■ サンプル
* 以下で実装してみる
+ 補正方法 : 擬似２次元アフィン変換
+ 補間方法 : 最近傍補間（ニアレストネイバー）
* ベースは、以下の関連記事の２次元アフィン変換と変わらない
=> 変わるのは、係数の数と等式のみ。
https://blogs.yahoo.co.jp/dk521123/38069294.html
* 等式については、以下のサイトを参照
http://www.civil.kumamoto-u.ac.jp/matsu/geome.pdf
Form1.cs
using System;
using System.Collections.Generic;
using System.Drawing;
using System.Windows.Forms;
namespace SampleForm
{
public partial class Form1 : Form
{
private const int DataNumberForPseudoAffineCoefficients = 8;
private Bitmap originalBitmap = null;
public Form1()
{
InitializeComponent();
}
private void Form1_Load(object sender, EventArgs e)
{
// 画像ファイルのImageオブジェクトを作成する
this.originalBitmap = new Bitmap(@"C:\temp\20161215052204.gif");
this.pictureBox1.Image = this.originalBitmap;
}
private void button1_Click(object sender, EventArgs e)
{
var inputs = new List<PointF>()
{
new PointF(0, 0),
new PointF(this.originalBitmap.Width, this.originalBitmap.Height),
new PointF(0, this.originalBitmap.Height),
new PointF(this.originalBitmap.Width, 0),
};
var outputs = new List<PointF>()
{
new PointF(0, 0),
new PointF((float)(this.originalBitmap.Width * 1.5), (float)(this.originalBitmap.Height * 1.5)),
new PointF(0, (float)(this.originalBitmap.Height * 1.5)),
new PointF((float)(this.originalBitmap.Width * 1.5), 0),
};
var pseudoAffineCoefficients = CalculatePseudoAffineCoefficients(inputs, outputs);
if (pseudoAffineCoefficients == null)
{
MessageBox.Show("Error...", "Error", MessageBoxButtons.OK, MessageBoxIcon.Error);
return;
}
// 逆変換
var transferedBitmap = new Bitmap(this.originalBitmap.Width, this.originalBitmap.Height);
for (int x = 0; x < this.originalBitmap.Width; ++x)
{
for (int y = 0; y < this.originalBitmap.Height; ++y)
{
Point correctedPoint = GetCorrectPointByPseudoAffineTransfer(pseudoAffineCoefficients, x, y);
Color color;
if (correctedPoint.X >= 0 && correctedPoint.X < this.originalBitmap.Width &&
correctedPoint.Y >= 0 && correctedPoint.Y < this.originalBitmap.Height)
{
color = this.originalBitmap.GetPixel(correctedPoint.X, correctedPoint.Y);
}
else
{
color = Color.Black;
}
transferedBitmap.SetPixel(x, y, color);
}
}
this.pictureBox2.Image = transferedBitmap;
}
/// <summary>
/// 擬似アフィン変換係数を求める
/// </summary>
/// <param name="observedPoints">観測点</param>
/// <param name="transferedPoints">変換点</param>
/// <returns></returns>
private double[] CalculatePseudoAffineCoefficients(
List<PointF> observedPoints, List<PointF> transferedPoints)
{
if (observedPoints.Count < 4 || observedPoints.Count != transferedPoints.Count)
{
// 4点未満の際は、計算不可なので、nullを返す
return null;
}
var matrixValues = new double[DataNumberForPseudoAffineCoefficients / 2][]
{
new double[] { 0.0, 0.0, 0.0, 0.0 },
new double[] { 0.0, 0.0, 0.0, 0.0 },
new double[] { 0.0, 0.0, 0.0, 0.0 },
new double[] { 0.0, 0.0, 0.0, 0.0 }
};
var vectors = new double[DataNumberForPseudoAffineCoefficients]
{
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0
};
int index = 0;
foreach (var observedPoint in observedPoints)
{
var observedX = (double)observedPoint.X;
var observedY = (double)observedPoint.Y;
var transferedX = (double)transferedPoints[index].X;
var transferedY = (double)transferedPoints[index].Y;
var xy = observedX * observedY;
var x2 = observedX * observedX;
var y2 = observedY * observedY;
var x2y = x2 * observedY;
var xy2 = observedX * y2;
var x2y2 = x2 * y2;
matrixValues[0][0] += 1;
matrixValues[0][1] += observedX;
matrixValues[0][2] += observedY;
matrixValues[0][3] += xy;
matrixValues[1][0] += observedX;
matrixValues[1][1] += x2;
matrixValues[1][2] += xy;
matrixValues[1][3] += x2y;
matrixValues[2][0] += observedY;
matrixValues[2][1] += xy;
matrixValues[2][2] += y2;
matrixValues[2][3] += xy2;
matrixValues[3][0] += xy;
matrixValues[3][1] += x2y;
matrixValues[3][2] += xy2;
matrixValues[3][3] += x2y2;
vectors[0] += transferedX;
vectors[1] += transferedX * observedX;
vectors[2] += transferedX * observedY;
vectors[3] += transferedX * observedX * observedY;
vectors[4] += transferedY;
vectors[5] += transferedY * observedX;
vectors[6] += transferedY * observedY;
vectors[7] += transferedY * observedX * observedY;
index++;
}
// 逆行列を計算する
if (!CalculateInverseMatrix(matrixValues, out double[][] inverseMatrixValues))
{
// 逆行列算出に失敗したため、null
return null;
}
var pseudoAffineCoefficients = new double[DataNumberForPseudoAffineCoefficients];
pseudoAffineCoefficients[0] =
inverseMatrixValues[0][0] * vectors[0] +
inverseMatrixValues[0][1] * vectors[1] +
inverseMatrixValues[0][2] * vectors[2] +
inverseMatrixValues[0][3] * vectors[3];
pseudoAffineCoefficients[1] =
inverseMatrixValues[1][0] * vectors[0] +
inverseMatrixValues[1][1] * vectors[1] +
inverseMatrixValues[1][2] * vectors[2] +
inverseMatrixValues[1][3] * vectors[3];
pseudoAffineCoefficients[2] =
inverseMatrixValues[2][0] * vectors[0] +
inverseMatrixValues[2][1] * vectors[1] +
inverseMatrixValues[2][2] * vectors[2] +
inverseMatrixValues[2][3] * vectors[3];
pseudoAffineCoefficients[3] =
inverseMatrixValues[3][0] * vectors[0] +
inverseMatrixValues[3][1] * vectors[1] +
inverseMatrixValues[3][2] * vectors[2] +
inverseMatrixValues[3][3] * vectors[3];
pseudoAffineCoefficients[4] =
inverseMatrixValues[0][0] * vectors[4] +
inverseMatrixValues[0][1] * vectors[5] +
inverseMatrixValues[0][2] * vectors[6] +
inverseMatrixValues[0][3] * vectors[7];
pseudoAffineCoefficients[5] =
inverseMatrixValues[1][0] * vectors[4] +
inverseMatrixValues[1][1] * vectors[5] +
inverseMatrixValues[1][2] * vectors[6] +
inverseMatrixValues[1][3] * vectors[7];
pseudoAffineCoefficients[6] =
inverseMatrixValues[2][0] * vectors[4] +
inverseMatrixValues[2][1] * vectors[5] +
inverseMatrixValues[2][2] * vectors[6] +
inverseMatrixValues[2][3] * vectors[7];
pseudoAffineCoefficients[7] =
inverseMatrixValues[3][0] * vectors[4] +
inverseMatrixValues[3][1] * vectors[5] +
inverseMatrixValues[3][2] * vectors[6] +
inverseMatrixValues[3][3] * vectors[7];
return pseudoAffineCoefficients;
}
// 逆行列算出。詳細は、以下の関連記事を参照
// https://blogs.yahoo.co.jp/dk521123/38068366.html
private static bool CalculateInverseMatrix(
double[][] targetMatrixes, out double[][] outInverseMatrixes)
{
var dataNumber = targetMatrixes.GetLength(0);
outInverseMatrixes = new double[dataNumber][];
//単位行列を作る
for (int i = 0; i < dataNumber; i++)
{
outInverseMatrixes[i] = new double[dataNumber];
for (int j = 0; j < dataNumber; j++)
{
outInverseMatrixes[i][j] = (i == j) ? 1.0f : 0.0f;
}
}
// 掃き出し法
for (int i = 0; i < dataNumber; i++)
{
if (targetMatrixes[i][i] == 0)
{
return false;
}
var tempValue = 1.0 / targetMatrixes[i][i];
for (int j = 0; j < dataNumber; j++)
{
targetMatrixes[i][j] *= tempValue;
outInverseMatrixes[i][j] *= tempValue;
}
for (int j = 0; j < dataNumber; j++)
{
if (i != j)
{
tempValue = targetMatrixes[j][i];
for (int k = 0; k < dataNumber; k++)
{
targetMatrixes[j][k] -= targetMatrixes[i][k] * tempValue;
outInverseMatrixes[j][k] -= outInverseMatrixes[i][k] * tempValue;
}
}
}
}
return true;
}
/// <summary>
/// 擬似アフィン変換による補正座標を返す
/// </summary>
/// <param name="pseudoAffineCoefficients">擬似アフィン係数</param>
/// <param name="targetPoint">対象座標</param>
/// <returns>擬似アフィン変換による補正座標</returns>
private Point GetCorrectPointByPseudoAffineTransfer(
double[] pseudoAffineCoefficients, int x, int y)
{
// u = a0xy + a1x + a2y + a4
var correctedX =
pseudoAffineCoefficients[0] * x * y +
pseudoAffineCoefficients[1] * x +
pseudoAffineCoefficients[2] * y +
pseudoAffineCoefficients[3];
// v = b0xy + b1x + b2y + b4
var correctedY =
pseudoAffineCoefficients[4] * x * y +
pseudoAffineCoefficients[5] * x +
pseudoAffineCoefficients[6] * y +
pseudoAffineCoefficients[7];
// 座標にするので四捨五入
return new Point(
(int)Math.Round(correctedX, MidpointRounding.AwayFromZero),
(int)Math.Round(correctedY, MidpointRounding.AwayFromZero));
}
}
}
