HDR in Microsoft Excel?! Kevin Chen !!Con 2017 Motivation N/A - PowerPoint PPT Presentation

HDR in Microsoft Excel?! Kevin Chen • !!Con 2017

Motivation • N/A

Background

brighten and replace?

Reciprocity Open the shutter 2x longer ➡ 2x more light

2x 2x brighten and replace?

250 200 150 100 50 ☀ 0 − 10 − 5 0 5 Nonlinearity 2x more light " 2x bigger number in JPG

Recovering High Dynamic Range Radiance Maps from Photographs Paul E. Debevec Jitendra Malik University of California at Berkeley ABSTRACT true measurements of relative radiance in the scene. For example, if one pixel has twice the value of another, it is unlikely that it observed We present a method of recovering high dynamic range radiance twice the radiance. Instead, there is usually an unknown, nonlinear maps from photographs taken with conventional imaging equip- mapping that determines how radiance in the scene becomes pixel ment. In our method, multiple photographs of the scene are taken values in the image. with different amounts of exposure. Our algorithm uses these dif- This nonlinear mapping is hard to know beforehand because it is ferently exposed photographs to recover the response function of the actually the composition of several nonlinear mappings that occur imaging process, up to factor of scale, using the assumption of reci- in the photographic process. In a conventional camera (see Fig. 1), procity. With the known response function, the algorithm can fuse the film is first exposed to light to form a latent image. The film is the multiple photographs into a single, high dynamic range radiance then developed to change this latent image into variations in trans- map whose pixel values are proportional to the true radiance values parency, or density , on the film. The film can then be digitized using in the scene. We demonstrate our method on images acquired with a film scanner, which projects light through the film onto an elec- both photochemical and digital imaging processes. We discuss how tronic light-sensitive array, converting the image to electrical volt- this work is applicable in many areas of computer graphics involv- ages. These voltages are digitized, and then manipulated before fi- ing digitized photographs, including image-based modeling, image nally being written to the storage medium. If prints of the film are compositing, and image processing. Lastly, we demonstrate a few scanned rather than the film itself, then the printing process can also applications of having high dynamic range radiance maps, such as introduce nonlinear mappings. synthesizing realistic motion blur and simulating the response of the In the first stage of the process, the film response to variations human visual system. in exposure (which is , the product of the irradiance the

31 78 183 2x more light 2x more light 31 78 183

digital number 183 78 31 log(amount of light) ☀

$ = f( ☀ ) digital number = f(brightness • shutter open time) Z = f ( E · ∆ t ) f − 1 ( Z ) = E · ∆ t flip it! g ( Z ) = E · ∆ t

A × x = b = ✅ ✅ ❓ ✕ Very Big Matrix™

A × x = b ya f¥:¥IE oo .ie#sEkEE!fxffti:*f LV is *e¥ is er

A × x = b x = A + × b MatheAss One of the most popular Shareware Math Programs in Germany Pseudo Inverse Matrix If the columns of a matrix A are linearly independent, so A T · A is invertible and we obtain with the following formula the pseudo inverse: A + = (A T · A) -1 · A T Here A + is a left inverse of A , what means: A + · A = E .

Microsoft Excel Time™

This helper sheet calculates the pixel coordinates that we will use in recovering g(Z). There are a total of 49 values that form a 7x7 grid.

x = A + × b MatheAss One of the most popular Shareware Math Programs in Germany

uses g(Z) to get light intensity

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