Illuminating the Big Picture

Transcription

1 EE6A Imaging 2

2 Why? Imaging : Finding a link between physical quantities and voltage is powerful If you can digitize it, you can do anything (IOT devices, internet, code, processing) Imaging 2: What measurements are good measurements? Remember Kody and Nara?

3 Kody and Nara

4 Illuminating the Big Picture Linear dependance When can you even recover your image? Does it matter what mask matrix you pick? Does it matter how you cover the pixels? Invertibility When can you solve Ax = b Why do we care? How does this affect the way we pick our imaging matrix?

5 Today s Lab: Single Pixel Scanning Circuit from last week measures light intensity Projector illuminates index card in a controlled way Python programming to reconstruct image

6 Setup:

7 Circuit From Last Week Circuit Diagram Breadboard Diagram

8 Sample Images

9 Sample Images Seiya:

10 Sample Images Nick:

11 Images, Matrices, Vectors What are the unknowns in our system? Want to do an experiment to get information about these unknowns. We can do a lot of interesting processing on vectors, but we need to convert the image into one first In lecture and discussion, you have seen how to turn an image into a vector. How?

12 Images, Matrices, Vectors [] [] [2] [3] [4] [5]

13 Images, Matrices, Vectors [] [] [] [2] [3] [4] [5] []

14 Images, Matrices, Vectors [] [] [2] [4] [] [3] [5] [] [2] [3]

15 Images, Matrices, Vectors [] [] [2] [4] [] [3] [5] [] [2] [3] [4] [5]

16 Images, Matrices, Vectors [] [] [2] [4] [] [3] [5] [] [2] [3] [4] [5]

17 Pixel-by-Pixel Scan of an Image

18 Pixel-by-Pixel Scan of an Image

19 Pixel-by-Pixel Scan of an Image Masked image Image

20 Pixel-by-Pixel Scan of an Image Masked image Image

21 Pixel-by-Pixel Scan of an Image Masked image Image

22 Question Time To read all the pixels of a 4x4 image, how many pixel-by-pixel scans do we need to do?

23 Representing our Masks in Python Imaging Mask mask = np.array([ [,,,, [,,,, 2 [,,,, 3 [,,,, 4 [,,,, ],],],],]] )

24 Representing our Masks in Python Imaging Mask mask = np.array([ [,,,, [,,,, 2 [,,,, 3 [,,,, 4 [,,,, ], ], ], ], ]] )

25 Turning the Masks Into Vectors [[ mask =,,,, ], Row Row Row 2 [,,,, ], [,,, ], Row 3, Row 4 ], [,,,, [,,,, ]] Row 24 T

26 Turning the Masks Into Vectors [[ mask =,,,, ], Row Row Row 2 [,,,, ], [,,, ], Row 3, Row 4 ], [,,,, [,,,, ]] Row 24 T

27 Generating the Masking Matrix from the Masks,,,,,,,, mask,,,,,,,,,,,,

28 Generating the Masking Matrix from the Masks mask,,,,,,,,,,,,,,,,,,,,

29 Generating the Masking Matrix from the Masks mask,,,,,,,,,,,,,,,,,,,,

30 Generating the Masking Matrix from the Masks,,,,,,,, mask,,,,,,,,,,,,

31 Generating the Masking Matrix from the Masks mask,,,,,,,,,,,,,,,,,,,,

32 Generating the Masking Matrix from the Masks mask,,,,,,,,,,,,,,,,,,,,

33 Generating the Masking Matrix from the Masks

34 Generating the Masking Matrix from the Masks

35 Each Row is a Different Experiment H=

36 Measuring a Pixel is Matrix-Vector Multiplication i s i2 s2 i3 s3 Masking Matrix H = in Unknown, vectorized image, sn Recorded Sensor readings,

37 Measuring a Pixel is Matrix-Vector Multiplication We know H and we have the sensor readings, how do we get the image? How do we solve this? When can we solve this? Conditions on H

38 Example What will the scanning matrix s dimensions be? How many pixels?

39 Example What will the scanning matrix s dimensions be? 5x5 How many pixels? 5

40 How Scanning Works: ipython H=

41 How Scanning Works: ipython H=

42 How Scanning Works: ipython H=

43 How Scanning Works: ipython H=,,,,,,,,,,,,,,,,,,,,

44 How Scanning Works: ipython H=,,,,,,,,,,,,,,,,,,,,

45 What Makes A Mask Good? Linearly independent columns -> Invertible Can t get a solution without this There is a unique solution What would be a bad mask? Food for thought: Are all invertible matrices equally as good? Find out next week

46 Tips for a Good Image READ CLOSELY. There are many small directions that help you get a good setup Focus projector using dial on the side Close the box firmly & scan under dark conditions

47 Notes No signal when testing the oscope on their previous circuit Unplug P6. from MSP and debug if necessary UART Application Com Port not showing up as an option when scanning Close serial monitor! Do not take sharpies and tape from the desk If something isn t working, close everything and turn it back on (works 9/ times)

48 Important Notes You should have your kit from last week Equipment in cardboard box: Don t break the plastic stand! Put everything back before you leave! Including Projector s Power Make sure you are using the right com port at all times Not COM, and not the debugger