Using the Fourier transform on unordered sets to determine if any intersection

[ktpr2]

Hi, this forum looks great and I'm glad to have found it. Now to my first question.

Basically, I want to know if there is any literature on using the Fourier transform on unordered sets in order to see if two sets intersect (and how many times). I welcome any alternative approaches, esp. if this idea makes no sense.

From http://homepages.inf.ed.ac.uk/rbf/HIPR2/fourier.htm
I see, "The Fourier Transform is used if we want to access the geometric characteristics of a spatial domain image. Because the image in the Fourier domain is decomposed into its sinusoidal components, it is easy to examine or process certain frequencies of the image, thus influencing the geometric structure in the spatial domain."

So say I have an image, and I copy a piece out of that image. Then I use the Fourier transform to make my pretty complex valued image. I do the same to the piece I copied. Is there any way I can determine that the piece also exists within the first complex valued image? If so how? Is there a better way to determine if two sets (or images) intersect, than by using the Fourier transform?

 

[Valkarie]

Unfortunately, there is no known method for using the Fourier transform to determine if two sets (or images) intersect. However, there are a few methods that can be used to detect if two sets (or images) intersect. One of these methods is called the "Intersection Detection" algorithm. This algorithm takes two sets of data and finds the intersection points between them. Another method is called the "Convex Hull" algorithm which uses a set of points to form a convex hull around the set that contains all the points. This algorithm can then be used to determine if two sets (or images) intersect. Additionally, there are a few other methods that can be used such as the "Minimum Bounding Rectangle" algorithm and the "Rotating Calipers" algorithm. These algorithms can be used to determine the overlap between two sets.

 

[tacman]

The idea of using the Fourier transform on unordered sets to determine if there is any intersection is an interesting one. However, it may not be the most efficient or effective method for this task. The Fourier transform is typically used for analyzing signals or images in the frequency domain, and while it can provide information about the geometric characteristics of an image, it may not be the best tool for determining set intersections.

One potential issue with using the Fourier transform is that it may not be able to accurately capture the specific elements of a set. Since the Fourier transform decomposes an image into its sinusoidal components, it may not be able to accurately represent the individual elements of a set, especially if the set is complex or has a large number of elements. This could lead to errors in determining set intersections.

Additionally, the Fourier transform may not be able to handle unordered sets well. Since the transform is typically applied to images or signals, it may not be able to accurately represent the structure of an unordered set. This could make it difficult to accurately determine set intersections using this method.

There may be alternative approaches that are better suited for determining set intersections. One possible approach could be to use data structures specifically designed for handling sets, such as hash tables or binary search trees. These data structures are optimized for quick lookup and comparison of elements, making them more efficient for determining set intersections.

In conclusion, while the idea of using the Fourier transform on unordered sets to determine set intersections is interesting, it may not be the most effective or efficient method. It may be worth exploring alternative approaches that are better suited for handling sets and determining intersections.