Planner graph on Kemp Ridley and Olive Ridley turtles' carapace

Kemp's Ridley or Lepidochelys kempii is the smallest of all sea turtle species. Reaching maturity at 2–3 feet (61–91 cm) long and averaging only 45 kilogram. It's carapace contains five vertebral scutes running down the midline, while five pairs of costal scutes border them. The resulting planar graph due to this scalation is 3-regular 28 vertices and 42 edges. Exactly same as as that of Loggerhead or Caretta Caretta.



Olive Ridley or Lepidochelys olivacea is also one of the smallest turtle species. its heart-shaped carapace is characterized by four pairs of pore-bearing inframarginal scutes on the bridge, two pairs of prefrontals, and up to nine lateral scutes per side. Scalation can be asymmetrical i.e. 6 lateral scutes on one side and 8 on the other.

Planner graph on Loggerhead Turtle's carapace

The Loggerhead sea turtle or Caretta Caretta is the world's largest hard-shelled turtle. It's carapace contains five vertebral scutes running down the midline, while five pairs of costal scutes border them. The resulting planar graph due to this scalation is 3-regular 28 vertices and 42 edges.

Planner graph on Green Turtle's carapace

In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints.

A graph is said to k-regular if all the vertices of the graph has dgree k.



The Green sea turtle or Chelonia mydas has a dorsoventrally flattened body. Its carapace is composed of five central scutes flanked by four pairs of lateral scutes. The resulting planner graph is 3-regular with 24 vertices and 36 edges.

Histogram smoothing with erosion

The idea of using erosion for smoothing histogram is actually borrowed from the realm of artificial terrain generation where it is a common practice. Recent experiments shows this is a better approach then using polynomial fit. Histogram is a one dimensional height map, after all. The result (smoothed histogram) closely follows the actual data points most of the time and structural property like rises and falls are well preserved.



The procedure is pretty straight forward, replace each entry in the vector containing the histogram with mean of that entry along with n entries backwards n entries forward. Boundary case arises when the index of the current entry is bellow n or beyond length_of_vector-n, I chose to keep those entries unchanged.

    result = arr ;

    for i=n+1:length(arr)-n
        sum=0;
        for j=i-n:i+n
            sum = sum + arr(j) ;
        end
        result(i) = sum/(2*n+1);
    end

Sea turtle carapace pattern as criterion for automatic species ID

The pattern seen on the carapace of sea turtles is one of the criterion used for identifying species, why not try to use this for automatic species ID as well ? The advantages of using this approach for automatic ID would be

1. Works for photos taken in wide range of environments and lighting condition varying from the animal's natural habitat (under water) to decaying carcass of stranded animals found on beaches
2. Only the carapace needs to be observed; other body parts, which decay sooner than the carapace in a dead animal, don't need to be observed
   
3. Can work for both color and bw photographs
4. Possibility of successful detection from broken or incomplete carapace if the key parts of the carapace is found

However, the challenges associated with this approach are also great. The challenges are encountered in two different phases, each of them are explained bellow.

• Feature Extraction
  The sought after feature here is the pattern on the carapace. To understand the challenges in extracting this feature, we should understand its origin first. What we are referring to as pattern in common English as 'Pattern' is actually the network of ridge lines between scutes on the turtles carapace. This is true for all the species of Cheloniida family. For Dermochelys coriacea or leatherback turtle, the only species of Dermochelyidae family, the pattern is originated by the seven ridge lines on its back. Experimentation with several photograph taken in varying environment reveals that the ridge lines are best visible, hence extractable, in case of underwater photos.
  
  
  
  The above image shows the result of gradient magnitude, a standard edge detection algorithm, applied on a photograph followed by edge thinning on the resulting gradient magnitude image. But this does not yield good extractable features from photographs of stranded animals found on beaches, specially the decaying ones. Worse, due to presence of debris or other objects inside the frame, wrong part of the image is extracted instead of the carapace by the gradient magnitude finding operation.
  
  




• Graph reconstruction
  The next challenge encountered is reconstruction of the pattern extracted from the photograph. Ideally, this would be the complete network of ridge lines. But the resulting image after feature extraction does not always have a complete network traced in most of the real life situations. So the graph reconstruction procedure should be robust enough to reconstruct a graph from incomplete or broken edges and at the same time be able to identify and discard edges that are not from the ridge lines on the turtles back.
  

Graph on sea turtle carapace

Sea turtles belong to the superfamily Chelonioidea and inhabit all of the world's oceans except the Arctic. There are seven species of sea turtles.

Family Cheloniida

Chelonia mydas or green turtle
Eretmochelys imbricata or hawksbill turtle
Natator depressus or flatback Turtle
Caretta caretta or Loggerhead Sea Turtle
Lepidochelys kempii or Kemp's Ridley turtle
Lepidochelys olivacea or Olive Ridley turtle

Family Dermochelyidae

Dermochelys coriacea or leatherback turtle



The above Image shows how to identify species of a sea turtle based on its carapace or the back. Anyone with idea of Graph theory would immediately recognize the graphs drawn on the carapace of different turtle species. I believe this is a good criterion for automated species identification from sea turtle photographs.