Find edges in a plot

I've been trying for a while to find the following edges on a graph as shown in the picture below

The following code is for the path and plot

path_test=[ 106 20;

107 19;

108 18;

109 17;

110 16;

111 15;

112 14;

113 13;

114 12;

114 11;

114 10;

115 9;

116 9;

117 9;

118 9;

119 9;

120 9;

121 9;

122 9;

123 9;

124 9;

125 9;

126 9;

127 9;

128 10;

129 10;

130 10];

plot(path_test(:,2),path_test(:,1),'b');

I've tried to use islocalmin and ischange as shown bellow

index1=islocalmin(path_test,'FlatSelection','first');

index2=islocalmin(path_test,'FlatSelection','last');

index3=ischange(path_test);

index = [index1 index2 index3];

path_index=[];

for i=1:length(index)

if (any(index(i,:))==1 && all(index(i,:))==0)

path_index = [path_index i];

end

end

figure(11)

plot(path_test(:,2),path_test(:,1),'b');

hold on

plot(path_test(path_index,2),path_test(path_index,1),'rX')

And to use all of these commands alone, but i only get the following points shown in the plot below

With only findlocalmin i get the following

I was woundering if anyone know about a way to find the points of interest?

Answer 1

[darova]

Better solution

x = path_test(:,2);
y = path_test(:,1);
dangle = diff( diff(y)./diff(x) );
ind = find(abs(dangle) > 0.1)+1;

hold on
plot(x(ind),y(ind),'or')
hold off

[Per Gunnar Torvund]

Thanks alot, this worked like a charm!

[Frank Pernett]

Thank you!. This worked even better than finding peaks!

Answer 2

[KSSV]

A very quck implementation.....canbe further refined and more elegant solution possible.

p =[   106   20;
                    107    19;
                    108    18;
                    109    17;
                    110    16;
                    111    15;
                    112    14;
                    113    13;
                    114    12;
                    114    11;
                    114    10;
                    115     9;
                    116     9;
                    117     9;
                    118     9;
                    119     9;
                    120     9;
                    121     9;
                    122     9;
                    123     9;
                    124     9;
                    125     9;
                    126     9;
                    127     9;
                    128    10;
                    129    10;
                    130    10];
x = p(:,2) ; 
y = p(:,1) ; 
m = gradient(y)./gradient(x) ;                     

[c,ia,ib] = unique(m) ; 

iwant = cell(length(c),1) ; 
for i = 1:length(c)
  iwant{i} = [x(ib==i) y(ib==i)] ; 
end

figure
hold on
plot(x,y,'r')
for i = 1:length(c)
  tx = iwant{i}(:,1) ; ty = iwant{i}(:,2) ; 
  plot([tx(1) tx(end)],[ty(1),ty(end)],'*k')
end