# Pattern recognition using splines

• Charles49
In summary, the conversation discusses a difficult problem of filling in broken curves in an image. The person is looking for a program or method to connect these curves with splines, but it is noted that there are no known methods that work on all types of images without some tweaking and trial and error. The problem is considered "ill posed" and requires specific conditions to define a correct solution. Some helpful keywords for searching for solutions include "computer vision curve completion" and "computer vision occlusion". A recommended paper for reference is "A Tangent Bundle Theory for Visual Curve Completion" by Guy Ben-Yosef and Ohad Ben-Shahar.
Charles49
I am supposed to have an image consisting of overlapping curves. What I have is an image where the curves are missing certain segments of them. However with the human eye we can tell that certain segments are part of the same curve. (see attached figures). I want to know how I can write a program to connect curves with splines that visually we know are related.

In other words if I have a bunch of segments, how do I connect them with splines so that I get what my human eye is telling me is the correct match.

This is a difficult problem so any reference would also be very helpful.

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Do you have a single image? Or a set of images drawn in a similar manner - say by the same person or process? Or are you looking for a method that works on all sorts of images?

There are no known methods that work on all sorts of images without your having to fiddle with adjusting them to the particular images you have.

Known methods that work on set of similar images would require some sort of tweaking and trial and error. For example, you might have to create a "training set" of images that gave the image and the correct fill-in. Then you'd need an algorithm to fit the method's parameters to the training set.

Fillling-in a curve from broken segments is, in the jargon of mathematics, an "ill posed problem". The statement of the problem does not define how to judge whether a given answer is correct or incorrect. Whether a method works or not depends on the opinion of the person evaluating it and people's opinions can vary depending on their artistic taste or what they want to accomplish once the curves are filled-in ( like detect what part of the image is a picture of a dog etc.).

I'm ducking specifics for now. I think it will be easy to find many papers on the web that show methods of filling-in broken curves. They will work on the set of images they werel developed for and they may or may not work on your images. Since this is the math section of the forum, the first thing to get straight is that you don't have a well posed problem. That's no reason to despair. For example, the simplest statement of the problem of reconstructing anatomy from MRI data is an ill-posed problem, but people develop useful images by adding conditions to the problem that are precise enough to define what a correct solution is.

Hi Stephen,

I have a single image. It is computer generated from a series of images. Since my background is not in computer science, could you please give me a few keywords that I can google to make my search for possible answers more effective? I am looking up training set now.

Charles

Charles49 said:
e a few keywords that I can google to make my search for possible answers more effective?

computer vision curve completion

For the more general problem of missing or blocked pieces of an image:

computer vision occlusion

For a little known top-down down approach to image recognition by the researcher Mike Alter:

computer vision Upwrite

You could also use "image recognition" instead of "computer vision".

Thank you very much.

Here is a good paper: A Tangent Bundle Theory for Visual Curve Completion

by guy ben-yosef and Ohad ben shahar

## 1. What is pattern recognition using splines?

Pattern recognition using splines is a mathematical technique that involves fitting smooth curves or surfaces through a set of data points. It is used to identify patterns and relationships in data, and is often used in fields such as computer vision, machine learning, and signal processing.

## 2. How does spline interpolation work?

Spline interpolation involves constructing a smooth curve or surface by connecting a series of polynomial functions called splines. These splines are fit to the data points in a way that minimizes the overall error, resulting in a more accurate representation of the data compared to other interpolation methods.

## 3. What are the advantages of using splines for pattern recognition?

One advantage of using splines for pattern recognition is their ability to handle noisy or incomplete data. They can also capture complex patterns and relationships in the data that may be missed by other methods. Additionally, splines offer a more flexible and customizable approach compared to traditional statistical methods.

## 4. What are some common applications of pattern recognition using splines?

Pattern recognition using splines has a wide range of applications, including image and speech recognition, medical diagnosis, financial modeling, and data analysis. It is also commonly used in fields such as computer graphics, robotics, and geology.

## 5. Are there any limitations of using splines for pattern recognition?

While splines are a powerful tool for pattern recognition, they do have some limitations. They may struggle with very large datasets, as the computational cost can become significant. Additionally, the accuracy of the results may be affected by the choice of spline type and the number of data points used.

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