COMPUTER PROBLEM-SOLVING IN



Computer Problem-Solving in EGR 141

Engineering and Computer Science Fall 2006

PROBLEM-SOLVING EXERCISE #5

NOISE AND FILTERING -- SOLUTION

IN MANY CASES, DATA CONTAIN NOISE. THIS NOISE MAY BE PROHIBITIVE TO INTERPRETING THE DATA INTO USEFUL, ACCURATE INFORMATION. NOISE CAN COME IN SEVERAL FORMS, AN ANOMALY FROM THE OUTPUT OF A SENSOR, NOISE WITH A NORMAL DISTRIBUTION, SALT AND PEPPER NOISE, DISTORTION AT A PARTICULAR FREQUENCY, AND OTHERS. FILTER CAN BE USED TO REMOVE OR REDUCE THE NOISE. USING FILTERS, YOU CAN ALSO REMOVE OR ALTER DATA THAT DOESN’T HAVE NOISE AND CREATE ‘NOISE’ OR SPECIAL EFFECTS. IN THIS PROBLEM SOLVING EXERCISE WE WILL USE SOME BASIC METHODS TO FILTER NOISE FROM DATA, INCLUDING FILTERING AN IMAGE.

PART A

FOR EACH OF THE FOLLOWING TABLES OF VALUES COMING FROM A SENSOR, WOULD IT BE BEST TO USE THE VALUES, THE FIRST DERIVATIVE, OR THE SECOND DERIVATIVE TO THRESHOLD NOISE? EXPLAIN. APPLY THE METHOD YOU CHOSE AND IDENTIFY THE THRESHOLD RULE (I.E. IF X > Y OR X < Y THEN NOISE)

i. ii.

|Sensor |First |Second |

|values |Deriv. |Deriv. |

|100 | | |

| |>2 | |

| |>2 |>0 |

| |>1 |>-1 |

| |>2 |>1 |

| |>1 |>-1 |

| |>7 |>6 |

| |>-5 |>-12 |

| |>2 |>7 |

| |>1 |>-1 |

| |>2 |>1 |

|102 | | |

|104 | | |

|105 | | |

|107 | | |

|108 | | |

|115 | | |

|110 | | |

|112 | | |

|113 | | |

|115 | | |

|Sensor |First |Second |

|values |Deriv. |Deriv. |

|235 | | |

| |>5 | |

| |>6 |>1 |

| |>-5 |>-11 |

| |>13 |>18 |

| |>9 |>-4 |

| |>10 |>1 |

| |>11 |>1 |

| |>12 |>1 |

| |>13 |>1 |

| |>14 |>1 |

|240 | | |

|246 | | |

|241 | | |

|254 | | |

|263 | | |

|273 | | |

|284 | | |

|296 | | |

|309 | | |

|323 | | |

FOR BOTH I. AND II., THE VALUES ARE INCREASING AND THEREFORE DO NOT LEND THEMSELVES TO A THRESHOLD RULE. FOR I. THE FIRST DERIVATIVE INDICATES CONSTANT CHANGE THAT CAN BE EXPRESSED AS A THRESHOLD RULE. FOR II., THE SECOND DERIVATIVE INDICATES A CONSTANT CHANGE THAT CAN BE EXPRESSED AS A THRESHOLD RULE.

I.

FIRST DERIVATIVE, IF X < 1 OR X > 2 THEN NOISE

II.

SECOND DERIVATIVE, IF X 1 THEN NOISE

PART B

GIVEN THE FOLLOWING IMAGE, APPLY FILTER F TO THIS IMAGE:

|20 |21 |20 |22 |21 |21 |

|20 |22 |55 |52 |51 |20 |

|20 |24 |255 |51 |51 |22 |

|20 |23 |53 |48 |0 |21 |

|20 |22 |21 |22 |21 |22 |

|1/9 |1/9 |1/9 |

|1/9 |1/9 |1/9 |

|1/9 |1/9 |1/9 |

Filter F:

THE ‘0’ AND ‘255’ REPRESENT BLACK AND WHITE NOISE, RESPECTIVELY. COMMENT ON WHAT HAPPENED TO THE NOISE AFTER THIS FILTER WAS APPLIED.

APPLYING THE FILTER:

|20 |21 |20 |22 |21 |21 |

|20 |51 |58 |64 |35 |20 |

|20 |55 |65 |68 |35 |22 |

|20 |54 |63 |66 |34 |21 |

|20 |27 |34 |33 |27 |22 |

|20 |22 |21 |22 |21 |22 |

After the filter was applied, the noise was smoothed out.

PART C

USE THE VISUAL BASIC IMAGE-FILTERING PROGRAM GIVEN IN THE PROBLEM SOLVING SESSION (AND POSTED ON THE WEB SITE) AND APPLY THE FOLLOWING FILTERS TO THE POSTED HALLWAY IMAGE (HALL.BMP). PRINT THE RESULTING SCREEN AND FOR EACH FILTER AND TURN THEM IN.

I. II.

|1/9 |1/9 |1/9 |

|1/9 |1/9 |1/9 |

|1/9 |1/9 |1/9 |

|-1 |-1 |0 |

|-1 |0 |1 |

|0 |1 |1 |

BIAS = 0 BIAS = 128

[pic]

[pic]

PART D

AN ADDITIONAL IMAGE HAS BEEN POSTED ON THE WEB SITE INCLUDING 2% SALT AND PEPPER NOISE (HALLNOISE.BMP). APPLY THE MEAN FILTER (PART CI) TO REMOVE THE NOISE. PRINT THE RESULTING SCREEN.

[pic]

PART E

MAKE YOUR OWN COOL 3 X 3 FILTER OR LOOK ONE UP ON THE INTERNET AND APPLY IT TO THE HALLNOISE IMAGE. REMEMBER THAT IT’S BEST IF YOUR FILTER ADDS TO 1. TURN IN A SCREEN SHOT OF THE RESULT AND THE VALUES OF YOUR FILTER.

| | | |

| | | |

| | | |

BIAS = ______

PROBLEM SOLVING DELIVERABLES

YOU SHOULD WORK IN TEAMS OF EITHER TWO OR THREE. YOU MAY NOT WORK ALONE. TURN IN PARTS A, B, C, D, AND E, BY TUESDAY, DECEMBER 5TH IN CLASS. ONE SET OF RESULTS SHOULD BE SUBMITTED PER TEAM. BE SURE TO CLEARLY LABEL EVERYTHING YOU TURN IN.

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