Design and Implementation of Digital Image Transformation Algorithms

International Journal of Trend in Scientific Research and Development (IJTSRD)
Volume: 3 | Issue: 3 | Mar-Apr 2019 Available Online: www.ijtsrd.com e-ISSN: 2456 - 6470
@ IJTSRD | Unique Paper ID – IJTSRD22918 | Volume – 3 | Issue – 3 | Mar-Apr 2019 Page: 623
Design & Implementation of Digital
Image Transformation Algorithms
Joe G. Saliby
Researcher, Lebanese Association for Computational Sciences, Beirut, Lebanon
How to cite this paper: Joe G. Saliby
"Design & Implementation of Digital
Image Transformation Algorithms"
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ABSTRACT
In computer science, Digital Image Processing or DIP is the use of computer
hardware and software to perform image processing and computations on
digital images. Generally, digital image processing requires the use of complex
algorithms, and hence, can be more sophisticated from a performance
perspective at doing simple tasks. Many applications exist for digital image
processing, one of which isDigitalImageTransformation. Basically, DigitalImage
Transformation or DITisanalgorithmicand mathematicalfunctionthatconverts
one set of digital objects into another set after performing some operations.
Some techniques used in DIT are image filtering, brightness, contrast, hue, and
saturation adjustment, blending and dilation, histogram equalization, discrete
cosine transform, discrete Fourier transform,edgedetection,amongothers.This
paper proposes a set of digital image transformation algorithms that deal with
converting digital images from one domain to another. The algorithms to be
implemented are grayscale transformation, contrastand brightnessadjustment,
hue and saturation adjustment, histogramequalization,blurringand sharpening
adjustment, blending and fading transformation, erosion and dilation
transformation, and finally edge detection and extraction. As future work, some
of the proposed algorithms aretobeinvestigatedwithparallelprocessingpaving
the way to make their execution time faster and more scalable.
KEYWORDS: Algorithms, Digital Image Processing, Digital Image Transformation
I. GRAYSCALE TRANSFORMATION
Grayscale is a range of shades of gray without
apparent color. The darkest possible shade is black,
which is the total absence of transmitted or reflected
light. The lightest possible shade is white, the total
transmission or reflection of light at all visible
wavelengths. Intermediate shades of gray are
represented by equal brightness levels of the three
primary colors (red, green and blue) for transmitted
light, or equal amounts of the three primary pigments
(cyan, magenta and yellow) for reflected light [1].
In photography and computing, a grayscale digital
image is an image in which the value of each pixel is a
single sample, that is, it carries only intensity
information. Images of this sort, also known as black-
and-white, are composed exclusively of shades of
gray, varying from black at the weakest intensity to
white at the strongest. Grayscale images are distinct
from one-bit bi-tonal black-and-white images, which
in the context of computer imaging are images with
only the two colors, black, and white. Grayscale
images have many shades of gray in between.
Grayscale images are also called monochromatic,
denoting the presence of only one color.
A. Implementation
Image img = pictureBox1.Image;
Bitmap bitmap = new Bitmap(img);
// Cycling over all the pixels in the image
for (int i = 0; i < bitmap.Size.Width; i++)
{
for (int j = 0; j < bitmap.Size.Height; j++)
{
Color color = bitmap.GetPixel(i, j); // Retreives
the color of a particular pixel
int R = color.R; // since the image is 8-bit
Grayscale
if (intensityTrackbar.Value == 2)
{
int upperBound = 271; // 271-16 = 255
int lowerBound = 0;
for (int k = 1; k <= 16; k++)
{
upperBound = upperBound - 16;
lowerBound = upperBound - 16;
if (R <= upperBound && R > lowerBound)
{
R = upperBound;
}
IJTSRD22918

International Journal of Trend in Scientific Research and Development (IJTSRD) @ www.ijtsrd.com eISSN: 2456-6470
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}
}
else if (intensityTrackbar.Value == 1)
{
int upperBound = 319; // 319-64 = 255
int lowerBound = 0;
for (int k = 1; k <= 4; k++)
{
upperBound = upperBound - 64;
lowerBound = upperBound - 64;
if (R <= upperBound && R > lowerBound)
{
R = upperBound;
}
}
}
else if (intensityTrackbar.Value == 0)
{
if (R <= 255 && R > 127)
R = 255;
else R = 0;
}
bitmap.SetPixel(i, j, Color.FromArgb(R, R, R));
}
}
Figure 1, 2, 3, and 4 depict an original image in 8 bits,
4 bits, 2 bits, and 1 bit grayscale mode respectively.
Figure 1: 8-bit Grayscale = 256 Levels
Figure 4: 1-bit Grayscale = 2 Levels (Black & White)
II. CONTRAST ADJUSTMENT
Contrast is created by the difference in luminance, the
amount of reflected light, reflected from two adjacent
surfaces. There is also the Weber definition of
contrast:
Contrast = Lmax – Lmin
Lmax
Lmax = Luminance on the lighter surface
Lmin = Luminance on the darker surface
When the darker surface is black and reflects no light,
the ratio is 1. Contrast is usually expressed as
percentage value; the ratio is multiplied by 100. The
maximum contrast is thus 100% contrast [2]. The
symbols of the visual acuity charts are close to the
maximum contrast. If the lowest contrast perceived is
5%, contrast sensitivity is 100/5=20. If the lowest
contrast perceived by a person is 0.6%, contrast
sensitivity is 100/0.6=170.
A. Implementation
public static Bitmap AdjustContrast(Bitmap Image,
float Value)
{
Value = (100.0f + Value) / 100.0f;
Value *= Value;
Bitmap NewBitmap = (Bitmap)Image.Clone();

BitmapData data = NewBitmap();
int Height = NewBitmap.Height;
int Width = NewBitmap.Width;
for (int y = 0; y < Height; ++y)
{
byte* row = (byte*)data.Scan0 + (y *
data.Stride);
int columnOffset = 0;
for (int x = 0; x < Width; ++x)
{
byte B = row[columnOffset];
byte G = row[columnOffset + 1];
byte R = row[columnOffset + 2];
float Red = R / 255.0f;
float Green = G / 255.0f;
float Blue = B / 255.0f;
Red = (((Red - 0.5f) * Value) + 0.5f) * 255.0f;
Green = (((Green - 0.5f) * Value) + 0.5f) *
255.0f;
Blue = (((Blue - 0.5f) * Value) + 0.5f) * 255.0f;
int iR = (int)Red;
iR = iR > 255 ? 255 : iR;
iR = iR < 0 ? 0 : iR;
int iG = (int)Green;
iG = iG > 255 ? 255 : iG;
iG = iG < 0 ? 0 : iG;
int iB = (int)Blue;
iB = iB > 255 ? 255 : iB;
iB = iB < 0 ? 0 : iB;
row[columnOffset] = (byte)iB;
row[columnOffset + 1] = (byte)iG;
row[columnOffset + 2] = (byte)iR;
columnOffset += 4;
}
}
}
III. BRIGHTNESS ADJUSTMENT
Brightness is an attribute of visual perception in
which a source appears to be radiating or reflecting
light. In other words, brightness is the perception
elicited by the luminance of a visual target [3]. This is
a subjective attribute/property of an object being
observed.
A. Implementation
Image img = pictureBox1.Image;
Bitmap bitmap = new Bitmap(img);
// Cycling over all the pixels in the image
for (int i = 0; i < bitmap.Size.Width; i++)
{
for (int j = 0; j < bitmap.Size.Height; j++)
{
Color color = bitmap.GetPixel(i, j); //
Retreives the color of a particular pixel
int R = color.R; // since the image is 8-bit
Grayscale --> R = G = B
int G = color.G; // since the image is 8-bit
int B = color.B; // since the image is 8-bit
R+= intensity_level;
G+= intensity_level;
B+= intensity_level;
bitmap.SetPixel(i, j, Color.FromArgb(R, G,
B)); // Updating the bitmap with the new
modified pixel
}
}
IV. HUE & SATURATION ADJUSTMENT
HSL stands for hue, saturation, and lightness, and is
often also called HLS. HSV stands for hue, saturation,
and value, and is also often called HSB. A third model,
common in computer vision applications, is HSI, for
hue, saturation, and intensity. However, while
typically consistent, these definitions are not
standardized, and any of these abbreviations might be
used for any of these three or several other related
cylindrical models [4].
HSL and HSV are the two most common cylindrical-
coordinate representations of points in an RGB color
model. The two representations rearrange the
geometry of RGB in an attempt to be more intuitive
and perceptually relevant than the Cartesian (cube)
representation. Developed in the 1970s for computer
graphics applications, HSL and HSV are used today in
color pickers, in image editing software, and less
commonly in image analysis and computer vision.
Figure 5 depicts the HSL and HSV color spectrum.
Figure 5: HSL & HSV

A. Implementation
public static Color[]
GetColorDiagram(List<ControlPoint> points)
{
Color[] colors = new Color[256];
points.Sort(new PointsComparer());
for (int i = 0; i < 256; i++)
{
ControlPoint leftColor = new ControlPoint(0,
GetNearestLeftColor(points[0].Color));
ControlPoint rightColor = new ControlPoint
(255,
GetNearestRigthColor(points[points.Count -
1].Color));
if (i < points[0].Level)
{
rightColor = points[0];
}
if (i > points[points.Count - 1].Level)
{
leftColor = points[points.Count - 1];
}
else
{
for (int j = 0; j < points.Count - 1; j++)
{
if ((points[j].Level <= i) & (points[j +
1].Level > i))
{
leftColor = points[j];
rightColor = points[j + 1];
}
}
}
if ((rightColor.Level - leftColor.Level) != 0)
{
double koef = (double)(i - leftColor.Level) /
(double)(rightColor.Level - leftColor.Level);
int r = leftColor.Color.R + (int)(koef *
(rightColor.Color.R - leftColor.Color.R));
int g = leftColor.Color.G + (int)(koef *
(rightColor.Color.G - leftColor.Color.G));
int b = leftColor.Color.B + (int)(koef *
(rightColor.Color.B - leftColor.Color.B));
colors[i] = Color.FromArgb(r, g, b);
}
else
{
colors[i] = leftColor.Color;
}
}
return colors;
}
V. HISTOGRAM
In image processing and photography, a color
histogram is a representation of the distribution of
colors in an image. For digital images, a color
histogram represents the number of pixels that have
colors in each of a fixed list of color ranges that span
the image's color space, the set of all possible colors
[5].
The color histogram can be built for any kind of color
space, although the term is more often used for three-
dimensional spaces like RGB or HSV. For
monochromatic images, the term intensity histogram
may be used instead. For multi-spectral images,
where each pixel is represented by an arbitrary
number of measurements (for example, beyond the
three measurements in RGB), the color histogram is
N-dimensional, with N being the number of
measurements taken. Each measurement has its own
wavelength range of the light spectrum, some of
which may be outside the visible spectrum.
A. Histogram Equalization Algorithm
1. Iterate over all the pixels and count the number of
pixels that have a particular intensity
2. Store the results in a table and calculate the
probability of each intensity using Number of
pixels of a particular intensity level / total number
of pixels in the image
3. Perform equalization using T(rk) = (L-1)
Sum[i=0 k] Pr(i) = sk
4. Store the new results in a table and update the
image by substituting the old intensity values by
the new equalized ones.
5. Calculate the histogram distribution of the new
generated image
B. Implementation
distribution = new double[256, 3];
// distribution[0]= # of pixels
// distribution[1]= probability
//distribution[2]= New Intensity level after
Equalization
Bitmap bitmap = new Bitmap(pictureBox1.Image);
for (int i = 0; i < bitmap.Height; i++)
{
for (int j = 0; j < bitmap.Width; j++)
{
int intensity = bitmap.GetPixel(j, i).R;
distribution[intensity, 0]++;
}
}
// working with LISTVIEW
listView1.Items.Clear();
int total = 0;
double totalProbability = 0.0;
for (int i = 0; i < distribution.GetLength(0); i++)
{
distribution[i, 1] = distribution[i, 0] / 87040.0;

total = total + Convert.ToInt32(distribution[i,
0]);
totalProbability = totalProbability +
distribution[i, 1];
// Updating the listview just for illustration
purposes
// i represents the INTENSITY level
ListViewItem item = new ListViewItem(new
string[] { "" + i, "" + distribution[i, 0],
distribution[i, 1].ToString("0.000000"), "" });
listView1.Items.Add(item);
}
listView1.Items.Add(""); // EMPTY row
listView1.Items.Add(new ListViewItem(new string[]{
"Totals:", "" + total, "" + totalProbability, "" }));
Figure 6 is about calculating the Intensity Distribution
prior to historgram equalization which is depicted in
Figure 7.
Figure 6: Calculating the Intensity Distribution
Figure 7: Performing Histogram Equalization
VI. BLURRING & SHARPENING ADJUSTMENT
A Gaussian blur (also known as Gaussian smoothing)
is the result of blurring an image by a Gaussian
function. It is a widely used effect in graphics
software, typically to reduce image noise and reduce
detail. The visual effect of this blurring technique is a
smooth blur resembling that of viewing the image
through a translucent screen, distinctly different from
the bokeh effect produced by an out-of-focus lens or
the shadow of an object under usual illumination.
Gaussian smoothing is also used as a pre-processing
stage in computer vision algorithms in order to
enhance image structures at different scales [7].
Mathematically, applying a Gaussian blur to an image
is the same as convolving the image with a Gaussian
function. This is also known as a two-dimensional
Weierstrass transform. By contrast, convolving by a
circle would more accurately reproduce the bokeh
effect. Since the Fourier transform of a Gaussian is
another Gaussian, applying a Gaussian blur has the
effect of reducing the image's high-frequency
components; a Gaussian blur is thus a low pass filter.
A. Implementation
double[] filter = new double[]{
Convert.ToDouble(textBox1.Text),
Convert.ToDouble(textBox9.Text) };
Bitmap bitmap = (Bitmap)pictureBox1.Image;
Bitmap bitmap2 = new Bitmap(bitmap.Width,
bitmap.Height);
for (int y = 0; y < bitmap.Height; y++)
{
for (int x = 0; x < bitmap.Width; x++)
{
int Rcenter = bitmap.GetPixel(x, y).R;
int R0 = 0;
R0 = bitmap.GetPixel(x - 1, y + 1).R;
int R1 = 0;
R1 = bitmap.GetPixel(x, y + 1).R;
int R2 = 0;
R2 = bitmap.GetPixel(x + 1, y + 1).R;
int R3 = 0;
R3 = bitmap.GetPixel(x - 1, y).R;
int R5 = 0;
R5 = bitmap.GetPixel(x + 1, y).R;
int R6 = 0;
R6 = bitmap.GetPixel(x - 1, y - 1).R;
int R7 = 0;
R7 = bitmap.GetPixel(x, y - 1).R;
int R8 = 0;
R8 = bitmap.GetPixel(x + 1, y - 1).R;
int sum = Convert.ToInt32(((R0 * filter[0]) +
(R1 * filter[1]) +
(R2 * filter[2]) + (R3 * filter[3]) + (Rcenter *
filter[4]) +

(R5 * filter[5]) + (R6 * filter[6]) + (R7 *
filter[7]) +
(R8 * filter[8])) / 9);
if (sum < 0)
sum = 0;
if (sum > 255)
sum = 255;
bitmap2.SetPixel(x, y, Color.FromArgb(sum,
sum, sum));
}
}
pictureBox2.Image = bitmap2;
Figure 8 demonstrates the blurring effect; while,
Figure 9 demonstrates the sharpening effect on a
particular image.
Figure 8: Applying Blurring Effect
Figure 9: Applying Sharpening Effect
VII. BLENDING & FADING TRANSFORMATION
Blending in graphics is about forming a blend of two
input images of the same size. The value of each pixel
in the output image is a linear combination of the
corresponding pixel values in the input images [8].
Below is the algorithm for blending two input images
together:
1. Iterate over all the pixels of both source images
namely image 1 and image 2
2. On each iteration, read the intensity value of a
particular pixel in image 1 and add it to the
intensity value of the corresponding pixel in
image 2 as in pixel(i , image3) = pixel(i , image1) +
pixel(i , image2)
3. Check if the obtained value is larger than 255 then
normalize it to 255 and if the obtained value is
less than 0 (in case of subtraction) then normalize
it to 0
4. Store the resulting value in a 3rd image
5. Upon scanning of all the pixel of both images 1
and 2, a new image 3 will be obtained and it is the
result of image 1 + image 2
A. Implementation
Button button = (Button)sender;
Bitmap bitmap1 = new Bitmap(pictureBox1.Image);
Bitmap bitmap2 = new Bitmap(pictureBox2.Image);
Bitmap bitmap3 = new Bitmap(300, 300);
for (int y = 0; y < bitmap1.Height; y++)
{
for (int x = 0; x < bitmap1.Width; x++)
{
Color color1 = bitmap1.GetPixel(x, y);
Color color2 = bitmap2.GetPixel(x, y);
int R1 = color1.R;
int R2 = color2.R;
int R3 = 0;
if (button.Text == "+")
R3 = R1 + R2;
else if (button.Text == "-")
R3 = R1 - R2;
else if (button.Text == "*")
R3 = R1 * R2;
else if (button.Text == "/")
{
if (R2 != 0)
R3 = R1 / R2;
}
if (R3 > 255)
R3 = 255;
else if (R3 < 0)
R3 = 0;
bitmap3.SetPixel(x, y, Color.FromArgb(R3, R3,
R3));
}
}
pictureBox3.Image = bitmap3;
pictureBox3.Refresh();
Figure 10 demonstrates the blending effect of two
images; while, Figure 11 demonstrates the shading
effect applied by a constant value to an image.

Figure 10: Blending of Two Images
Figure 11: Shading by a Constant
VII. EROSION & DILATION TRANSFORMATION
Erosion is about performing a special processing on a
binary image. We successively place the center pixel
of the structuring element on each foreground pixel
(value 1). If any of the neighborhood pixels are
background pixels (value 0), the foreground pixel is
switched to background. On the other hand, to
perform dilation, we successively place the center
pixel of the structuring element on each background
pixel [9]. If any of the neighborhood pixels are
foreground pixels (value 1), the background pixel is
switched to foreground.
AND operation (Intersection)
Scan both images A and B simultaneously pixel-
by-pixel
if pixelA is black AND pixelB is black
then Set ResultPixel to black
else then Set ResultPixel to white
OR operation (Union)
by-pixel
if pixelA is black OR pixelB is black
NOT operation (Complement)
Scan images A pixel-by-pixel
if pixelA is black
then Set ResultPixel to white
else then Set ResultPixel to black
XOR operation
by-pixel
if pixelA is black AND pixelB is black
then Set ResultPixel to white
else if pixelA is black OR pixelB is black
Difference operation (A-B)
by-pixel
Apply the complement of B
Then Apply the AND operation on A and B
A AND (NOT B)
Boundary Extraction
Apply erosion on A and B
Subtract the result form A (Use logical set
differencing)
A – (A erosion B) [10]
Connected Components
Connected component labeling works by scanning
an image, pixel-by-pixel (from top to bottom and
left to right) in order to identify connected pixel
regions, i.e. regions of adjacent pixels which share
the same set of intensity values V.
When a point p is encountered (p denotes the
pixel to be labeled at any stage in the scanning
process for which V={1}), it examines the four
neighbors of p which have already been
encountered in the scan. Based on this
information, the labeling of p occurs as follows:
If all four neighbors are 0, assign a new label to
p, else
if only one neighbor has V={1}, assign its label to
p, else
if one or more of the neighbors have V={1},
assign one of the labels to p and make a note of
the equivalences.
After completing the scan, the equivalent label
pairs are sorted into equivalence classes and a
unique label is assigned to each class. As a final
step, a second scan is made through the image,
during which each label is replaced by the label
assigned to its equivalence classes [11].
A. Implementation
AND Operation
Bitmap A = (Bitmap)pictureBox1.Image;
Bitmap B = (Bitmap)pictureBox2.Image;
Bitmap C = new Bitmap(319 , 240) ;
for (int i = 0; i < A.Height; i++)

{
for (int j = 0; j < A.Width; j++)
{
int colorA = A.GetPixel(j, i).R;
int colorB = B.GetPixel(j, i).R;
if (colorA < 200 && colorB < 200)
C.SetPixel(j,i,Color.FromArgb(0,0,0)) ;
else
C.SetPixel(j,i,Color.FromArgb(255,255,255)) ;
}
}
pictureBox3.Image = C ;
pictureBox3.Refresh();
Dilation
byte* ptr = (byte*)data.Scan0;
byte* tptr = (byte*)data2.Scan0;
ptr += data.Stride + 3;
tptr += data.Stride + 3;
int remain = data.Stride - data.Width * 3;
for (int i = 1; i < data.Height - 1; i++)
{
for (int j = 1; j < data.Width - 1; j++)
{
if (ptr[0] == 255)
{
byte* temp = tptr - data.Stride - 3;
for (int k = 0; k < 3; k++)
{
for (int l = 0; l < 3; l++)
{
temp[data.Stride * k + l * 3] =
temp[data.Stride * k + l * 3 + 1] =
temp[data.Stride * k + l * 3 + 2] =
(byte)(sElement[k, l] * 255);
}
}
}
ptr += 3;
tptr += 3;
}
ptr += remain + 6;
tptr += remain + 6;
}
bmpimg.UnlockBits(data);
tempbmp.UnlockBits(data2);
bmpimg = (Bitmap)tempbmp.Clone();
pictureBox2.Image = bmpimg;
Figure 12 demonstrates the erosion and dilation
effects when applied to a black and white image.
Likewise, Figure 13 shows the difference logical
operation over a particular image. Finally, Figure 14
shows the boundary extraction effect.
Figure 12: Erosion Morphology
Figure 13: A – B (Difference)
Figure 14: Boundary Extraction
VIII. CONCLUSIONS & FUTURE WORK
This paper proposed the design and implementation
of a set of digital image transformation algorithms
that deal with converting digital images from one
domain to another. The algorithms implemented
were grayscale transformation, contrast and
brightness adjustment, hue and saturation
adjustment, histogram equalization, blurring and
sharpening adjustment, blending and fading
transformation, erosion and dilation transformation,
and finally edge detection and extraction. The
proposed algorithms were implemented using
C#.NET and .NET Framework 3.5.

As future work, the proposed algorithms are to be
reprogrammed to fit in a multiprocessing
environment with the purpose of speeding up their
execution and processing time.
Acknowledgment
This research was funded by the Lebanese
Association for Computational Sciences (LACSC),
Beirut, Lebanon, under the “Parallel Programming
Algorithms Research Project – PPARP2019”.
References
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Image Processing”, 3rd Edition, Prentice Hall,
2007.
[2] Maria Petrou, Costas Petrou, “Image Processing:
The Fundamentals”, 2nd edition, Wiley, 2010
[3] Mike Reed, "Graphic arts, digital imaging and
technology education", THE Journal, vol.21 no.5,
p.69, 2002.
[4] S. Naik and C. Murthy, "Hue-preserving color
image enhancement without gamut problem,"
IEEE Trans, Image Processing, vol. 12, no. 12, pp.
1591–1598, 2003
[5] Kenneth Castleman, “Digital Image Processing”,
Prentice Hall, 1995
[6] N. Bassiou, C. Kotropoulos, "Color image
histogram equalization by absolute discounting
back-off," Computer Vision and Image
Understanding, vol. 107, no. 1-2, pp.108-122,
2007
[7] John C. Russ, “The Image Processing Handbook”,
6th Edition, CRC Press, 2011.
[8] Ronny Richardson, "Digital imaging: The wave of
the future", THE Journal, vol. 31, no.3, 2003
[9] Qi-Yu Liang, et al, "Observation of three-photon
bound states in a quantum nonlinear medium",
Science, vol. 359, no.6377, pp.783–786, 2018
[10] Pietro Perona, Jitendra Malik, "Scale-space and
edge detection using anisotropic diffusion",
Proceedings of IEEE Computer Society
Workshop on Computer Vision, vol.1, pp. 16–22,
1987
[11] Guillermo Sapiro, "Geometric partial differential
equations and image analysis", Cambridge
University Press, 2001

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