Here are the resulting images
Fig 4. Original gray-scale picture, which is over-exposed (Camera set
to +2 exposure level)
Fig 5. Corrected image using the pixel intensity curve for a photographic
film
Fig 6. Corrected image using the pixel intensity linear curve for a
digital camera
Fig 7. Corrected image using the pixel intensity curve fitted for the linear curve obtained for a digital camera
Clearly, Fig 7 is a vast improvement of Fig 6, and it takes into account of the characteristics of the digital camera, and its response to different exposure levels.