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Description of the method:

Graphical double integration performed by Matblab program.

We calculated the mass of the North african theropod dinosaur Spinosaurus aegyptiacus, using a graphical double integration method. We believe GDI is in itself, and without a doubt, one of the best methods to calculatte the mass of extint organisms, and the best that can be used using a multi views silhouette from the animal. The method averages a big amount of eliptical sections to aproximate the volume of a complex 3D object. The more eliptical sections, the more accurate the result will be, when a number of slices made is surpassed the result will be almost real life-like.

This matlab program utilizes digital image processing technology to analize two silhouettes from different views. It counts the number of non white pixels in every pixel-wide column from the image, and produces one slice per pixel. In response, the program is extremely sensitive to irregularities in the silhouette's perimeter.

This all means that being the torso 910 pixels long in axial length, the program produced 910 slices, and thus 910 eliptical sections for the torso, preserving the shape of the silhoettes intact in the process, and being as accurate as it can be from a mathematical point of view (when using this GDI method).

We associate the error bars to the human factor when drawing the silhouettes, and the non exact numbers for the density figures.

Figures used:

The densities aim to replicate those used by the renowned paleontologist and paleoartist known as Scott Hartman, owner of www.skeletaldrawing.com. Theese average density figures were the ones he used for calculating the mass of other two big Cretaceous theropods; Tyrannosaurus and Giganotosaurus. We did this because we intended our spinosaurus stimate to be fairly comparable to theese other stimates.

The silhouette for the Spinosaurus was made using the proportions suggested by Ibrahim et al (2014). The silhouette itself was made by RandomDinos, giving the Spinosaurus a similar amount of added soft tissue to that of Hartman's reconstructions of Giganotosaurus and Tyrannosaurus.

The dorsal view was infered from the 3D models from Ibrahim et al and anterior views from the composite Spinosaurus mount, which is now housed at Berlin's Museum für Naturkunde. The result is a barrel- like chested Spinosaurus. The gastrila was repositioned and as a result the torso got a more rounded shape compared to Ibrahim's totally speculative figure.

What we don't intend to do:

We don't inted to do an study of Spinosaurus lifestyle, locomotion, stance, biomechanis, or swimming or fighting capabilites. This is purely an study on the dimensions of the animal, linear measurements and specially and more importantly, mass.

Although the results of this study can be used by anyone as he pleases and for any kind of study/ investigation that person wants to make.

Example of the matlab script working: (The results at the end are for the torso of Giraffatitan Brancai)

Captura de pantalla 2016-09-20 02.30.19 by Franoys



Silhouettes used:

Forearms: (Anterior/Lateral views)

Dorsalview by Franoys

Lateralview by Franoys


Torso: (Dorsal/Lateral views)

Torsoviews by Franoys



Tail: (Dorsal/ Lateral views)

Dorsalview by Franoys

Lateralview by Franoys



Sail: (Dorsal/Lateral views)

Dorsalview by Franoys


Lateralview by Franoys

Hindlimbs (distal): (Anterior/Lateral views)

Spinohindlfrontal by Franoys

Lateralview by Franoys

Head: (Lateral/dorsal views)
Lateralview by Franoys

Dorsalview by Franoys

We used a 15,16 meters long spinosaurus for the study. For it, the results went as follows.

FOR THE HYPOTHETICAL 15,16 METERS LONG SPINOSAURUS:

Total length (axial)= 14,80 meters

Total length (Over the curves)= 15,16

Total mass: 7708, 54 kgs (~7.7 tonnes)

However, then we scaled Ibrahim's model using MSNM v 4047 rostrum, which includes premaxila, maxilla, and rostral part of the nassals (988 mm) ( Dal sasso; 2005). And we got a result of 15,063 meters total length for the Spinosaurus Aegyptiacus biggest referable specimen. So we isometrically scaled the 15,16 meters results for a 15,063 spinosaurus. The accuracy of the results remains unchanged, since isometrical scale equations for the same model don't have error bars associated to them.

Spinosaurus total length calculation:
Spinosauruslength by Franoys

FOR THE LARGEST REFERABLE SPECIMEN TO SPINOSAURUS AEGYPTIACUS; MSNM v 4047. (Definitive results)

Total length measurement for MSNM v 4047: 15,06 meters. ~15,1 m

Mass for 15,06 meters: 7557 kgs. (~ 7.6 tonnes)

Compiled values for each body part:

Spinotable by Franoys

A link for Randomdinos version of this:

Weighing the Fisher King - biggest... or is it?Spinosaurus aegyptiacus has, for quite a long time (the furthest I can trace it in scientific papers is 2005, but we all know what Jurassic Park /// was like), been described as the biggest theropod that ever existed. Even the, rather, well, dramatically updated version given by Ibrahim et al. (2014) didn't seem to spark the paleocommunity into doubting this perpetual title.
But should we really be repeating that claim?
Most methods to estimate dinosaur weights are, of course, rather imprecise, and references are often difficult to find. Double Graphic Integration (GDI) is currently the, well, least inaccurate of possible methods, but I've never had the capability to do it on my own.
However, Franoys recently proposed that we should work on one of those together, and (much to my surprise) he had the mathematical skills necessary to create a program that could do it for us. I don't want to expand too much on this, as maths aren't a field I enjoy working with, but for such things you can


Special thanks to my girlfriend, who helped me inmensely with all of this and she worked as much as Randomdinos and I, but she doesn't own a Deviantart account. So a big shoutout to her! Her programming and image-analizing skills have been proven as very good and useful. I love and admire her so much.

Add a Comment:
 
:iconscotthartman:
ScottHartman Featured By Owner Dec 2, 2016  Professional Digital Artist
I'm notorious??!
Reply
:iconfranoys:
Franoys Featured By Owner Dec 2, 2016
Very much so, but in a good way of course (as in renowned and admired). Most people interested in paleontology admire you and your work greatly, and so do I of course. (sorry if the election of the word was poor, perhaps it is due to a language barrier due to me being spanish xD)
Reply
:iconscotthartman:
ScottHartman Featured By Owner Dec 3, 2016  Professional Digital Artist
No offense taken - you are right about the definition of the term, but in the U.S. it often has a more negative connotation (e.g. a really famous criminal, or the sports star who plays dirty might be "notorious). But mostly I just wanted to respond in fun.

By the way, this is really cool. If you end up sharing your matlab script I'd be very interested in taking a peek at it myself. Right now I'm using an Excel spreadsheet I set up but it's probably sacrificing some precision relative to what you've done.
Reply
:iconfranoys:
Franoys Featured By Owner Dec 5, 2016
I've sent you the programm via note. Fell free to ask any questions if anything goes wrong!
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:iconscotthartman:
ScottHartman Featured By Owner Dec 5, 2016  Professional Digital Artist
Thanks!
Reply
:iconfranoys:
Franoys Featured By Owner Dec 5, 2016
You are welcome!
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:iconfranoys:
Franoys Featured By Owner Dec 3, 2016
Oh I see, sorry then. I'll change the term.

I did share it with a few people, and I of course would very gladly share it with you. I can send you the script via note along with the instructions on how to use it. 

You are right, I've used excel for doing GDI in the past and it is really time consuming when compared to this, and also less accurate because the lesser number of eliptical sections makes it have a bigger error margin. And thank you for the kind words. This GDI in particular has a few problems that you might alredy have noticed, like the dorsal view being very aproximate and not based of off a lot of evidence ( just the looks of the mount really), the low density or the probably overestimated sail.

I'd really like having better references for a Spinosaurus dorsal view or for a length figure for it, but for now this all that I was able to get.

And I'm glad that you commented!
Reply
:iconpcawesomeness:
PCAwesomeness Featured By Owner Sep 20, 2016
Thank you both!
Reply
:iconfranoys:
Franoys Featured By Owner Sep 20, 2016
You are welcome!
Reply
:iconspinoinwonderland:
SpinoInWonderland Featured By Owner Sep 20, 2016
My Spinosaurus is ~16.5ish meters long, so ... ~9.9 tonnes? ... I think the back would go higher than depicted here (~1/3 of the ridge height IMO based on Ibrahim's chameleon analogue) and that the ridge would extend into the tail, so 10+ tonnes?
Reply
:iconfranoys:
Franoys Featured By Owner Sep 20, 2016
If it scaled isometrically from Ibrahim's, that would be about right. But does it scale isometrically though? If not ( I suspect not because of the changes you made to vertebrae possition) , we can make a comparative study on how larger each part is, for example we can compare how much bigger the tail is when compared to ibrahims and calculate it's mass, same with the legs of it etc. I can also GDI your skeletal for you if you wish, you can send it to me and it won't take me much time. I would be grateful if you made the silhouettes and the different views for each part. For the program to work, it is important for the silhouettes to be black, and to be pasted in a white background ( they can't be in a transparent one). If you want me to do this, you can contact me via private note.

For now I can do some preliminary calculations:

Your spinosaurus has 27% longer legs ( i feel like you should check on what has been going on after Hartman made that blog post, like ibrahim's response and the reactions os some other authors of the 1.27 longer legs claim), so if it was the same linear length as this one, it would be 7672,225 kgs, and isometrically scaling it up it would be 10,047 tonnes. But is seems like it also has a proportionally longer tail? So maybe the mass will vary a bit from that. Plus the sail changes as you mentioned.

Ill probably do a more complex sail for this study at some point. It shouldn't change that much though, the distal part of the sail is wider than it should be and it overall is denser, so adding some bulk to the lower part of it would only augment this by 100-200 kgs, at most.
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:iconspinoinwonderland:
The body should scale pretty isometrically, since I pretty much traced the bones of Ibrahim's skeletal model and Stromer's holotype, I just used Dal Sasso's reconstruction for MSNM v4047's head. I'll try making some top views (front view for the limbs) for my skeletal when I have the time. I won't draw multiviews of the bones though, that's gonna be tedious as heck ;) (Wink) 

Yeah, I've seen Ibrahim's response, they had the legs splay out a bit, masking their true length. I plan to tweak my skeletal sometime, as I found some mistakes in the tail vertebrae or so. But the overall size should be fine.

Anyway, a bit off-topic, but do you know a working download for a program called PaleoMass? I checked the PaleoNet website and it seems they don't have it anymore. I've been looking for it so I could do mass estimates without the considerable time consumption of the GDI method.

mygeologypage.ucdavis.edu/mota…
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:iconfranoys:
Franoys Featured By Owner Edited Sep 20, 2016
The silhouettes are good enough, as long as they are reasonable. The limbs dont have that big of an impact in the overall mass. A lot of authors just do cilindrical sections for the limbs. But we can do better than that :p.


No, i do not know any working link for that I'm afraid. But the matlab script does do a very very similar thing, although the surface of it's slice is substituted by an elyptical section of the same surface. If you manage to download matlab you would be able to use this script. Also I made an excel calculus sheet prior to the matlab program, but you need to take the measurements for each slice and write it down manually (that's how Scott Hartman did his stimates).

I used MSNM v 4047 rostrum, but ibrahim's model head. So that might be the difference between mine and ours. The holotype's bones would vary great deal when using a different skull reconstruction.
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:iconspinoinwonderland:
SpinoInWonderland Featured By Owner Sep 20, 2016
Looks like a lot of time will be consumed when I try to estimate volumes and masses then :(
Reply
:iconfranoys:
Franoys Featured By Owner Sep 20, 2016
I plan on doing a couple tutorials on GDI and include both the excel program and the matlab script. So be sure to check for that. They do save a lot of time.
Reply
:iconfranoys:
Franoys Featured By Owner Edited Sep 20, 2016
BTW, about Dal Sasso, did you know he is a co author of the Ibrahim et al publication? Probably he changed his mind about the skull reconstruction for some reason since the skull at ibrahim et al is differenty proportioned. I think FSAC KK 11888 included some skull fragments, so maybe it was that.
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:iconspinoinwonderland:
Yeah, I know.

FSAC-KK 11888 did have a few skull fragments, but those skull fragments were well, too fragmentary to sufficiently constrain the proportions of the skull (making Dal Sasso's 2005 skull reconstruction pretty much just as likely as the newer one), and there's some private spinosaurine skulls that actually suggest a skull longer than Dal Sasso's 2005 reconstruction for MSNM v4047.
Reply
:iconkirkseven:
kirkseven Featured By Owner Edited Sep 19, 2016
so your 7.5 tonne estimate was pretty close to the mark.

nice
Reply
:iconfranoys:
Franoys Featured By Owner Sep 19, 2016
Lol, it does seem like it was!
Reply
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