function perimeter = ConvexPerim( bwImage )

    STATS = regionprops(bwImage,'ConvexHull');  

    vertex = STATS.ConvexHull;

    perimeter = 0;

    if size(vertex,1) > 2

        for i=2:size(vertex,1)

            % if it is a vertical segment

            if vertex(i,1)== vertex (i-1,1) 

                if vertex(i,2) ~= vertex(i-1,2)

                    perimeter = perimeter + abs( vertex(i,2) - vertex(i-1,2) ); 

                end

            end

            % if it is a horizontal segment

            if vertex(i,1)~= vertex (i-1,1) 

                if vertex(i,2) == vertex(i-1,2)

                    perimeter = perimeter + abs( vertex(i,1) - vertex(i-1,1) ); 

                end

            end

            % if it is any other segment

            if vertex(i,1)~= vertex (i-1,1) 

                if vertex(i,2) ~= vertex(i-1,2)

                    perimeter = perimeter + sqrt( (vertex(i,1) - vertex(i-1,1) )^2 + (vertex(i,2) - vertex(i-1,2) )^2 ); 

                end

            end

        end

    end

    %Consider special cases, because very small objects have large

    %errors, so call the facet midpoint method for these, and the exceptional

    %cases will be handled correctly.

    Icontour = bwboundaries(bwImage, 'noholes');

    pixel = Icontour{1};

    % If the shape is a single pixel, make the perimeter equal to the perimeter of

    % a circle with area = 1

    if size(pixel,1)== 2

        perimeter = FacetMidpointPerim(bwImage);

    end

    %If the shape is two pixels aligned, make the perimeter equal to the perimeter

    % of an eliipse with area = 2 and minor axis equal to 0.5.  

    if size(pixel,1) == 3 && ( pixel(1,1) == pixel(2,1) || pixel(1,2) == pixel(2,2) )

        perimeter = 6.0774;

    end

    %If it is four pixels arranged as a square, make the perimeter equal to

    %the periemter of a circle with area = 4

    if(size(pixel, 1) == 5) 

        x = FacetMidpointPerim(bwImage);

        if x == 7.089815;

            perimeter = 7.089815;

        end

    end

end