Digital Image Calculations

Homework Content

Equations and Assumptions

Please read about Binary Prefixes.

Memory Conversions

\[\begin{split}1 \textrm { Byte (B)} &= 8 \textrm { Bits (b)} \\ 1000 \textrm { Bytes} &= 1 \textrm { Kilobytes (KB)} \\ 1000 \textrm { Kilobytes (KB)} &= 1 \textrm { Megabytes (MB)} \\ 1024 \textrm { Bytes} &= 1 \textrm { Kibibytes (KiB)} \\ 1024 \textrm { Kibibytes (KiB)} &= 1 \textrm { Mebibytes (MiB)}\end{split}\]

Histogram Normalization

\[g(x, y) = \frac{f(x, y) - f_{min}}{f_{max} - f_{min}} \textrm{bit depth}_{g}\]

Problems

Show all your work clearly with all units and in detail, leading up to the answer:

  1. A digital image consists of 1200 x 1200 pixels.

    1. If it is a 24 bit image, What is the memory required to store this image in MB?

  2. A Satellite image has 7 bands each of 9000 x 9000 pixels and 8 bit radiometric resolution.

    1. What is the total memory needed to store this image in MB?
    2. If this satellite can transmit the image at 10 MB per second, how long will it take to transmit the image to the ground?

  3. The AVIRIS sensor can take an image in 224 bands at 8 bit radiometric resolution.

    1. If each image has 2000 x 2000 pixels, what is the memory required for this image in MB?
    2. If the image can be transmitted at 10 Mb per second, what is the time taken to transmit this image to the ground?

  4. A proposed replacement for the existing AVIRIS sensor would acquire a 14 bit image in 224 bands.

    1. If each image has 2000 x 2000 pixels, what is the memory required for this image in MB?
    2. If the image can be transmitted at 10 MB per second, what is the time taken to transmit this image to the ground?
    3. If each image has 2000 x 2000 pixels, what is the memory required for this image in MiB?
    4. What is the difference between the image size in MB and MiB?
    5. What is the percentage difference between the image size in MB and MiB?

5) A given 8 bit digital image has a maximum pixel value of 187 and a minimum pixel value of 23. What is the 8 bit equalized value of a pixel that has a value of 72?

6) A four by five digital image with a three bit radiometric resolution has pixel values of: 0, 1, 3, 3, 1, 2, 3, 3, 3, 3, 4, 7, 4, 4, 7, 5, 6, 6, 5, 7. Construct a histogram and a cumulative histogram for the given image.

7) A given 8 bit digital image has a maximum pixel value of 180 and a minimum pixel value of 44. What is the 16 bit equalized value of a pixel that has a value of 72?

Metadata

Title:Digital Image Calculations
CreationDate:06/20/2013
ModifiedDate:02/27/2016
SoftwareUsed:None
SoftwareVersion:None