1. Enlarging or Contracting a Digital Image
Zoom, zoom, zoom…

2. Image Resizing
May either increase or decrease the total number of pixels used to represent the image
The process may be viewed as projecting samples from one scale to another
11/30/2018
Gene A. Tagliarini, PhD

3. Pixel Arrays Start with an M row x N column array of image samples
Assume a zoom factor zf so that the number of rows M* and columns N* in the zoomed image are
M* = zf * M
N* = zf * N
11/30/2018
Gene A. Tagliarini, PhD

4. Visualizing An Image Zoom
11/30/2018
Gene A. Tagliarini, PhD

5. More Notation and Conventions
Let (assume Java):
M* = (int) zf * M;
N* = (int) zf * N;
Assume ms and ns are row and column indices of the source, respectively, and that mz and nz are row and column indices, respectively, of the zoomed image
ms ε {0,…,M} and ns ε {0,…,N}
mz ε {0,…,M*} and nz ε {0,…,N*}
11/30/2018
Gene A. Tagliarini, PhD

6. Zooming By Pixel Replication
Map the pixel coordinates (mz, nz) back to the source image coordinates (ms, ns)
ms = (int) (mz/zf)
ns = (int) (nz /zf)
Use the value v of the nearby source image pixel v(ms, ns)
11/30/2018
Gene A. Tagliarini, PhD

7. Visualizing An Image Zoomnz mz m n
11/30/2018
Gene A. Tagliarini, PhD

8. Pixel Replication Uses a neighbor of the contracted representation
May give rise to a pixelated representation
11/30/2018
Gene A. Tagliarini, PhD

9. A Useful Parametric Form
Let:
a and b be constants with a < b
x ε [0, 1]
y = a + (b-a) * x
Note
y(0) = a
y(1) = b
If x ε (0, 1), then a < y < b a b
y(x)
11/30/2018
Gene A. Tagliarini, PhD

10. Extending A Useful Parametric Form
Let:
a and b be vectors
x ε [0, 1] is scalar
y = a + (b-a) * x
Note
y(0) = a
y(1) = b
If x ε (0, 1), then y lies “between” a and b in the plane determined by a and b
b-a y b a
11/30/2018
Gene A. Tagliarini, PhD

11. Bilinear Interpolation
Zoomed pixel at (mz, nz)
When mapped back to the source image coordinates likely lies in a region bounded by 4 original image pixels (ms, ns) (ms+1, ns) (ms, ns+1) (ms+1, ns+1)
Where
ms = (int) (mz/zf)
ns = (int) (nz /zf)
11/30/2018
Gene A. Tagliarini, PhD

12. Bilinear Interpolation (continued)
The intensity of pixel P can be calculated given the intensities of pixels A, B, C, and D, with scalars x, y ε [0, 1] using:
E = A + (B-A)*x
F = C + (D-C)*x
P = E + (F-E)*y ms ns
ms+1
ns+1 A B C D P x nz F E mz y
11/30/2018
Gene A. Tagliarini, PhD

13. Bilinear Interpolation (continued)F E
11/30/2018
Gene A. Tagliarini, PhD