a curve defined by points. Outliers are data points that are significantly different from the rest of the data, and they can skew the results and affect the overall shape of the curve. It is important to identify and handle outliers appropriately when finding the peak of a curve.

4. Is it possible to have multiple peaks in a curve defined by points?

Yes, it is possible to have multiple peaks in a curve defined by points. This can occur when the data has multiple local maximum values. In such cases, it is important to specify which peak is being considered, as the highest point may not necessarily be the most relevant or useful peak in the data set.

5. Can finding the peak of a curve defined by points be automated?

Yes, finding the peak of a curve defined by points can be automated using computer programs or algorithms. This can save time and increase accuracy, especially for large data sets. However, it is important to validate the results and ensure that the chosen method is appropriate for the specific data set.

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