问题
Following up with this, I have a bunch of coordinates and I draw them on a bitmap image as a coordinate system. Now, I would like to get rid of all the noise, and filter coordinates to give a "clearer" or "cleaner" path and "less" or "better" data to work on. To explain more, I will need to expose my awesome painting skills as follows:
Current:
Desired:
Notice:
I will need to delete coordinates
I might need to add coordinates
I might need to ignore shortest neighbor in some cases
The only thing I can think of, is to use a shortest path algorithm such as A* and Dijkstra. And populate data in some sort of data structure to contain neighbors and costs for every node and then to execute the algorithm. I don't want to start something that might be wrong or waste. I would love to see a pseudo code if possible on how could I solve such a problem?
P.S I am currently on Wpf C# but I am open to use C# or C++ for any task. Thanks
回答1:
What you're after is a path finding application. There are several ways to approach this, but one of the simpler ways is to:
Pick a starting point, add to list
While True:
For each border_pt bordering last point on list:
Count number of points bordering border_pt
If count > best_count:
Mark border_pt as best
if border_pt is empty:
break
Add border_pt to list
Here's some C# code that does just that, it generates a simple list based on your cloud:
using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Drawing;
using System.Linq;
using System.Threading.Tasks;
using System.Windows.Forms;
namespace WindowsFormsApplication1
{
class ExampleProgram : Form
{
const int GridWidth = 24;
const int GridHeight = 15;
List<Point> m_points = new List<Point>();
List<Point> m_trail = new List<Point>();
[STAThread]
static void Main()
{
Application.EnableVisualStyles();
Application.SetCompatibleTextRenderingDefault(false);
Application.Run(new ExampleProgram());
}
ExampleProgram()
{
// Simple little tool to add a bunch of points
AddPoints(
0, 4, 1, 3, 1, 4, 1, 5, 2, 4, 2, 5, 2, 6, 3, 4, 3, 5, 4, 5, 4, 6, 5, 5, 6, 5,
6, 4, 5, 4, 7, 4, 7, 3, 8, 3, 8, 4, 8, 5, 8, 6, 9, 6, 9, 5, 9, 4, 9, 3, 10, 2,
10, 3, 10, 4, 10, 5, 10, 6, 11, 5, 11, 4, 11, 3, 11, 2, 12, 4, 12, 5, 13, 5,
13, 6, 13, 8, 14, 8, 14, 7, 14, 6, 15, 7, 15, 8, 15, 9, 14, 9, 14, 10, 13, 10,
12, 10, 11, 10, 13, 11, 14, 11, 15, 11, 15, 12, 16, 12, 17, 12, 18, 12, 19,
12, 18, 11, 17, 11, 17, 10, 18, 10, 19, 10, 19, 9, 19, 8, 20, 8, 21, 8, 18,
7, 19, 7, 20, 7, 21, 7, 21, 6, 22, 6, 23, 6, 21, 5, 20, 5, 19, 5, 19, 4, 18,
4, 17, 4, 20, 3, 21, 3, 22, 3, 20, 2, 19, 2, 18, 2, 19, 1, 20, 1, 21, 1, 19,
0, 18, 0, 10, 0, 4, 1);
// Very basic form logic
ClientSize = new System.Drawing.Size(GridWidth * 20, GridHeight * 20);
DoubleBuffered = true;
Paint += ExampleProgram_Paint;
// Add a new point to the form (commented out)
// MouseUp += ExampleProgram_MouseUp_AddPoint;
// Draw the trail we find
MouseUp += ExampleProgram_MouseUp_AddTrail;
// Pick a starting point to start finding the trail from
// TODO: Left as an excersize for the reader to decide how to pick
// the starting point programatically
m_trail.Add(new Point(0, 4));
}
IEnumerable<Point> Border(Point pt)
{
// Return all points that border a give point
if (pt.X > 0)
{
if (pt.Y > 0)
{
yield return new Point(pt.X - 1, pt.Y - 1);
}
yield return new Point(pt.X - 1, pt.Y);
if (pt.Y < GridHeight - 1)
{
yield return new Point(pt.X - 1, pt.Y + 1);
}
}
if (pt.Y > 0)
{
yield return new Point(pt.X, pt.Y - 1);
}
if (pt.Y < GridHeight - 1)
{
yield return new Point(pt.X, pt.Y + 1);
}
if (pt.X < GridWidth - 1)
{
if (pt.Y > 0)
{
yield return new Point(pt.X + 1, pt.Y - 1);
}
yield return new Point(pt.X + 1, pt.Y);
if (pt.Y < GridHeight - 1)
{
yield return new Point(pt.X + 1, pt.Y + 1);
}
}
}
void AddPoints(params int[] points)
{
// Helper to add a bunch of points to our list of points
for (int i = 0; i < points.Length; i += 2)
{
m_points.Add(new Point(points[i], points[i + 1]));
}
}
void ExampleProgram_MouseUp_AddTrail(object sender, MouseEventArgs e)
{
// Calculate the trail
while (true)
{
// Find the best point for the next point
int bestCount = 0;
Point best = new Point();
// At the current end point, test all the points around it
foreach (var pt in Border(m_trail[m_trail.Count - 1]))
{
// And for each point, see how many points this point borders
int count = 0;
if (m_points.Contains(pt) && !m_trail.Contains(pt))
{
foreach (var test in Border(pt))
{
if (m_points.Contains(test))
{
if (m_trail.Contains(test))
{
// This is a point both in the original cloud, and the current
// trail, so give it a negative weight
count--;
}
else
{
// We haven't visited this point, so give it a positive weight
count++;
}
}
}
}
if (count > bestCount)
{
// This point looks better than anything we've found, so
// it's the best one so far
bestCount = count;
best = pt;
}
}
if (bestCount <= 0)
{
// We either didn't find anything, or what we did find was bad, so
// break out of the loop, we're done
break;
}
m_trail.Add(best);
}
Invalidate();
}
void ExampleProgram_MouseUp_AddPoint(object sender, MouseEventArgs e)
{
// Just add the point, and dump it out
int x = (int)Math.Round((((double)e.X) - 10.0) / 20.0, 0);
int y = (int)Math.Round((((double)e.Y) - 10.0) / 20.0, 0);
m_points.Add(new Point(x, y));
Debug.WriteLine("m_points.Add(new Point(" + x + ", " + y + "));");
Invalidate();
}
void ExampleProgram_Paint(object sender, PaintEventArgs e)
{
// Simple drawing, just draw a grid, and the points
e.Graphics.Clear(Color.White);
for (int x = 0; x < GridWidth; x++)
{
e.Graphics.DrawLine(Pens.Black, x * 20 + 10, 0, x * 20 + 10, ClientSize.Height);
}
for (int y = 0; y < GridHeight; y++)
{
e.Graphics.DrawLine(Pens.Black, 0, y * 20 + 10, ClientSize.Width, y * 20 + 10);
}
foreach (var pt in m_points)
{
e.Graphics.FillEllipse(Brushes.Black, (pt.X * 20 + 10) - 5, (pt.Y * 20 + 10) - 5, 10, 10);
}
foreach (var pt in m_trail)
{
e.Graphics.FillEllipse(Brushes.Red, (pt.X * 20 + 10) - 6, (pt.Y * 20 + 10) - 6, 12, 12);
}
}
}
}
回答2:
You are looking for an operation called thinning or skeletonization, possibly followed by some post-processing to remove small components. There are different algorithms for this that offer different properties. For example Guo and Hall's and Zhang and Suen's.
回答3:
You might want to consider treating your coordinates as a binary image and apply some Morphological techniques to the image.
Thinning might give you good results, but processing like this can be tricky to get working well in a wide range of cases.
来源：https://stackoverflow.com/questions/38513619/how-can-i-get-thinner-graph-for-my-coordinate-system