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Basic I mage ManipulationPowerPoint Presentation

Basic I mage Manipulation

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Agenda

- Region of Interest (ROI)
- Basic geometric manipulation.
- Enlarge
- shrink
- Reflection

- Arithmetic and logical combination of images.
- Addition and averaging.
- Subtraction.
- Division.
- AND & OR.

- Transformation and Rotation

Region of Interest (ROI)

- A region of interest (ROI) is a rectangular area within the image, defined either by the coordinates of the pixels at its upper-left and lower-right corners or by the coordinates of its upper-left corner and its dimensions.

Basic Geometric Manipulation.

Enlargingor shrinking an image can be accomplished by replicating or skipping pixels. These techniques can be used to magnify small details in an image, or reduce a large image in size so that it fits on the screen. They have the advantage of being fast, but can only resize an image by an integer factor.

Basic Geometric Manipulation.

Enlarge:

To enlarge an image by an integer factor n, we must replicate pixels such that each pixel in the input image becomes an n x n block of identical pixels in the output image. The most straightforward implementation of this involves iterating over the pixels in the larger output image and computing the coordinates of the input image pixel from which a value must be taken. For a pixel (x, y) in the output image, the corresponding pixel in the input image is at (x/n, y/n). Calculation of the coordinates is done using integer arithmetic.

Basic Geometric Manipulation.

ALGORITHM Image_Enlarge 3.1

01 INPUT Image, n

02 OUTPUTEnlargeImage

03 BEGIN

04 Create new image EnlargeImage; // with multiple size (n);

05 For each row in EnlargeImage

06 For each column in EnlargeImage

07 SETEnlargeImage(column,row) = Image(column/n,row/n)

08 END For

09 END For

10 RETURN EnlargeImage;

11 END

Basic Geometric Manipulation.

Shrink:

To shrink an image by an integer factor n, we must sample every nthpixel in the horizontal and vertical dimensions and ignore the others. Again, this technique is most easily implemented by iterating over pixels in the output image and computing the coordinates of the corresponding input image pixel.

Basic Geometric Manipulation.

ALGORITHM Image_Shrink 3.2

01 INPUT Image, n

02 OUTPUTShrinkImage

03 BEGIN

04 Create new image ShrinkImage; // with divided size (n)

05 For each row in ShrinkImage

06 For each column in ShrinkImage

07 SETShrinkImage(column,row) = Image(column*n, row*n);

08 END For

09 END For

10 RETURN ShrinkImage;

11 END

Basic Geometric Manipulation.

Reflection:

Reflection along either of the image axes can also be performed in place. This simply involves reversing the ordering of pixels in the rows or columns of the image.

Basic Geometric Manipulation.

ALGORITHM Image_Vertical_ Refliction 3.3

01 INPUT Image

02 OUTPUTReflectionImage

03 BEGIN

04 Create new image ReflectionImage;

05 SET W = Image Width;

06 For each row in Image

07 For each column in Image

08 SETReflectionImage(column,row) = Image(W – column – 1,row);

09 END For

10 END For

11 RETURN ReflectionImage;

12 END

Arithmetic and logical combination of images.

Addition and averaging:

I f we add two 8-bit greyscale images, then pixels in the resulting image can have values in the range0 - 510. We should therefore choose a 16-bit representation for the output image or divide every pixel's value by two. If we do the latter, then we are computing an average of the two images.

g(x,y) = αf1(x,y) + (1 - α)f2(x,y)

Arithmetic and logical combination of images.

α = 0%

α = 0%

α = 0%

α = 0%

α = 0%

α = 0%

α = 0%

α = 100%

α = 50%

α = 50%

α = 100%

α = 0%

Arithmetic and logical combination of images.

ALGORITHM Image_Addition_Averaging 3.4

01 INPUTImage1, Image2, α

02 OUTPUTAddintionImage

03 BEGIN

04 Create new image AddintionImage;

06 For each row in Image1 and Image2

07 For each column in Image1 and Image2

08 SETAddintionImage(column,row) = α * Image1(column,row) + ( 1 - α ) * Image2(column,row);

09 END For

10 END For

11 RETURN AddintionImage;

12 END

Arithmetic and logical combination of images.

Subtraction:

Subtracting two 8-bit greyscale images can produce values between -255 and +255. This necessitates the use of 16-bit signed integers in the output image unless sign is unimportant, in which case we can simply take the modulus of the result and store it using 8-bit integers:

g(x,y) = |f1(x,y) - f2(x,y)|

Arithmetic and logical combination of images.

ALGORITHM Image_Subtraction 3.5

01 INPUTImage1, Image2

02 OUTPUTSubtractionImage

03 BEGIN

04 Create new image SubtractionImage;

06 For each row in Image1 and Image2

07 For each column in Image1 and Image2

08 SETSubtractionImage(column,row) = | Image1(column,row) - Image2(column,row) |;

09 END For

10 END For

11 RETURN SubtractionImage;

12 END

Arithmetic and logical combination of images.

Subtraction:

Arithmetic and logical combination of images.

Division:

For division of images to produce meaningful results, floating-point arithmetic must be used. The ratio image can be of the floating-point type, or we can rescale and round pixel values to be in a more convenient 0-255 range.

Arithmetic and logical combination of images.

ALGORITHM Image_Division3.5

01 INPUTImage1, Image2

02 OUTPUTDivisionImage

03 BEGIN

04 Create new image DivisionImage;

06 For each row in Image1 and Image2

07 For each column in Image1 and Image2

08 SETDivisionImage(column,row) = Rescale(Image1(column,row) / Image2(column,row));

09 END For

10 END For

11 RETURN DivisionImage;

12 END

Arithmetic and logical combination of images.

AND & OR:

Logical AND andOR operations are useful for the masking and compositing of images. For example, if we compute the AND of a binary image with some other image, then pixels for which the corresponding value in the binary image is 1 will be preserved, but pixels for which the corresponding binary value is 0 will be set to 0 themselves. Thus the binary image acts as a 'mask' that removes information from certain parts of the image.

Arithmetic and logical combination of images.

ALGORITHM Image_AND 3.6

01 INPUTImage1, Image2

02 OUTPUTANDImage

03 BEGIN

04 Create new image ANDImage;

06 For each row in Image1 and Image2

07 For each column in Image1 and Image2

08 SETANDImage(column,row) = Image1(column,row) AND Image2(column,row);

09 END For

10 END For

11 RETURN ANDImage;

12 END

Arithmetic and logical combination of images.

ALGORITHM Image_OR 3.7

01 INPUTImage1, Image2

02 OUTPUTORImage

03 BEGIN

04 Create new image ORImage;

06 For each row in Image1 and Image2

07 For each column in Image1 and Image2

08 SETORImage(column,row) = Image1(column,row) OR Image2(column,row);

09 END For

10 END For

11 RETURN ORImage;

12 END

Transformation and Rotation

ALGORITHM Image_Transformation 3.8

01 INPUTImage, Tx ,Ty

02 OUTPUTTransformationImage

03 BEGIN

04 Create new image TransformationImage;

06 For each row in Image

07 Foreach column in Image

08 SETNewCol = column + Tx;

09 SETNewRow= row + Ty;

10 SETTransformationImage(NewCol,NewRow) = Image(column,row);

11 END For

12 END For

13 RETURN TransformationImage;

14 END

Transformation and Rotation

Transformation and Rotation

- The pixel at (0, 100) after a 90° rotation
- The pixel at (50, 0) after a 35° rotation
x' = x cosθ - y sin θ = 50 cos(35o ) = 40.96,

y' = x sin θ + y cosθ = 50 sin(35o ) = 28.68.

In case 1, cos 90' is 0 and sin 90' is 1, so the pixel moves to coordinates (-100,0). This is clearly a problem, since pixels cannot have negative coordinates. Case 2 illustrates a different problem.

Transformation and Rotation

The first problem can be solved by testing coordinates to check that they lie within the bounds of the output image before attempting to copy pixel values. A simple solution to the second problem is to find the nearest integers to x' and y' and use these as the coordinates of the transformed pixel.

Transformation and Rotation

ALGORITHM Image_Rotation3.9

01 INPUTImage, θ

02 OUTPUTRotationImage

03 BEGIN

04 Create new image RotationImage;

05 SETa0= Cos(θ), b0= Sin(θ), a1= - b0, b1= a0;

06 For each row in Image

07 Foreach column in Image

08 SETNewCol = Round(a0 * column + a1 * row);

09 SETNewRow= Round(b0* column + b1* row);

10 IFNewColANDNewRowinside RotationImageTHEN

11 SETRotationImage(NewCol,NewRow) = Image(column,row);

12 END IF

13 END For

14 END For

15 RETURN RotationImage;

16 END

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