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EEE2048: Computer Algorithms and Architecture 2018/19 ProgrammingAssignment

Quadtree Encoding of a BinaryImage


Deadline for Submission to SurreyLearn: 4:00pm, Tuesday 4th December 2018


Introduction

Silhouettes contain much of the shape information necessary to recognise simple objects. For this reason they have been used widely in machine vision systems that check the shape of industrial parts or provide grasping information to robots. The digital version of a silhouette is a binary image

i.e. an array of 1's and 0's. Figure 1 shows a digital image. In a binary image version of this, 0 represents a dark area and 1 represents a light area. The positions of pixels are defined with respect to the coordinate system shown in the figure.

A significant problem of image processing is the large amount of storage needed for image data and the consequent computational load of performing calculations on large numbers of pixels. There has therefore been much effort in developing data representations or codings which are more compact but still capture the relevant features of the data. One promising data structure is the quadtree. The quadtree encoding of the binary image shown in Figure 1 is given in Figure 2.

 

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Figure 1: Binary image array

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Figure 2: Quadtree corresponding to binary image array

 

Quadtrees are created from images whose sizes are integer powers of 2. Each node of the quadtree corresponds to a square area in the binary image. The node at level 0 of the tree corresponds to the whole image area. Child nodes correspond to the areas given by dividing the image into 4 non-overlapping quadrants. The quadrants are denoted NW (north-west), NE (north- east), SE (south-east) and SW (south-west) respectively, as shown in the inset part of Figure 1. Nodes at lower levels of the tree again correspond to splitting of parent areas into smaller quadrants. Each node is labelled to indicate the type of pixels contained within its area. Three labels are distinguished: W for white (all pixels in area are of value 1), B for black (all pixels in area are of value 0) and G for grey (area contains both pixels of value 1 and pixels of value 0). Splitting of areas into sub-quadrants terminates when nodes contain only one type of pixel i.e. when nodes are labelled B or W. The resultant data structure generally contains far fewer nodes than the number of pixels in the original image. Nodes near the root of the tree correspond to large blocks  of the image and if the binary image contains objects which are large and convex then they will be represented naturally by few nodes.

 

Programming Task

The programming assignment consists of writing procedures which will

1. Read a square binary image from a text file into an array structure,

2. Generate a pointer based quadtree from the binary image,

3. Traverse through the pointer based quadtree and print out for each black terminal node the position of the top left of the quadrant and its size.

The program must read the image data from a text file which contains coded information on the size of the image and the number and position of black pixels in the image. The image file contains


integers and the file has the following format: image width in pixels

number of black pixels

x y location of each black pixel

 

For the example of the image in Figure 1, the file would contain the data shown in Figure 3. You can assume that the image size will never exceed 64 columns by 64 rows.

 

8

15

4 1

5 1

2 2

3 2

4 2

5 2

2 3

3 3

4 3

5 3

4 4

5 4

6 4

4 5

5 5

Figure 3: Input file example

 

Use an integer array as an intermediate data structure to help in generating the pointer based quadtree. Producing the pointer based quadtree involves taking the array and generating a node  to represent it. The array can then be tested for colour uniformity. If it is not of a uniform colour  then the array must be divided into four quadrants and nodes created for these. Each quadrant must then be tested and the same process recursively performed until all terminal nodes of the tree represent uniformly coloured areas. Internally your program should represent each node of the quadtree as a struct datatype containing 9 fields. The first five pieces of information are pointers to the parent, P, and four children of the node (NW, NE, SE, SW), the next piece of information is the colour of the node (i.e. B, W or G), and the final three pieces of information are the size and the location of the block of pixels that the node represents (the location is represented by the coordinates of the top left pixel of that block).


Input parameters

Your program should read data from a file with path specified using a command line parameter. This parameters should be the only parameter expected by the program, and should be required to be specified immediately after the executable name at run-time e.g. quadtree my_image.txt

The input file will contain the image data in a format as illustrated in Figure 3 and in the example file input.txt provided on SurreyLearn.

 

Output data

Your program should print out on the screen the list of all terminal black nodes. The output should indicate for each black terminal node the position of the top left of the quadrant and its size. For example, the output of processing the example file input.txt provided on SurreyLearn is shown in Figure 4. It should be noted that there is no specific requirement in terms of the order in which the black terminal nodes are printed out. Therefore any output where the lines shown in Figure 4 are permuted would be equally valid.

 

Black terminal node at position (2,2) with size 2 Black terminal node at position (4,1) with size 1 Black terminal node at position (5,1) with size 1 Black terminal node at position (4,2) with size 2 Black terminal node at position (4,4) with size 2 Black terminal node at position (6,4) with size 1

 

Figure 4: Example screen output when processing input file shown in Figure 3

 

Coding standards

All programs should be clearly structured with good indentation to indicate the structure. Aim to make all code largely self-documenting. Comments should indicate the purpose and means of implementation of each program section. Procedures should be kept self-contained with well- defined interfaces to other procedures. Each procedure should contain a commented header explaining:

· The purpose of the procedure or function,

· The description of all input and output parameters.

 

Deliverables

When trying to solve a problem using a computer, the major effort should be directed at the design of the algorithm and choice of the best data structures. Actual coding is only a small part of the exercise. The deliverables for the project will be:


1) A short writtenreport

The report should include:

· The design of the program. It should define what the program and its functions do and what assumptions or restrictions are made on its use. It should include a description of the purpose and functionality of each function. It should give a brief structural description of the program with a simple top-down structured diagram which indicates the inter-relationship of functions (calling hierarchy). It should also describe to a naïve user how to run the program.

· A section presenting example results of the run of the program. This should demonstrate the correct operation of the program on a range of input images.

 

The report should not exceed 4 pages in length (excluding the cover page and table of contents). Any pages beyond 4 will be ignored for assessment purposes. The report should be submitted to SurreyLearn in pdf format.

 

2) C source codeprograms


These should be submitted to SurreyLearn. Submitted files should include quadtree.c and any necessary header files included from the C code that are not standard C header files.

 

The code must be capable of being compiled using the Linux machines in the Otter lab. If students develop code elsewhere then they will need to ensure it meets this requirement prior to submitting it.


Assessment Criteria

Criteria for the assessment of the coursework are: clarity of program description, inclusion of suitable results, appropriate analysis of results, and presentation.

 

Assessment of the code will involve a mix of automated test procedures and human assessment. Checking will test for compilation warnings and errors, run-time errors and correctness of information. Human assessment will consider structure, design and clarity of the solution. Aspects which the human marker will pay attention to include: modularity of solution, internal re-use of code, good commenting of code, sensible and clear layout, avoidance of global declarations, appropriate use of data-types, good error checking, easily understandable output and efficiency of implementation. You should aim to make the code easy to use and modify. Accuracy of output will be checked manually, therefore you need not worry about formatting the output to exactly match the example provided above (for example, white space or carriage return characters), as long as your program clearly returns the expected information.

 

You must work individually and independently to develop the code and produce the report. Source code will be compared using TurnItIn to check that it is original code and has not been written in collaboration with other students.


Marking Scheme


Criteria

Maximum marks

Explanation

Tests: Compilation

5

Code compiles cleanly without errors or warnings

Tests: Execution

5

Code executes cleanly for a variety of test cases,

including “no data” and “bad-data”

Tests: Accuracy of output results

20

Results are output correctly for a variety of test cases, including all the information specified (4 tests will be performed with a maximum of 5 marks

allocated to each test)

Code: Modularisation

5

Code is broken down into sensible functions

Code: Variables

5

Appropriate data types used, global variables avoided where possible, any dynamically allocated

memory is freed

Code: Error checking

5

Anticipated errors such as incorrect data, file

access problems or failure for calls to malloc are handled so that the program exits cleanly

Code: Control flow

5

Flow through the program is correct, there are no

unnecessary loops or blocks of code

Code: Code commenting

5

Comments are thorough and explain all key

aspects of processing

Code: Function headers

5

Comment blocks are included at the top of each

function as specified

Code: Code layout

5

Code is indented appropriately so that code in a

given block is aligned and indented. Refer to C code in lecture notes as a guide

Report: presentation

10

General presentation of the report including structure, formatting, writing style and use of

figures/tables as appropriate

Report: description of program design

15

Description of the program and of the purpose and functionality of each function including diagram indicating the inter-relationship of functions (calling

hierarchy).

Report: program testing

10

Example results illustrating the operation of the program on a range of pertinently chosen input test

images.


Tips


* Remember   the   steps   in    problem    solving    using    computers:    defining    the  problem, outlining a solution, developing an algorithm, programming the algorithm and testing the program.

 

* Feel free to discuss the problem with your fellow students or in a tutorial. However, exchange of ideas is very different from copying of code and the latter is strongly discouraged and will be dealt with via the University procedures for academic misconduct.

 

* Do the bookwork first - make sure that your algorithm is correct, and familiarise yourself with its behaviour, before you start to code it.

 

* Design your program on paper before starting to work on the computer. Only with considerable experience is it possible to hand-craft code directly into the editor, and even then the probability of success is considerably diminished.

 

* In the early stages of testing include extra diagnostic statements in your code so that you can confirm in the initial stages that your algorithm is working as expected.


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