While no one can answer that question just yet, I believe you will find some truly interesting data at the web site below.
If the Shroud is an authentic burial cloth of a much wounded crucified man (it is if it is not a hoax) then is it a lucky fluke that the images are so visually correct? A truly natural explanation requires that a chemical reaction starts and ends. And this is key: The reaction must end sufficiently late for there to be discernible images. And, it must end early enough that the images are not oversaturated. Analysis of the images shows no saturation plateaus. Timing is everything. In photographic terms this is correct exposure. Is this mere luck?
It is also interesting to note that the man of the shroud's legs were not broken, a common practice at that time. Also, the marks on the head attest to the excruciating wounds inflicted by the crown of thorns imposed on Jesus Christ. Who, other than Christ, do we know for certain, was crowned with thorns?
I don't know if you're interested in the physics of image formation, but you can find an explanation of Beer's Law by clicking here. What it boils down to is that the Density of the image (which is the logarithm of its reflectivity in the case of the Shroud), suitably normalized, is proportional to the logarithm of the relative luminance (i.e., the logarithm of the Exposure) of the incident radiation. The slope of the line relating these two quantities is known as the "gamma" of the exposure. In real film, the "line" is in fact roughly S-shaped, linear in the middle portion, but rolling off at the top in a "shoulder", and at the bottom in a "toe".
The Shroud's image seems to be "toasted" on the surface of the fibers of the cloth, suggesting it was caused by a burst of infrared radiation. The tonal distribution of the image is what one would expect from the physics of this process. But what could have caused the burst of radiation itself? That's the intriguing question, and we physicists love such a mystery. Naturally, we Christians would fill in the blank, so to speak, by saying it was caused by the glory associated with Christ's resurrection from the dead.
With regard to Protestant objections, my observation is that they tend to be distrustful of the Word actually being made Flesh, which is to say the Incarnation. This seems to arise from the Manichean influences the Reformers were subject to. The Catholic faith is nothing if not incarnational, so disagreements are bound to arise on these points.
While it's not Scripture, of course, I'm reminded of the passage in the ancient hymn and Easter sequence, Victimae pascali laudes:
Angelicos testes,This suggests that the "moderately early" Church understood there to have been "grave clothes" in addition to a "head cloth".
sudarium et vestes.