Proximal Hyperspectral data calibration using white and dark reference images.

I am using a proximal Hyperspectral (HSI) sensor called Specim FX10 with spectral range of 400-780 nm. These HSI images need to be calibrated with white and dark reference images before further analysis. These reference images are collected everytime with individual data image.

The following is the screenshot of the data collection folder:

The formula used to calibrate the image is:

The way the camera collects the dark reference is by simply closing the shutter and for white reference it captures a small block of teflon. The scanning area (height) for both reference images are very small compared to the data image and that is the problem I think I am having. When I try to do any analysis using these values the array size don't match.('100x1024x448' VS '1100x1024x448') [height x width x bands]

Difference between the value size of dark, white and raw data:

This is the code I am running to get the above values:

I am new to MATLAB and learning how to complete my analysis. Can anyone point out what I am missing or how should I approch this problem? Any additional resources for proximal HSI data analysis would be really helpful. Thanks!

[Billy Ram]

Just to reiterate on the problem I want to solve. See the formula for calibrating the image for reference. I have three, 3D arrays. They are white reference image of size (100x1024x448), dark reference image of size (100x1024x448) and image data of size (1100x1024x448). I want to use these arrays to get the calibrated image denoted by R in the formula above.

Answer 1

[Image Analyst]

I don't think you want W and D to be images. You need them to be scalars so the image size doesn't matter. For each wavelength you just need to get the W and D values, like by taking the mean of the whole image assuming the teflon takes up the whole field of view. So knowing that, you will know the spectral responsivity of your camera/lens system. And therefore the size of the reference image doesn't matter. Though I don't know why the white and dark images would have a different size than the actual test images. And I don't know what "100x1024x448" means. Which is rows, which is columns, and which is wavelengths (or number of images)?

The only reason that the W and D should be images instead of scalars is in situations where the spectral reflectance varies over the image. But that should not be the case if you have a uniform, homogenous block of teflon filling the field of view.

[Billy Ram]

Yes, I agree that W and D need to be scalar. The raw image has Height = 1100, Width = 1024 and Bands = 448 and the dark-white reference images have Height= 100, Width =1024 and Bands = 448. The white and dark images have different sizes as we only capture the black reference (with a closed shutter) for a small duration of time. Same with the white reference capture of teflon bar. Since this is a push broom sensor it only captures a height of 100 for white and dark reference images and for the actual data it captures a longer distance. I want to know how to do the above corrected image calculations in matlab. The following is the whole information about the images from their respective .hdr file

rawimageinfo = 

  struct with fields:

                 Filename: "directory"
              FileModDate: "13-Sep-2021 12:00:12"
                 FileSize: 8084
                   Format: "HDR"
            FormatVersion: ''
               SensorType: "FX10e , Lumo - Scanner v2018-517"
              Description: "File Imported into ENVI"
          AcquisitionTime: [0×0 string]
             RasterFormat: "ENVI"
                   Height: 1100
                    Width: 1024
                    Bands: 448
                 DataType: "uint16"
               Interleave: "bil"
             HeaderOffset: 0
                ByteOrder: "ieee-le"
                BandNames: [0×0 string]
               Wavelength: [448×1 double]
                     FWHM: [448×1 double]
                     Gain: []
                   Offset: []
          ReflectanceGain: []
        ReflectanceOffset: []
                 BadBands: []
               CloudCover: []
               SunAzimuth: []
             SunElevation: []
                 FileType: "ENVI"
          AcquisitionDate: "DATE(yyyy-mm-dd): 2021-09-13"
                StartTime: "UTC TIME: 16:59:44"
                 StopTime: "UTC TIME: 17:00:12"
                   Errors: "none"
                   XStart: 0
                   YStart: 0
             DefaultBands: [3×1 double]
                     Himg: [1 1024]
                     Vimg: [1 448]
                     Hroi: [1 1024]
                     Vroi: [1 448]
                      Fps: 40.5200
                  Fps_qpf: 40.4300
                     Tint: 3
                  Binning: [1 1]
              TriggerMode: "Internal"
                    Fodis: [0 0]
                 Sensorid: 000000
    AcquisitionwindowLeft: 128
     AcquisitionwindowTop: 245
          CalibrationPack: "calpack.scp"
          VNIRTemperature: 0
              Temperature: 0

>> whiteimageinfo

whiteimageinfo = 

  struct with fields:

                 Filename: "directory"
              FileModDate: "13-Sep-2021 11:59:42"
                 FileSize: 8083
                   Format: "HDR"
            FormatVersion: ''
               SensorType: "FX10e , Lumo - Scanner v2018-517"
              Description: "File Imported into ENVI"
          AcquisitionTime: [0×0 string]
             RasterFormat: "ENVI"
                   Height: 100
                    Width: 1024
                    Bands: 448
                 DataType: "uint16"
               Interleave: "bil"
             HeaderOffset: 0
                ByteOrder: "ieee-le"
                BandNames: [0×0 string]
               Wavelength: [448×1 double]
                     FWHM: [448×1 double]
                     Gain: []
                   Offset: []
          ReflectanceGain: []
        ReflectanceOffset: []
                 BadBands: []
               CloudCover: []
               SunAzimuth: []
             SunElevation: []
                 FileType: "ENVI"
          AcquisitionDate: "DATE(yyyy-mm-dd): 2021-09-13"
                StartTime: "UTC TIME: 16:59:39"
                 StopTime: "UTC TIME: 16:59:42"
                   Errors: "none"
                   XStart: 0
                   YStart: 0
             DefaultBands: [3×1 double]
                     Himg: [1 1024]
                     Vimg: [1 448]
                     Hroi: [1 1024]
                     Vroi: [1 448]
                      Fps: 40.5200
                  Fps_qpf: 40.5100
                     Tint: 3
                  Binning: [1 1]
              TriggerMode: "Internal"
                    Fodis: [0 0]
                 Sensorid: 0000000
    AcquisitionwindowLeft: 128
     AcquisitionwindowTop: 245
          CalibrationPack: "calpack.scp"
          VNIRTemperature: 0
              Temperature: 0

[Image Analyst]

OK, so is there any problem? If the images are uint8 you probably need to convert them to double before doing any math on them to avoid clipping.

[Billy Ram]

The images have DataType: "uint16". I don't get your point about converting them to double. It already shows in the workspace window as 'double'. I am currently clueless about how to get the calibrated images with the information and data I have (I am very new to MATLAB).

[Image Analyst]

If they're already double, then fine. I'm just saying that if you try to subtract uint8 numbers, they will clip to 0 and won't give you the correct difference if that difference would be negative. Observe:

v1 = uint8(9);
v2 = uint8(150);
result = v1-v2

result = uint8 0

% Now for double
v1 = 9;
v2 = 150;
result = v1-v2

result = -141