How to speed up my color thresholding in C#

Question

I'm working on tracking objects based on color and I was using EmguCV library to threshold my color image to binary black and white image. Thresholding itself was quite fast, 50 ms on 320x240 image. I'm using RG Chromaticity color space, so there are some necessarily calculations.

Now I'm trying to speed it up using pointers, but the result is very similar with what I did with emguCV (around 50 ms per image).

I want to ask, if there is some expert who can help me, what I am doing wrong. Here is my short code snippet of my color thresholding implementation. It's based on this one: https://web.archive.org/web/20140906075741/http://bobpowell.net/onebit.aspx.

public static Bitmap ThresholdRGChroma(Bitmap original, double angleMin,
            double angleMax, double satMin, double satMax)
{
    Bitmap bimg = new Bitmap(original.Width, original.Height, PixelFormat.Format1bppIndexed);

    BitmapData imgData = original.LockBits(new Rectangle(0, 0, original.Width, original.Height), ImageLockMode.ReadOnly, original.PixelFormat);
    BitmapData bimgData = bimg.LockBits(new Rectangle(0, 0, bimg.Width, bimg.Height), ImageLockMode.ReadWrite, bimg.PixelFormat);

    int pixelSize = 3;

    double r, g, angle, sat;

    unsafe
    {
        byte* R, G, B;
        byte* row;
        int RGBSum;

        for (int y = original.Height - 1; y >= 0; y--)
        {
            row = (byte*)imgData.Scan0 + (y * imgData.Stride);

            for (int x = original.Width - 1; x >= 0; x--)
            {
                // get rgb values
                B = &row[x * pixelSize];
                G = &row[x * pixelSize + 1];
                R = &row[x * pixelSize + 2];

                RGBSum = *R + *G + *B;

                if (RGBSum == 0)
                {
                    SetIndexedPixel(x, y, bimgData, false);
                    continue;
                }

                //calculate r ang g for rg chroma color space
                r = (double)*R / RGBSum;
                g = (double)*G / RGBSum;

                //and angle and saturation
                angle = GetAngleRad(r, g) * (180.0 / Math.PI);
                sat = Math.Sqrt(Math.Pow(g, 2) + Math.Pow(r, 2));

                //conditions to set pixel black or white
                if ((angle >= angleMin && angle <= angleMax) && (sat >= satMin && sat <= satMax))
                    SetIndexedPixel(x, y, bimgData, true);
                else
                    SetIndexedPixel(x, y, bimgData, false);
            }

        }
    }

    bimg.UnlockBits(bimgData);
    original.UnlockBits(imgData);

    return bimg;
}

private unsafe static void SetIndexedPixel(int x, int y, BitmapData bmd, bool pixel)
{
    int index = y * bmd.Stride + (x >> 3);
    byte* p = (byte*)bmd.Scan0.ToPointer();
    byte mask = (byte)(0x80 >> (x & 0x7));

    if (pixel)
        p[index] |= mask;
    else
        p[index] &= (byte)(mask ^ 0xff);
}

private static double GetAngleRad(double x, double y)
{
    if (x - _rgChromaOriginX == 0)
        return 0.0;
    double angle = Math.Atan((y - _rgChromaOriginY) / (x - _rgChromaOriginX)); // 10ms

    if (x < _rgChromaOriginX && y > _rgChromaOriginY)
        angle = angle + Math.PI;
    else if (x < _rgChromaOriginX && y < _rgChromaOriginY)
        angle = angle + Math.PI;
    else if (x > _rgChromaOriginX && y < _rgChromaOriginY)
        angle = angle + 2 * Math.PI;

    return angle;
}

Unflinching

Answer 1

You're doing a lot of unnecessary math for each pixel, calculating exact values only to check to see if they're inside some limits. You can simplify the comparisons by precomputing some adjustments to the limits.

The easiest substitution is for the saturation. You're doing a square root which you can avoid by squaring the limits instead.

double satMin2 = satMin*satMin;
double satMax2 = satMax*satMax;
// ...
sat2 = g*g + r*r;

//conditions to set pixel black or white
if ((angle >= angleMin && angle <= angleMax) && (sat2 >= satMin2 && sat <= satMax2))

A similar trick can be used with the angle. Rather than calculating the angle with Math.Atan, figure out what those limits equate to in your r and g ranges.

Nondisjunction

Thank you very much. Only modifying saturation and its ranges speeds up thresholding with about 20 ms, from 50 to 30. I have also found this nice paper about RG-chromaticity where they show how to speed it up even more, exactly like you said, by removing Atan. I'll post my corrected version, which thresholds 320x240 image on my computer in 18ms. – Unflinching

Answer 2

For completeness, here is modified version of thresholding image in RG Chromaticity color space it's more than 2 times faster than the version in my Question.

public static Bitmap ThresholdRGChroma(Bitmap original, Rectangle roi, double angle,
            double width, double satMin, double satMax)
        {
            Bitmap bimg = new Bitmap(original.Width, original.Height, PixelFormat.Format1bppIndexed);

        BitmapData imgData = original.LockBits(new Rectangle(0, 0, original.Width, original.Height), ImageLockMode.ReadOnly, original.PixelFormat);
        BitmapData bimgData = bimg.LockBits(new Rectangle(0, 0, bimg.Width, bimg.Height), ImageLockMode.ReadWrite, bimg.PixelFormat);

        int pixelSize = 3;

        double r, g, sat, m;

        double satMin2 = satMin * satMin;
        double satMax2 = satMax * satMax;

        double cr = Math.Sin((2 * Math.PI * angle) / 360.0);
        double cg = Math.Cos((2 * Math.PI * angle) / 360.0);

        // Instead of (Math.Cos(2 * width / 180.0) + 1) / 2.0 I'm using pre-calculated <1; 0> values.
        double w2 = -width;

        unsafe
        {
            byte* R, G, B;
            byte* row;
            int RGBSum;

            for (int y = original.Height - 1; y >= 0; y--)
            {
                row = (byte*)imgData.Scan0 + (y * imgData.Stride);

                for (int x = original.Width - 1; x >= 0; x--)
                {
                    B = &row[x * pixelSize];
                    G = &row[x * pixelSize + 1];
                    R = &row[x * pixelSize + 2];

                    RGBSum = *R + *G + *B;

                    if (RGBSum == 0)
                    {
                        SetIndexedPixel(x, y, bimgData, false);
                        continue;
                    }

                    r = (double)*R / RGBSum - _rgChromaOriginX;
                    g = (double)*G / RGBSum - _rgChromaOriginY;

                    m = cr * r + cg * g;
                    sat = r * r + g * g;

                    if (m > 0 && m * m > w2 * w2 * sat && sat >= satMin2 && sat <= satMax2)
                        SetIndexedPixel(x, y, bimgData, true);
                    else
                        SetIndexedPixel(x, y, bimgData, false);
                }
            }
        }

        bimg.UnlockBits(bimgData);
        original.UnlockBits(imgData);

        return bimg;
    }

Unflinching