Penentuan tepian suatu objek dalam citra merupakan salah satu wilayah pengolahan citra digital yang paling awal dan paling banyak diteliti. Proses ini seringkali ditempatkan sebagai langkah pertama dalam aplikasi segmentasi citra, yang bertujuan untuk mengenali objek-objek yang terdapat dalam citra ataupun konteks citra secara keseluruhan.

Deteksi tepi berfungsi untuk mengidentifikasi garis batas (boundary) dari suatu objek yang terdapat pada citra. Tepian dapat dipandang sebagai lokasi piksel dimana terdapat nilai perbedaan intensitas citra secara ekstrem. Sebuah edge detector bekerja dengan cara mengidentifikasi dan menonjolkan lokasi-lokasi piksel yang memiliki karakteristik tersebut.

Berikut ini merupakan contoh aplikasi programmatic GUI matlab untuk mendeteksi tepi suatu objek dalam citra menggunakan operator gradien, operator laplacian, dan operator canny. (Coding dapat dijalankan minimal menggunakan matlab versi r2014b).

1. Operator Gradien
a. Operator Gradien Orde Satu

b. Operator Selisih Terpusat

c. Operator Roberts

d. Operator Prewitt

e. Operator Sobel

f. Operator Isotropic

g. Operator Compass

h. Operator Kirsch

2. Operator Laplacian
a. Operator Laplacian dengan kernel I

b. Operator Laplacian dengan kernel II

c. Operator Laplacian dengan kernel III

d. Operator Laplacian of Gaussian

3. Operator Canny

File source code lengkap beserta citra untuk deteksi tepi pada pemrograman di atas dapat diperoleh melalui halaman berikut ini: Source Code

Sedangkan tampilan source codenya adalah:

function deteksi_tepi
f = figure('Name','Deteksi Tepi','MenuBar','none',...
    'ToolBar','none','NumberTitle','off','Position',[250 130 800 500]);

tgroup1 = uitabgroup('Parent', f);
tab1 = uitab('Parent', tgroup1, 'Title', 'Operator Gradien');
tab2 = uitab('Parent', tgroup1, 'Title', 'Operator Laplacian');
tab3 = uitab('Parent', tgroup1, 'Title', 'Operator Canny');

tgroup2 = uitabgroup('Parent', tab1);
tab4 = uitab('Parent', tgroup2, 'Title', 'Gradien Orde Satu');
tab5 = uitab('Parent', tgroup2, 'Title', 'Selisih Terpusat');
tab6 = uitab('Parent', tgroup2, 'Title', 'Roberts');
tab7 = uitab('Parent', tgroup2, 'Title', 'Prewitt');
tab8 = uitab('Parent', tgroup2, 'Title', 'Sobel');
tab9 = uitab('Parent', tgroup2, 'Title', 'Isotropic');
tab10 = uitab('Parent', tgroup2, 'Title', 'Compass');
tab11 = uitab('Parent', tgroup2, 'Title', 'Kirsch');

ax1 = axes('Parent',tab4,'Position',[.2 .53 .25 .4]);
ax2 = axes('Parent',tab4,'Position',[.55 .53 .25 .4]);
ax3 = axes('Parent',tab4,'Position',[.2 .1 .25 .4]);
ax4 = axes('Parent',tab4,'Position',[.55 .1 .25 .4]);

I = double(imread('cameraman.tif'));
% Gradien orde satu pada arah horizontal
gx = [-1 1];
I1 = conv2(I,gx,'same');
% Gradien orde satu pada arah vertikal
gy = [-1;1];
I2 = conv2(I,gy,'same');
% Magnitudo gradien
J = sqrt((I1.^2)+(I2.^2));
% Gambar hasil
axes(ax1)
imagesc(I ),axis image,colormap gray,colorbar,title('Citra asli');
axes(ax2)
imagesc(I1),axis image,colormap gray,colorbar,title('Gradien arah horizontal');
axes(ax3)
imagesc(I2),axis image,colormap gray,colorbar,title('Gradien arah vertikal');
axes(ax4)
imagesc(J ),axis image,colormap gray,colorbar,title('Magnitudo gradien');

ax5 = axes('Parent',tab5,'Position',[.2 .53 .25 .4]);
ax6 = axes('Parent',tab5,'Position',[.55 .53 .25 .4]);
ax7 = axes('Parent',tab5,'Position',[.2 .1 .25 .4]);
ax8 = axes('Parent',tab5,'Position',[.55 .1 .25 .4]);

I = double(imread('cameraman.tif'));
% Gradien orde satu pada arah horizontal
gx = [-1 0 1];
I1 = conv2(I,gx,'same');
% Gradien orde satu pada arah vertikal
gy = [-1;0;1];
I2 = conv2(I,gy,'same');
% Magnitudo gradien
J = sqrt((I1.^2)+(I2.^2));
% Gambar hasil
axes(ax5)
imagesc(I ),axis image,colormap gray,colorbar,title('Citra asli');
axes(ax6)
imagesc(I1),axis image,colormap gray,colorbar,title('Gradien arah horizontal');
axes(ax7)
imagesc(I2),axis image,colormap gray,colorbar,title('Gradien arah vertikal');
axes(ax8)
imagesc(J ),axis image,colormap gray,colorbar,title('Magnitudo gradien');

ax9 = axes('Parent',tab6,'Position',[.2 .53 .25 .4]);
ax10 = axes('Parent',tab6,'Position',[.55 .53 .25 .4]);
ax11 = axes('Parent',tab6,'Position',[.2 .1 .25 .4]);
ax12 = axes('Parent',tab6,'Position',[.55 .1 .25 .4]);

I = double(imread('cameraman.tif'));
% Konvolusi dengan operator Roberts
robertshor = [0 1; -1 0];
robertsver = [1 0; 0 -1];
I1 = conv2(I,robertshor,'same');
I2 = conv2(I,robertsver,'same');
J = sqrt((I1.^2)+(I2.^2));
% Gambar Hasil
axes(ax9)
imagesc(I ),axis image,colormap gray,colorbar,title('Citra asli');
axes(ax10)
imagesc(I1),axis image,colormap gray,colorbar,title('Gradien arah horizontal');
axes(ax11)
imagesc(I2),axis image,colormap gray,colorbar,title('Gradien arah vertikal');
axes(ax12)
imagesc(J ),axis image,colormap gray,colorbar,title('Magnitudo gradien');

ax13 = axes('Parent',tab7,'Position',[.2 .53 .25 .4]);
ax14 = axes('Parent',tab7,'Position',[.55 .53 .25 .4]);
ax15 = axes('Parent',tab7,'Position',[.2 .1 .25 .4]);
ax16 = axes('Parent',tab7,'Position',[.55 .1 .25 .4]);

I = double(imread('cameraman.tif'));
%Konvolusi dengan operator Prewitt
prewitthor = [-1 0 1; -1 0 1; -1 0 1];
prewittver = [-1 -1 -1; 0 0 0; 1 1 1];
I1 = conv2(I,prewitthor,'same');
I2 = conv2(I,prewittver,'same');
J = sqrt((I1.^2)+(I2.^2));
%Gambar Hasil
axes(ax13)
imagesc(I ),axis image,colormap gray,colorbar,title('Citra asli');
axes(ax14)
imagesc(I1),axis image,colormap gray,colorbar,title('Gradien arah horizontal');
axes(ax15)
imagesc(I2),axis image,colormap gray,colorbar,title('Gradien arah vertikal');
axes(ax16)
imagesc(J ),axis image,colormap gray,colorbar,title('Magnitudo gradien');

ax17 = axes('Parent',tab8,'Position',[.2 .53 .25 .4]);
ax18 = axes('Parent',tab8,'Position',[.55 .53 .25 .4]);
ax19 = axes('Parent',tab8,'Position',[.2 .1 .25 .4]);
ax20 = axes('Parent',tab8,'Position',[.55 .1 .25 .4]);

I = double(imread('cameraman.tif'));
%Konvolusi dengan operator Sobel
sobelhor = [-1 0 1; -2 0 2; -1 0 1];
sobelver = [-1 -2 -1; 0 0 0; 1 2 1];
I1 = conv2(I,sobelhor,'same');
I2 = conv2(I,sobelver,'same');
J = sqrt((I1.^2)+(I2.^2));
%Gambar Hasil
axes(ax17)
imagesc(I ),axis image,colormap gray,colorbar,title('Citra asli');
axes(ax18)
imagesc(I1),axis image,colormap gray,colorbar,title('Gradien arah horizontal');
axes(ax19)
imagesc(I2),axis image,colormap gray,colorbar,title('Gradien arah vertikal');
axes(ax20)
imagesc(J ),axis image,colormap gray,colorbar,title('Magnitudo gradien');

ax21 = axes('Parent',tab9,'Position',[.2 .53 .25 .4]);
ax22 = axes('Parent',tab9,'Position',[.55 .53 .25 .4]);
ax23 = axes('Parent',tab9,'Position',[.2 .1 .25 .4]);
ax24 = axes('Parent',tab9,'Position',[.55 .1 .25 .4]);

I = double(imread('cameraman.tif'));
%Konvolusi dengan operator isotropic
L1 = [-1 0 1; -sqrt(2) 0 sqrt(2); -1 0 1];
isover = [-1 -sqrt(2) -1; 0 0 0; 1 sqrt(2) 1];
I1 = conv2(I,L1,'same');
I2 = conv2(I,isover,'same');
J = sqrt((I1.^2)+(I2.^2));
%Gambar Hasil
axes(ax21)
imagesc(I ),axis image,colormap gray,colorbar,title('Citra asli');
axes(ax22)
imagesc(I1),axis image,colormap gray,colorbar,title('Gradien arah horizontal');
axes(ax23)
imagesc(I2),axis image,colormap gray,colorbar,title('Gradien arah vertikal');
axes(ax24)
imagesc(J ),axis image,colormap gray,colorbar,title('Magnitudo gradien');

ax25 = axes('Parent',tab10,'Position',[.08 .53 .25 .4]);
ax26 = axes('Parent',tab10,'Position',[.4 .53 .25 .4]);
ax27 = axes('Parent',tab10,'Position',[.72 .53 .25 .4]);
ax28 = axes('Parent',tab10,'Position',[.08 .1 .25 .4]);
ax29 = axes('Parent',tab10,'Position',[.4 .1 .25 .4]);
ax30 = axes('Parent',tab10,'Position',[.72 .1 .25 .4]);

I = double(imread('cameraman.tif'));
%Konvolusi dengan operator compass
L1 = [1 1 1; 1 -2 1; -1 -1 -1];
K2 = [-1 -1 -1; 1 -2 1; 1 1 1];
K3 = [-1 1 1; -1 -2 1; -1 1 1];
K4 = [1 1 -1; 1 -2 -1; 1 1 -1];
I1 = conv2(I,L1,'same');
I2 = conv2(I,K2,'same');
I3 = conv2(I,K3,'same');
I4 = conv2(I,K4,'same');
J = sqrt((I1.^2)+(I2.^2)+(I3.^2)+(I4.^2));
%Gambar Hasil
axes(ax25)
imagesc(I ),axis image,colormap gray,colorbar,title('Citra asli');
axes(ax26)
imagesc(I1),axis image,colormap gray,colorbar,title('Gradien arah utara');
axes(ax27)
imagesc(I2),axis image,colormap gray,colorbar,title('Gradien arah selatan');
axes(ax28)
imagesc(I3),axis image,colormap gray,colorbar,title('Gradien arah timur');
axes(ax29)
imagesc(I4),axis image,colormap gray,colorbar,title('Gradien arah barat');
axes(ax30)
imagesc(J ),axis image,colormap gray,colorbar,title('Magnitudo gradien');

ax31 = axes('Parent',tab11,'Position',[.03 .58 .15 .25]);
ax32 = axes('Parent',tab11,'Position',[.23 .58 .15 .25]);
ax33 = axes('Parent',tab11,'Position',[.43 .58 .15 .25]);
ax34 = axes('Parent',tab11,'Position',[.63 .58 .15 .25]);
ax35 = axes('Parent',tab11,'Position',[.83 .58 .15 .25]);
ax36 = axes('Parent',tab11,'Position',[.03 .13 .15 .25]);
ax37 = axes('Parent',tab11,'Position',[.23 .13 .15 .25]);
ax38 = axes('Parent',tab11,'Position',[.43 .13 .15 .25]);
ax39 = axes('Parent',tab11,'Position',[.63 .13 .15 .25]);
ax40 = axes('Parent',tab11,'Position',[.83 .13 .15 .25]);

I = double(imread('cameraman.tif'));
%Konvolusi dengan operator kirsch
L1 = [-3 -3 5; -3 0 5; -3 -3 5];
K2 = [-3 5 5; -3 0 5; -3 -3 -3];
K3 = [5 5 5; -3 0 -3; -3 -3 -3];
K4 = [5 5 -3; 5 0 -3; -3 -3 -3];
K5 = [5 -3 -3; 5 0 -3; 5 -3 -3];
K6 = [-3 -3 -3; 5 0 -3; 5 5 -3];
K7 = [-3 -3 -3; -3 0 -3; 5 5 5];
K8 = [-3 -3 -3; -3 0 5; -3 5 5];
I1 = conv2(I,L1,'same');
I2 = conv2(I,K2,'same');
I3 = conv2(I,K3,'same');
I4 = conv2(I,K4,'same');
I5 = conv2(I,K5,'same');
I6 = conv2(I,K6,'same');
I7 = conv2(I,K7,'same');
I8 = conv2(I,K8,'same');
J = sqrt((I1.^2)+(I2.^2)+(I3.^2)+(I4.^2)+(I5.^2)+(I6.^2)+(I7.^2)+(I8.^2));
%Gambar Hasil
axes(ax31)
imagesc(I ),axis off,colormap gray,title('Citra asli');
axes(ax32)
imagesc(I1),axis off,colormap gray,title('Timur');
axes(ax33)
imagesc(I2),axis off,colormap gray,title('Timur laut');
axes(ax34)
imagesc(I3),axis off,colormap gray,title('Utara');
axes(ax35)
imagesc(I4),axis off,colormap gray,title('Barat laut');
axes(ax36)
imagesc(I5),axis off,colormap gray,title('Barat');
axes(ax37)
imagesc(I6),axis off,colormap gray,title('Barat daya');
axes(ax38)
imagesc(I7),axis off,colormap gray,title('Selatan');
axes(ax39)
imagesc(I8),axis off,colormap gray,title('Tenggara');
axes(ax40)
imagesc(J ),axis off,colormap gray,title('Magnitudo gradien');

tgroup2 = uitabgroup('Parent', tab2);
tab11 = uitab('Parent', tgroup2, 'Title', 'Laplacian I');
tab12 = uitab('Parent', tgroup2, 'Title', 'Laplacian II');
tab13 = uitab('Parent', tgroup2, 'Title', 'Laplacian III');
tab14 = uitab('Parent', tgroup2, 'Title', 'Laplacian of Gaussian');

ax41 = axes('Parent',tab11,'Position',[.1 .23 .35 .6]);
ax42 = axes('Parent',tab11,'Position',[.55 .23 .35 .6]);

I = double(imread('cameraman.tif'));
%Konvolusi dengan operator laplacian
L1 = [0 -1 0; -1 4 -1; 0 -1 0];
I1 = conv2(I,L1,'same');
%Gambar Hasil
axes(ax41)
imagesc(I ),axis image,colormap gray,colorbar,title('Citra asli');
axes(ax42)
imagesc(I1),axis image,colormap gray,colorbar,title('Hasil deteksi tepi');

ax43 = axes('Parent',tab12,'Position',[.1 .23 .35 .6]);
ax44 = axes('Parent',tab12,'Position',[.55 .23 .35 .6]);

I = double(imread('cameraman.tif'));
%Konvolusi dengan operator laplacian
L2 = [-1 -1 -1; -1 8 -1; -1 -1 -1];
I2 = conv2(I,L2,'same');
%Gambar Hasil
axes(ax43)
imagesc(I ),axis image,colormap gray,colorbar,title('Citra asli');
axes(ax44)
imagesc(I2),axis image,colormap gray,colorbar,title('Hasil deteksi tepi');

ax45 = axes('Parent',tab13,'Position',[.1 .23 .35 .6]);
ax46 = axes('Parent',tab13,'Position',[.55 .23 .35 .6]);

I = double(imread('cameraman.tif'));
%Konvolusi dengan operator laplacian
L3 = [1 -2 1; -2 4 -2; 1 -2 1];
I3 = conv2(I,L3,'same');
%Gambar Hasil
axes(ax45)
imagesc(I ),axis image,colormap gray,colorbar,title('Citra asli');
axes(ax46)
imagesc(I3),axis image,colormap gray,colorbar,title('Hasil deteksi tepi');

ax47 = axes('Parent',tab14,'Position',[.1 .23 .35 .6]);
ax48 = axes('Parent',tab14,'Position',[.55 .23 .35 .6]);

I = double(imread('cameraman.tif'));
J = edge(I,'log');
axes(ax47)
imagesc(I),axis image,colormap gray,colorbar,title('Citra asli');
axes(ax48)
imagesc(J),axis image,colormap gray,colorbar,title('Hasil deteksi tepi');

ax49 = axes('Parent',tab3,'Position',[.1 .23 .35 .6]);
ax50 = axes('Parent',tab3,'Position',[.55 .23 .35 .6]);

I = double(imread('cameraman.tif'));
J = edge(I,'canny');
axes(ax49)
imagesc(I),axis image,colormap gray,colorbar,title('Citra asli');
axes(ax50)
imagesc(J),axis image,colormap gray,colorbar,title('Hasil deteksi tepi');

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