Find known sub image in larger image

Question

Does anyone know of an algorithm (or search terms / descriptions) to locate a known image within a larger image?

e.g.

I have an image of a s

Answer 1

Your don't need fuzzy as in "neural network" because (as I understand) you don't have rotation, tilts or similar. If OS display differences are the only modifications the difference should be minimal. So WernerVanBelle's paper is nice but not really necessary and MrFooz's code works - but is terribly innefficient (O(width * height * patter_width * pattern_height)!).

The best algorithm I can think of is the Boyer-Moore algorithm for string searching, modified to allow 2 dimensional searches. http://en.wikipedia.org/wiki/Boyer%E2%80%93Moore_string_search_algorithm

Instead of one displacement you will have to store a pair of displacements dx and dy for each color. When checking a pixel you move only in the x direction x = x + dx and store only the minimum of the dy's DY = min(DY, dy) to set the new y value after a whole line has been tested (ie x > width).

Creating a table for all possible colors probably is prohibitve due to the imense number of possible colors, so either use a map to store the rules (and default to the pattern dimensions if a color is not inside the map) or create tables for each color seperately and set dx = max(dx(red), dx(green), dx(blue)) - which is only an approximation but removes the overhead of a map.

In the preprocessing of the bad-character rule, you can account for small deviations of colors by spreading rules from all colors to their "neighbouring" colors (however you wish to define neighbouring).

Answer 2

You said your image may not be exactly the same, but then say you don't want "fuzzy" algorithms. I'm not sure those are compatible. In general, though, I think you want to look at image registration algorithms. There's an open source C++ package called ITK that might provide some hints. Also ImageJ is a popular open source Java package. Both of these have at least some registration capabilities available if you poke around.

Answer 3

Here's the skeleton of code you'd want to use:

// look for all (x,y) positions where target appears in desktop
List<Loc> findMatches(Image desktop, Image target, float threshold) {
  List<Loc> locs;
  for (int y=0; y<desktop.height()-target.height(); y++) {
      for (int x=0; x<desktop.width()-target.width(); x++) {
          if (imageDistance(desktop, x, y, target) < threshold) {
              locs.append(Loc(x,y));
          }
      }
   }
   return locs;
}

// computes the root mean squared error between a rectangular window in 
// bigImg and target.
float imageDistance(Image bigImg, int bx, int by, Image target) {
    float dist = 0.0;
    for (int y=0; y<target.height(); y++) {
        for (int x=0; x<target.width(); x++) {
            // assume RGB images...
            for (int colorChannel=0; colorChannel<3; colorChannel++) {
                dist += Math.pow(target.getPixel(x,y) - bigImg.getPixel(bx+x,by+y), 2);
            }
         }
    }
    return Math.sqrt(dist) / target.width() / target.height();
}

You could consider other image distances (see a similar question). For your application, the RMS error is probably a good choice.

There are probably various Java libraries that compute this distance for you efficiently.

Answer 4

Have a look at the paper I wrote: http://werner.yellowcouch.org/Papers/subimg/index.html. It's highly detailed and appears to be the only article discussing how to apply fourier transformation to the problem of subimage finding.

In short, if you want to use the fourier transform one could apply the following formula: the correlation between image A and image B when image A is shifted over dx,dy is given in the following matrix: C=ifft(fft(A) x conjugate(fft(B)). So, the position in image C that has the highest value, has the highest correlation and that position reflects dx,dy.

This result works well for subimages that are relatively large. For smaller images, some more work is necessary as explained in the article. Nevertheless, such fourier transforms are quite fast. It results in around 3*sxsylog_2(sx*sy)+3*sx*sy operations.

Answer 5

You could use unique visual elements of this target area to determine its position. These unique visual elements are like a "signature". Examples: unique icons, images and symbols. This approach works independently of the window resolution if you have unique elements in the corners. For fixed sized windows, just one element is sufficient to find all window coordinates.

Below I illustrate the idea with a simple example using Marvin Framework.

Unique elements:

Program output:

Original Image:
window.png

Source code:

import static marvin.MarvinPluginCollection.*;

public class FindSubimageWindow {
    public FindSubimageWindow(){
        MarvinImage window = MarvinImageIO.loadImage("./res/window.png");
        MarvinImage eclipse = MarvinImageIO.loadImage("./res/eclipse_icon.png");
        MarvinImage progress = MarvinImageIO.loadImage("./res/progress_icon.png");

        MarvinSegment seg1, seg2;
        seg1 = findSubimage(eclipse, window, 0, 0);
        drawRect(window, seg1.x1, seg1.y1, seg1.x2-seg1.x1, seg1.y2-seg1.y1);

        seg2 = findSubimage(progress, window, 0, 0);
        drawRect(window, seg2.x1, seg2.y1, seg2.x2-seg2.x1, seg2.y2-seg2.y1);

        drawRect(window, seg1.x1-10, seg1.y1-10, (seg2.x2-seg1.x1)+25, (seg2.y2-seg1.y1)+20);

        MarvinImageIO.saveImage(window, "./res/window_out.png");
    }
    private void drawRect(MarvinImage image, int x, int y, int width, int height){
        x-=4; y-=4; width+=8; height+=8;
        image.drawRect(x, y, width, height, Color.red);
        image.drawRect(x+1, y+1, width-2, height-2, Color.red);
        image.drawRect(x+2, y+2, width-4, height-4, Color.red);
    }
    public static void main(String[] args) {
        new FindSubimageWindow();
    }   
}

Answer 6

I considered the solution of Werner Van Belle (since all other approaches are incredible slow - not practicable at all):

An Adaptive Filter for the Correct Localization of Subimages: FFT based Subimage Localization Requires Image Normalization to work properly

I wrote the code in C# where I need my solution, but I am getting highly inaccurate results. Does it really not work well, in contrary to Van Belle's statement, or did I do something wrong? I used https://github.com/tszalay/FFTWSharp as a C# wrapper for FFTW.

Here is my translated code: (original in C++ at http://werner.yellowcouch.org/Papers/subimg/index.html)

using System.Diagnostics;
using System;
using System.Runtime.InteropServices;
using System.Drawing;
using System.Drawing.Imaging;
using System.IO;

using FFTWSharp;

using unsigned1 = System.Byte;
using signed2 = System.Int16;
using signed8 = System.Int64;

public class Subimage
{
    /**
     * This program finds a subimage in a larger image. It expects two arguments.
     * The first is the image in which it must look. The secon dimage is the
     * image that is to be found. The program relies on a number of different
     * steps to perform the calculation.
     *
     * It will first normalize the input images in order to improve the
     * crosscorrelation matching. Once the best crosscorrelation is found
     * a sad-matchers is applied in a grid over the larger image.
     *
     * The following two article explains the details:
     *
     *   Werner Van Belle; An Adaptive Filter for the Correct Localization
     *   of Subimages: FFT based Subimage Localization Requires Image
     *   Normalization to work properly; 11 pages; October 2007.
     *   http://werner.yellowcouch.org/Papers/subimg/
     *
     *   Werner Van Belle; Correlation between the inproduct and the sum
     *   of absolute differences is -0.8485 for uniform sampled signals on
     *   [-1:1]; November 2006
     */
    unsafe public static Point FindSubimage_fftw(string[] args)
    {
        if (args == null || args.Length != 2)
        {
            Console.Write("Usage: subimg\n" + "\n" + "  subimg is an image matcher. It requires two arguments. The first\n" + "  image should be the larger of the two. The program will search\n" + "  for the best position to superimpose the needle image over the\n" + "  haystack image. The output of the the program are the X and Y\n" + "  coordinates.\n\n" + "  http://werner.yellowouch.org/Papers/subimg/\n");
            return new Point();
        }

        /**
         * The larger image will be called A. The smaller image will be called B.
         *
         * The code below relies heavily upon fftw. The indices necessary for the
         * fast r2c and c2r transforms are at best confusing. Especially regarding
         * the number of rows and colums (watch our for Asx vs Asx2 !).
         *
         * After obtaining all the crosscorrelations we will scan through the image
         * to find the best sad match. As such we make a backup of the original data
         * in advance
         *
         */
        int Asx = 0, Asy = 0;
        signed2[] A = read_image(args[0], ref Asx, ref Asy);
        int Asx2 = Asx / 2 + 1;

        int Bsx = 0, Bsy = 0;
        signed2[] B = read_image(args[1], ref Bsx, ref Bsy);

        unsigned1[] Asad = new unsigned1[Asx * Asy];
        unsigned1[] Bsad = new unsigned1[Bsx * Bsy];

        for (int i = 0; i < Bsx * Bsy; i++)
        {
            Bsad[i] = (unsigned1)B[i];
            Asad[i] = (unsigned1)A[i];
        }
        for (int i = Bsx * Bsy; i < Asx * Asy; i++)
            Asad[i] = (unsigned1)A[i];

        /**
         * Normalization and windowing of the images.
         *
         * The window size (wx,wy) is half the size of the smaller subimage. This
         * is useful to have as much good information from the subimg.
         */
        int wx = Bsx / 2;
        int wy = Bsy / 2;
        normalize(ref B, Bsx, Bsy, wx, wy);
        normalize(ref A, Asx, Asy, wx, wy);

        /**
         * Preparation of the fourier transforms.
         * Aa is the amplitude of image A. Af is the frequence of image A
         * Similar for B. crosscors will hold the crosscorrelations.
         */
        IntPtr Aa = fftw.malloc(sizeof(double) * Asx * Asy);
        IntPtr Af = fftw.malloc(sizeof(double) * 2 * Asx2 * Asy);
        IntPtr Ba = fftw.malloc(sizeof(double) * Asx * Asy);
        IntPtr Bf = fftw.malloc(sizeof(double) * 2 * Asx2 * Asy);

        /**
         * The forward transform of A goes from Aa to Af
         * The forward tansform of B goes from Ba to Bf
         * In Bf we will also calculate the inproduct of Af and Bf
         * The backward transform then goes from Bf to Aa again. That
         * variable is aliased as crosscors;
         */
        //#original: fftw_plan_dft_r2c_2d
        //IntPtr forwardA = fftwf.dft(2, new int[] { Asy, Asx }, Aa, Af, fftw_direction.Forward, fftw_flags.Estimate);//equal results
        IntPtr forwardA = fftwf.dft_r2c_2d(Asy, Asx, Aa, Af, fftw_flags.Estimate);
        //#original: fftw_plan_dft_r2c_2d
        //IntPtr forwardB = fftwf.dft(2, new int[] { Asy, Asx }, Ba, Bf, fftw_direction.Forward, fftw_flags.Estimate);//equal results
        IntPtr forwardB = fftwf.dft_r2c_2d(Asy, Asx, Ba, Bf, fftw_flags.Estimate);
        double* crosscorrs = (double*)Aa;
        //#original: fftw_plan_dft_c2r_2d
        //IntPtr backward = fftwf.dft(2, new int[] { Asy, Asx }, Bf, Aa, fftw_direction.Backward, fftw_flags.Estimate);//equal results
        IntPtr backward = fftwf.dft_c2r_2d(Asy, Asx, Bf, Aa, fftw_flags.Estimate);

        /**
         * The two forward transforms of A and B. Before we do so we copy the normalized
         * data into the double array. For B we also pad the data with 0
         */
        for (int row = 0; row < Asy; row++)
            for (int col = 0; col < Asx; col++)
                ((double*)Aa)[col + Asx * row] = A[col + Asx * row];
        fftw.execute(forwardA);

        for (int j = 0; j < Asx * Asy; j++)
            ((double*)Ba)[j] = 0;
        for (int row = 0; row < Bsy; row++)
            for (int col = 0; col < Bsx; col++)
                ((double*)Ba)[col + Asx * row] = B[col + Bsx * row];
        fftw.execute(forwardB);

        /**
         * The inproduct of the two frequency domains and calculation
         * of the crosscorrelations
         */
        double norm = Asx * Asy;
        for (int j = 0; j < Asx2 * Asy; j++)
        {
            double a = ((double*)Af)[j * 2];//#Af[j][0];
            double b = ((double*)Af)[j * 2 + 1];//#Af[j][1];
            double c = ((double*)Bf)[j * 2];//#Bf[j][0];
            double d = ((double*)Bf)[j * 2 + 1];//#-Bf[j][1];
            double e = a * c - b * d;
            double f = a * d + b * c;
            ((double*)Bf)[j * 2] = (double)(e / norm);//#Bf[j][0] = (fftw_real)(e / norm);
            ((double*)Bf)[j * 2 + 1] = (double)(f / norm);//Bf[j][1] = (fftw_real)(f / norm);
        }
        fftw.execute(backward);

        /**
         * We now have a correlation map. We can spent one more pass
         * over the entire image to actually find the best matching images
         * as defined by the SAD.
         * We calculate this by gridding the entire image according to the
         * size of the subimage. In each cel we want to know what the best
         * match is.
         */
        int sa = 1 + Asx / Bsx;
        int sb = 1 + Asy / Bsy;
        int sadx = 0;
        int sady = 0;
        signed8 minsad = Bsx * Bsy * 256L;
        for (int a = 0; a < sa; a++)
        {
            int xl = a * Bsx;
            int xr = xl + Bsx;
            if (xr > Asx) continue;
            for (int b = 0; b < sb; b++)
            {
                int yl = b * Bsy;
                int yr = yl + Bsy;
                if (yr > Asy) continue;

                // find the maximum correlation in this cell
                int cormxat = xl + yl * Asx;
                double cormx = crosscorrs[cormxat];
                for (int x = xl; x < xr; x++)
                    for (int y = yl; y < yr; y++)
                    {
                        int j = x + y * Asx;
                        if (crosscorrs[j] > cormx)
                            cormx = crosscorrs[cormxat = j];
                    }
                int corx = cormxat % Asx;
                int cory = cormxat / Asx;

                // We dont want subimages that fall of the larger image
                if (corx + Bsx > Asx) continue;
                if (cory + Bsy > Asy) continue;

                signed8 sad = 0;
                for (int x = 0; sad < minsad && x < Bsx; x++)
                    for (int y = 0; y < Bsy; y++)
                    {
                        int j = (x + corx) + (y + cory) * Asx;
                        int i = x + y * Bsx;
                        sad += Math.Abs((int)Bsad[i] - (int)Asad[j]);
                    }

                if (sad < minsad)
                {
                    minsad = sad;
                    sadx = corx;
                    sady = cory;
                    // printf("* ");
                }
                // printf("Grid (%d,%d) (%d,%d) Sip=%g Sad=%lld\n",a,b,corx,cory,cormx,sad);
            }
        }
        //Console.Write("{0:D}\t{1:D}\n", sadx, sady);
        /**
         * Aa, Ba, Af and Bf were allocated in this function
         * crosscorrs was an alias for Aa and does not require deletion.
         */
        fftw.free(Aa);
        fftw.free(Ba);
        fftw.free(Af);
        fftw.free(Bf);
        return new Point(sadx, sady);
    }

    private static void normalize(ref signed2[] img, int sx, int sy, int wx, int wy)
    {
        /**
         * Calculate the mean background. We will subtract this
         * from img to make sure that it has a mean of zero
         * over a window size of wx x wy. Afterwards we calculate
         * the square of the difference, which will then be used
         * to normalize the local variance of img.
         */
        signed2[] mean = boxaverage(img, sx, sy, wx, wy);
        signed2[] sqr = new signed2[sx * sy];
        for (int j = 0; j < sx * sy; j++)
        {
            img[j] -= mean[j];
            signed2 v = img[j];
            sqr[j] = (signed2)(v * v);
        }
        signed2[] var = boxaverage(sqr, sx, sy, wx, wy);
        /**
         * The normalization process. Currenlty still
         * calculated as doubles. Could probably be fixed
         * to integers too. The only problem is the sqrt
         */
        for (int j = 0; j < sx * sy; j++)
        {
            double v = Math.Sqrt(Math.Abs((double)var[j]));//#double v = sqrt(fabs(var[j])); <- ambigous
            Debug.Assert(!double.IsInfinity(v) && v >= 0);
            if (v < 0.0001) v = 0.0001;
            img[j] = (signed2)(img[j] * (32 / v));
            if (img[j] > 127) img[j] = 127;
            if (img[j] < -127) img[j] = -127;
        }
        /**
         * As a last step in the normalization we
         * window the sub image around the borders
         * to become 0
         */
        window(ref img, sx, sy, wx, wy);
    }

    private static signed2[] boxaverage(signed2[] input, int sx, int sy, int wx, int wy)
    {
        signed2[] horizontalmean = new signed2[sx * sy];

        Debug.Assert(horizontalmean != null);
        int wx2 = wx / 2;
        int wy2 = wy / 2;
        int from = (sy - 1) * sx;
        int to = (sy - 1) * sx;
        int initcount = wx - wx2;
        if (sx < initcount) initcount = sx;
        int xli = -wx2;
        int xri = wx - wx2;
        for (; from >= 0; from -= sx, to -= sx)
        {
            signed8 sum = 0;
            int count = initcount;
            for (int c = 0; c < count; c++)
                sum += (signed8)input[c + from];
            horizontalmean[to] = (signed2)(sum / count);
            int xl = xli, x = 1, xr = xri;
            /**
             * The area where the window is slightly outside the
             * left boundary. Beware: the right bnoundary could be
             * outside on the other side already
             */
            for (; x < sx; x++, xl++, xr++)
            {
                if (xl >= 0) break;
                if (xr < sx)
                {
                    sum += (signed8)input[xr + from];
                    count++;
                }
                horizontalmean[x + to] = (signed2)(sum / count);
            }
            /**
             * both bounds of the sliding window
             * are fully inside the images
             */
            for (; xr < sx; x++, xl++, xr++)
            {
                sum -= (signed8)input[xl + from];
                sum += (signed8)input[xr + from];
                horizontalmean[x + to] = (signed2)(sum / count);
            }
            /**
             * the right bound is falling of the page
             */
            for (; x < sx; x++, xl++)
            {
                sum -= (signed8)input[xl + from];
                count--;
                horizontalmean[x + to] = (signed2)(sum / count);
            }
        }

        /**
         * The same process as aboe but for the vertical dimension now
         */
        int ssy = (sy - 1) * sx + 1;
        from = sx - 1;
        signed2[] verticalmean = new signed2[sx * sy];
        Debug.Assert(verticalmean != null);
        to = sx - 1;
        initcount = wy - wy2;
        if (sy < initcount) initcount = sy;
        int initstopat = initcount * sx;
        int yli = -wy2 * sx;
        int yri = (wy - wy2) * sx;
        for (; from >= 0; from--, to--)
        {
            signed8 sum = 0;
            int count = initcount;
            for (int d = 0; d < initstopat; d += sx)
                sum += (signed8)horizontalmean[d + from];
            verticalmean[to] = (signed2)(sum / count);
            int yl = yli, y = 1, yr = yri;
            for (; y < ssy; y += sx, yl += sx, yr += sx)
            {
                if (yl >= 0) break;
                if (yr < ssy)
                {
                    sum += (signed8)horizontalmean[yr + from];
                    count++;
                }
                verticalmean[y + to] = (signed2)(sum / count);
            }
            for (; yr < ssy; y += sx, yl += sx, yr += sx)
            {
                sum -= (signed8)horizontalmean[yl + from];
                sum += (signed8)horizontalmean[yr + from];
                verticalmean[y + to] = (signed2)(sum / count);
            }
            for (; y < ssy; y += sx, yl += sx)
            {
                sum -= (signed8)horizontalmean[yl + from];
                count--;
                verticalmean[y + to] = (signed2)(sum / count);
            }
        }
        return verticalmean;
    }

    private static void window(ref signed2[] img, int sx, int sy, int wx, int wy)
    {
        int wx2 = wx / 2;
        int sxsy = sx * sy;
        int sx1 = sx - 1;
        for (int x = 0; x < wx2; x++)
            for (int y = 0; y < sxsy; y += sx)
            {
                img[x + y] = (signed2)(img[x + y] * x / wx2);
                img[sx1 - x + y] = (signed2)(img[sx1 - x + y] * x / wx2);
            }

        int wy2 = wy / 2;
        int syb = (sy - 1) * sx;
        int syt = 0;
        for (int y = 0; y < wy2; y++)
        {
            for (int x = 0; x < sx; x++)
            {
                /**
                 * here we need to recalculate the stuff (*y/wy2)
                 * to preserve the discrete nature of integers.
                 */
                img[x + syt] = (signed2)(img[x + syt] * y / wy2);
                img[x + syb] = (signed2)(img[x + syb] * y / wy2);
            }
            /**
             * The next row for the top rows
             * The previous row for the bottom rows
             */
            syt += sx;
            syb -= sx;
        }
    }

    private static signed2[] read_image(string filename, ref int sx, ref int sy)
    {
        Bitmap image = new Bitmap(filename);
        sx = image.Width;
        sy = image.Height;
        signed2[] GreyImage = new signed2[sx * sy];
        BitmapData bitmapData1 = image.LockBits(new Rectangle(0, 0, image.Width, image.Height), ImageLockMode.ReadOnly, PixelFormat.Format32bppArgb);
        unsafe
        {
            byte* imagePointer = (byte*)bitmapData1.Scan0;

            for (int y = 0; y < bitmapData1.Height; y++)
            {
                for (int x = 0; x < bitmapData1.Width; x++)
                {
                    GreyImage[x + y * sx] = (signed2)((imagePointer[0] + imagePointer[1] + imagePointer[2]) / 3.0);
                    //4 bytes per pixel
                    imagePointer += 4;
                }//end for x
                //4 bytes per pixel
                imagePointer += bitmapData1.Stride - (bitmapData1.Width * 4);
            }//end for y
        }//end unsafe
        image.UnlockBits(bitmapData1);
        return GreyImage;
    }
}