Image Rotation and Error Evaluation Solution

$30.00

Description

Write a program that loads in an image and repeatedly rotates it by x degrees until the image has been rotated 360⁰ in total.

Your program should include the following:

A parameter for the angle to rotate by at each step

A function for multiplying two arbitrary nxm matrices (n and m should be dynamic)

• A rotation matrix of the format below. Each pixel in the image must be multiplied by R

cos

sin

using the matrix multiplication function (prior bullet).

= sin

cos

  • An array variable for your image that is large enough for the entire image to be visible during all the intermediate rotations (when you’ve rotated 45⁰, the corners of your image should not be clipped)

  • Absolute color error calculation: Code to compute the absolute error between the colors of the original image’s pixels and the colors of the image after it’s been rotated 360⁰

  • Pixel displacement calculation: Code to compute the distance each pixel moves during rotation. This total value should be divided by:

(numPixelsInImage * numTimesImageWasRotated)

You can use the OpenCV and Numpy libraries for opening, displaying, and saving images and to create empty arrays/images. You may also use the math library built into Python for sine, cosine, and PI calculations. You may not use any other built-in functions or libraries.

Submit your code and a report. Your report must be a PDF and contain the following:

  • Summary of the assignment goals

  • 3+ images showing your code at intermediate stages (image rotated x degrees) with captions saying what angle stepsize is being used and the total rotation of the image so far (i.e. Image rotated 60⁰ with steps of 20⁰, 3 rotation operations applied so far.)

  • A chart with the following information filled in:

Angle Step Size

# Rotations

Absolute Color Error

Pixel Displacement

(# Rotations) * (Pixel

Displacement)

45⁰

8

60⁰

6

90⁰

4

120⁰

3

180⁰

2

360⁰

1

  • Conclusions drawn from the completed chart

  • Discussion of any issues encountered