A Spreadsheet-based Manipulative

1. A Spreadsheet-based Manipulative Support for Teaching Convolution STEM Teaching and Learning Conference March 7, 2014 Georgia Gwinnett College School of Science and Technology Dr. Jim Rowan

2. Sections of today’s talk -A moment about GGC and Digital Media -About blurring images before digital images Camera Artistically -About blurring digital images -The powerpoint manipulative

3. GGC and Digital Media GGC has been built from the ground up since it’s founding in 2005 I arrived in 2007 before any classes were being offered to Freshmen or Sophomores This was an extraordinary opportunity Digital Media, a sophomore level class, was my choice

4. GGC and Digital Media Two parts: Projects and Theory Projects: Using Open Source software… Audacity for audio Inkscape for 2D vector graphics GIMP for bitmapped graphics Blender for 3D animation Theory look under the covers know a little about what is going on strip away the “magic” banish the wizards empowering students

5. GGC and Digital Media In this class we deal with bitmapped images how they are stored on a computer how to manipulate them how to do editing Part of the editing involves the use of filters One of the filters we use on a project is blur So… The question is How does a digital image get blurred?

6. Image Blur…How does this happen?

7. Pre-Digital Image Blur: The entire image Photographically you can de-focus the lens If you are an aging diva you can insist that vaseline be applied to the lens to get this “soft” focus

8. Pre-Digital Image Blur: Just the background Photographically you can adjust the F stop imageSource

9. Pre-Digital Image Blur: Artistically You can use your fingers to smooth and spread out the charcoal imageSource

10. Image Blur: Digital? You can’t reach into the computer to smear the charcoal… What do you do? The simple answer is use some image software… But how does that work?

11. Digital Blur Blur (as well as many other digital image filters) use a process known as convolution Convolution is simple… it’s just multiplication and addition Convolution is hard… there’s a lot to keep up with

12. Underlying any digital image… Is a huge collection of numbers In the case of 24 bit color depth there are 3 bytes -one for red -one for green -one for blue for each pixel! This image measures 1983 X 2252 pixels Doing the math you get 4,465,716 pixels and a file size of 4,465,716 X 3 or 13,397,148 bytes

13. Homing in on the car’s front grill If you drill down you can finally see the pixels and the numbers that define the colors

14. Digital Blur Blur is accomplished by applying a “convolution matrix” to every pixel of the image to create a new blurred image This convolution matrix is a square matrix that contains numbers that frequently add up to 1 can be negative can be as small as 3 X 3 can be much larger The choice of convolution matrix determines the affect that it has on the image

15. GIMP Convolution Matrix GIMP allows up to a 5 X 5 convolution matrix as well as showing a preview. Design and test your own. BUT how does it work?

16. Showing how it works To show the underlying workings of convolution simplifications must be made -Use a 3 X 3 convolution matrix -Operate on black/white/grey scale images -each pixel then has only one number associated with it -Select a very small but representative sample of the original image -Calculate only a few but representative pixels in the new blurred image -Extrapolate the result to the rest of the image

17. A simple example: A two pixel wide horizontal line The image The underlying numbers

18. The convolution matrix To calculate a single pixel (X) in the new blurred image you need center the matrix over the pixel of interest and then multiply each cell of the matrix by the associated color value of it’s underlying pixel and then add all 9 of these up

19. The calculations are blinding!

28. That’s a lot of work to make my point!Students get lost in the trees and miss the forest!

29. Instead use a powerpoint slide to do the calculation It is much easier to keep track of where you are… short enough to make the point

30. Made easier with powerpoint! Select the convolution matrix

31. Made easier with powerpoint! Drag and center the matrix over the pixel of interest in the original image… You can “see” the multiplications and the additions

32. Made easier with powerpoint! You can “see” the multiplications! 0X255 + 1/3X255 + 0X255 + 0X255 + 1/3X255 + 0X255 + 0X0 + 1/3X0 + 0X0 = 85 + 85 = 170

33. This method made a HUGE differencein student success

34. One Complete Example!

37. 0/9 x 255 + 3/9 x 255 + 0/9 x 255 + 0/9 x 255 + 3/9 x 255 + 0/9 x 255 + 0/9 x 255 + 3/9 x 255 + 0/9 x 255 = 0 + 85 + 0 + 0 + 85 + 0 + 0 + 85 + 0 = 255

39. 0/9 x 255 + 3/9 x 255 + 0/9 x 255 + 0/9 x 255 + 3/9 x 255 + 0/9 x 255 + 0/9 x 0+ 3/9 x 0 + 0/9 x 0= 0 + 85 + 0 + 0 + 85 + 0 + 0 + 0 + 0 = 170

41. 0/9 x 255 + 3/9 x 255 + 0/9 x 255 + 0/9 x 0 + 3/9 x 0+ 0/9 x 0+ 0/9 x 255 + 3/9 x 255 + 0/9 x 255 = 0 + 85 + 0 + 0 + 0 + 0 + 0 + 85+ 0 = 170

43. 0/9 x 0 + 3/9 x 0 + 0/9 x 0 + 0/9 x 255 + 3/9 x 255 + 0/9 x 255 + 0/9 x 255 + 3/9 x 255 + 0/9 x 255 = 0 + 0 + 0 + 0 + 85+ 0 + 0 + 85+ 0 = 170

45. 0/9 x 255 + 3/9 x 255+ 0/9 x 255 + 0/9 x 255 + 3/9 x 255 + 0/9 x 255 + 0/9 x 255 + 3/9 x 255 + 0/9 x 255 = 0 + 85 + 0 + 0 + 85 + 0 + 0 + 85+ 0 = 255

46. This matrix blurs horizontal lines (but not vertical ones!)

47. Another complete example…Sometimes a mask has no effect

49. 0/9 x 255 + 0/9 x 255 + 0/9 x 255 + 3/9 x 255 + 3/9 x 255 + 3/9 x 255 + 0/9 x 255 + 0/9 x 255 + 0/9 x 255 = 0 + 0 + 0 + 85 + 85 + 85 + 0 + 0 + 0 = 255

50. 0/9 x 255 + 0/9 x 255 + 0/9 x 255 + 3/9 x 255 + 3/9 x 255 + 3/9 x 255 + 0/9 x 255 + 0/9 x 255 + 0/9 x 255 = 0 + 0 + 0 + 85 + 85 + 85 + 0 + 0 + 0 = 255