Dev C++ Arithmetic Operation Area

Goal

• Learn several arithmetic operations on images, like addition, subtraction, bitwise operations, and etc.

Math Operations. Before reading this tutorial, you should learn about variables and input values using cin. BASIC OPERATORS. In any language, there are some operators to perform arithmetic, logical and control operations. The basic operators which are used to perform arithmetic operations.

You can add two images with the OpenCV function, cv.add(), or simply by the numpy operation res = img1 + img2. Both images should be of same depth and type, or the second image can just be a scalar value.

Note
There is a difference between OpenCV addition and Numpy addition. OpenCV addition is a saturated operation while Numpy addition is a modulo operation.

For example, consider the below sample:

>>> y = np.uint8()
>>> print( cv.add(x,y) ) # 250+10 = 260 => 255


This will be more visible when you add two images. Stick with OpenCV functions, because they will provide a better result.

Image Blending

This is also image addition, but different weights are given to images in order to give a feeling of blending or transparency. Images are added as per the equation below:

[g(x) = (1 - alpha)f_{0}(x) + alpha f_{1}(x)]

By varying (alpha) from (0 rightarrow 1), you can perform a cool transition between one image to another.

Here I took two images to blend together. The first image is given a weight of 0.7 and the second image is given 0.3. cv.addWeighted() applies the following equation to the image:

[dst = alpha cdot img1 + beta cdot img2 + gamma]

Here (gamma) is taken as zero.

cv.imshow('dst',dst)
cv.destroyAllWindows()

Check the result below:

Bitwise Operations

This includes the bitwise AND, OR, NOT, and XOR operations. They will be highly useful while extracting any part of the image (as we will see in coming chapters), defining and working with non-rectangular ROI's, and etc. Below we will see an example of how to change a particular region of an image.

I want to put the OpenCV logo above an image. If I add two images, it will change the color. If I blend them, I get a transparent effect. But I want it to be opaque. If it was a rectangular region, I could use ROI as we did in the last chapter. But the OpenCV logo is a not a rectangular shape. So you can do it with bitwise operations as shown below:

# I want to put logo on top-left corner, So I create a ROI
roi = img1[0:rows, 0:cols]
# Now create a mask of logo and create its inverse mask also
ret, mask = cv.threshold(img2gray, 10, 255, cv.THRESH_BINARY)
# Take only region of logo from logo image.
cv.waitKey(0)

See the result below. Left image shows the mask we created. Right image shows the final result. For more understanding, display all the intermediate images in the above code, especially img1_bg and img2_fg.

Exercises

1. Create a slide show of images in a folder with smooth transition between images using cv.addWeighted function
Once introduced to variables and constants, we can begin to operate with them by using operators. What follows is a complete list of operators. At this point, it is likely not necessary to know all of them, but they are all listed here to also serve as reference.

Assignment operator (=)

The assignment operator assigns a value to a variable.
This statement assigns the integer value 5 to the variable x. The assignment operation always takes place from right to left, and never the other way around:

This statement assigns to variable x the value contained in variable y. The value of x at the moment this statement is executed is lost and replaced by the value of y.
Consider also that we are only assigning the value of y to x at the moment of the assignment operation. Therefore, if y changes at a later moment, it will not affect the new value taken by x.
For example, let's have a look at the following code - I have included the evolution of the content stored in the variables as comments:
This program prints on screen the final values of a and b (4 and 7, respectively). Notice how a was not affected by the final modification of b, even though we declared a = b earlier.
Assignment operations are expressions that can be evaluated. That means that the assignment itself has a value, and -for fundamental types- this value is the one assigned in the operation. For example:

In this expression, y is assigned the result of adding 2 and the value of another assignment expression (which has itself a value of 5). It is roughly equivalent to:
With the final result of assigning 7 to y.
The following expression is also valid in C++:

It assigns 5 to the all three variables: x, y and z; always from right-to-left.

Arithmetic operators ( +, -, *, /, % )

The five arithmetical operations supported by C++ are:
operatordescription
-subtraction
*multiplication
/division
%modulo

Operations of addition, subtraction, multiplication and division correspond literally to their respective mathematical operators. The last one, modulo operator, represented by a percentage sign (%), gives the remainder of a division of two values. For example:
results in variable x containing the value 2, since dividing 11 by 3 results in 3, with a remainder of 2.

Compound assignment (+=, -=, *=, /=, %=, >>=, <<=, &=, ^=, =)

Compound assignment operators modify the current value of a variable by performing an operation on it. They are equivalent to assigning the result of an operation to the first operand:
expressionequivalent to...
y += x;y = y + x;
x -= 5;x = x - 5;
x /= y;x = x / y;
price *= units + 1;price = price * (units+1);

and the same for all other compound assignment operators. For example:

Increment and decrement (++, --)

Some expression can be shortened even more: the increase operator (++) and the decrease operator (--) increase or reduce by one the value stored in a variable. They are equivalent to +=1 and to -=1, respectively. Thus:
are all equivalent in its functionality; the three of them increase by one the value of x.

Dev C++ Arithmetic Operation Area Map

In the early C compilers, the three previous expressions may have produced different executable code depending on which one was used. Nowadays, this type of code optimization is generally performed automatically by the compiler, thus the three expressions should produce exactly the same executable code.
A peculiarity of this operator is that it can be used both as a prefix and as a suffix. That means that it can be written either before the variable name (++x) or after it (x++). Although in simple expressions like x++ or ++x , both have exactly the same meaning; in other expressions in which the result of the increment or decrement operation is evaluated, they may have an important difference in their meaning: In the case that the increase operator is used as a prefix (++x) of the value, the expression evaluates to the final value of x, once it is already increased. On the other hand, in case that it is used as a suffix (x++), the value is also increased, but the expression evaluates to the value that x had before being increased. Notice the difference:
Example 1Example 2
x = 3;
y = ++x;
// x contains 4, y contains 4
x = 3;
y = x++;
// x contains 4, y contains 3

In Example 1, the value assigned to y is the value of x after being increased. While in Example 2, it is the value x had before being increased.

Relational and comparison operators ( , !=, >, <, >=, <= )

Two expressions can be compared using relational and equality operators. For example, to know if two values are equal or if one is greater than the other.
The result of such an operation is either true or false (i.e., a Boolean value).
The relational operators in C++ are:
operatordescription
Equal to
!=Not equal to
<Less than
>Greater than
<=Less than or equal to
>=Greater than or equal to

Here there are some examples:

Of course, it's not just numeric constants that can be compared, but just any value, including, of course, variables. Suppose that a=2, b=3 and c=6, then:
Be careful! The assignment operator (operator

C++ Arithmetic Operators

=, with one equal sign) is not the same as the equality comparison operator (operator , with two equal signs); the first one (=) assigns the value on the right-hand to the variable on its left, while the other () compares whether the values on both sides of the operator are equal. Therefore, in the last expression ((b=2) a), we first assigned the value 2 to b and then we compared it to a (that also stores the value 2), yielding true.

Logical operators ( !, &&, )

The operator ! is the C++ operator for the Boolean operation NOT. It has only one operand, to its right, and inverts it, producing false if its operand is true, and true if its operand is false. Basically, it returns the opposite Boolean value of evaluating its operand. For example:

The logical operators && and are used when evaluating two expressions to obtain a single relational result. The operator && corresponds to the Boolean logical operation AND, which yields true if both its operands are true, and false otherwise. The following panel shows the result of operator && evaluating the expression a&&b:
&& OPERATOR (and)
aba && b
truetruetrue
truefalsefalse
falsetruefalse
falsefalsefalse

The operator corresponds to the Boolean logical operation OR, which yields true if either of its operands is true, thus being false only when both operands are false. Here are the possible results of a b:
OPERATOR (or)
aba b
truetruetrue
truefalsetrue
falsetruetrue
falsefalsefalse

For example:
When using the logical operators, C++ only evaluates what is necessary from left to right to come up with the combined relational result, ignoring the rest. Therefore, in the last example ((55) (3>6)), C++ evaluates first whether 55 is true, and if so, it never checks whether 3>6 is true or not. This is known as short-circuit evaluation, and works like this for these operators:
operatorshort-circuit
&&if the left-hand side expression is false, the combined result is false (the right-hand side expression is never evaluated).
if the left-hand side expression is true, the combined result is true (the right-hand side expression is never evaluated). This is mostly important when the right-hand expression has side effects, such as altering values:

Here, the combined conditional expression would increase i by one, but only if the condition on the left of && is true, because otherwise, the condition on the right-hand side (++i<n) is never evaluated.

Conditional ternary operator ( ? )

The conditional operator evaluates an expression, returning one value if that expression evaluates to true, and a different one if the expression evaluates as false. Its syntax is:
condition ? result1 : result2
If condition is true, the entire expression evaluates to result1, and otherwise to result2.
For example:

In this example, a was 2, and b was 7, so the expression being evaluated (a>b) was not true, thus the first value specified after the question mark was discarded in favor of the second value (the one after the colon) which was b (with a value of 7).

Comma operator ( , )

The comma operator (,) is used to separate two or more expressions that are included where only one expression is expected. When the set of expressions has to be evaluated for a value, only the right-most expression is considered.
For example, the following code:
would first assign the value 3 to b, and then assign b+2 to variable a. So, at the end, variable a would contain the value 5 while variable b would contain value 3.

Bitwise operators ( &, , ^, ~, <<, >> )

Bitwise operators modify variables considering the bit patterns that represent the values they store.
operatorasm equivalentdescription
&ANDBitwise AND
ORBitwise inclusive OR
^XORBitwise exclusive OR
~NOTUnary complement (bit inversion)
<<SHLShift bits left
>>SHRShift bits right

Explicit type casting operator

Type casting operators allow to convert a value of a given type to another type. There are several ways to do this in C++. The simplest one, which has been inherited from the C language, is to precede the expression to be converted by the new type enclosed between parentheses (()):

The previous code converts the floating-point number 3.14 to an integer value (3); the remainder is lost. Here, the typecasting operator was (int). Another way to do the same thing in C++ is to use the functional notation preceding the expression to be converted by the type and enclosing the expression between parentheses:
Both ways of casting types are valid in C++.

sizeof

This operator accepts one parameter, which can be either a type or a variable, and returns the size in bytes of that type or object:

Here, x is assigned the value 1, because char is a type with a size of one byte.
The value returned by sizeof is a compile-time constant, so it is always determined before program execution.

Other operators

Later in these tutorials, we will see a few more operators, like the ones referring to pointers or the specifics for object-oriented programming.

Precedence of operators

A single expression may have multiple operators. For example:
In C++, the above expression always assigns 6 to variable x, because the % operator has a higher precedence than the + operator, and is always evaluated before. Parts of the expressions can be enclosed in parenthesis to override this precedence order, or to make explicitly clear the intended effect. Notice the difference:

From greatest to smallest priority, C++ operators are evaluated in the following order:
LevelPrecedence groupOperatorDescriptionGrouping
1Scope::scope qualifierLeft-to-right
2Postfix (unary)++ --postfix increment / decrementLeft-to-right
()functional forms
[]subscript
. ->member access
3Prefix (unary)++ --prefix increment / decrementRight-to-left
~ !bitwise NOT / logical NOT
+ -unary prefix
& *reference / dereference
new deleteallocation / deallocation
sizeofparameter pack
(type)C-style type-casting
4Pointer-to-member.* ->*access pointerLeft-to-right
5Arithmetic: scaling* / %multiply, divide, moduloLeft-to-right
7Bitwise shift<< >>shift left, shift rightLeft-to-right
8Relational< > <= >=comparison operatorsLeft-to-right
9Equality !=equality / inequalityLeft-to-right
10And&bitwise ANDLeft-to-right
11Exclusive or^bitwise XORLeft-to-right
12Inclusive orbitwise ORLeft-to-right
13Conjunction&&logical ANDLeft-to-right
14Disjunctionlogical ORLeft-to-right
15Assignment-level expressions= *= /= %= += -=
>>= <<= &= ^= =
assignment / compound assignmentRight-to-left
?:conditional operator
16Sequencing,comma separatorLeft-to-right

When an expression has two operators with the same precedence level, grouping determines which one is evaluated first: either left-to-right or right-to-left.

Arithmetic Operation Examples

Enclosing all sub-statements in parentheses (even those unnecessary because of their precedence) improves code readability.

C++ Arithmetic Examples

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