Image Thresholding and Error Diffusion: Techniques and Analysis

This is an open-book assessment. This means you may consult your notes, textbooks, and other resources, including calculators, as you see fit. You must submit before the deadline. Allow some spare time for technical submission issues.

This assessment is designed to take 2 hours to complete (maybe a little longer to  account for typing speed). The deadline has been set to give you a longer window

than necessary to allow you time to deal with technical issues, provide some flexibility of starting times, and to help students with disability access plans that require rest breaks and extra time.

It is suggested that you use Microsoft Word (or any other editor of your choice) to type your answers, then save as PDF when you are ready to submit. All submitted text must be word-processed, but you may include images (or photos of hand drawn images) as part of the document.

This is an individual assessment. Under no circumstances are you to discuss any aspect of this assessment with anyone; nor are you allowed to share this document, ideas or solutions with others using email, social media, instant messaging, websites, or any other means. Your attempts at these questions must be entirely your own work. Those found to have collaborated with others will receive a mark of 0.

Given the following 6x3 grey level image (with intensities between 0 and 255):

-------------------------------------

| 110 | 110 | 120 | 130 | 140 | 150 |

| 110 | 110 | 120 | 120 | 150 | 160 |

| 110 | 150 | 160 | 160 | 190 | 190 |

-------------------------------------

conduct thresholding. Clearly show the final black and white image. Find the total intensity of the input image. Compare this to the total intensity of your black and white .

Question 2

Error diffusion Given the following 6x3 grey level image (with intensities between 0 and 255):

-------------------------------------

| 110 | 110 | 120 | 130 | 140 | 150 |

| 110 | 110 | 120 | 120 | 150 | 160 |

| 110 | 150 | 160 | 160 | 190 | 190 |

-------------------------------------

conduct error diffusion dithering. Clearly show the error passed to each pixel and the final black and white image.  Find the total intensity of the input image. Compare this to the total intensity of your black and white image.

We assume that the scene is lit by only white ambient light (intensity=1.0), the background is black (0.0), and all surfaces are of the same colour (0.5 grey). The intensity of each surface and its physical properties are given in the table.

--------------------------------------------------------

| Object | Object Colour | Reflection | Refraction |

| | (grey proportion) | Proportion | Proportion |

--------------------------------------------------------

| S1 | 0.5 | 0.1 (10%) | 0.2 (20%) |

| S2 | 0.5 | 0.6 (60%) | 0.2 (20%) |

| S3 | 0.5 | 0.0 (0%) | 0.8 (80%) |

| S4 | 0.5 | 0.6 (60%) | 0.3 (30%) |

--------------------------------------------------------

What is the light intensity to be drawn at the concerned pixel after ray tracing? Show all the main calculation steps. Which of the following changes to the conditions would result in a different light intensity of the pixel? You do not need to do any calculation, but rather explain your reasoning for any change or lack of change.

 (i) Changing the grey intensity of surface S4;

(ii) Changing the refractive index of surface S1;

(iii) Moving the centre of projection away from the view plane in the opposite direction of the view plane normal;

(iv) Introducing a recursive cut-off by discarding any ray at recursion level 4 or more;