Neighborhood Processing Image Enhancement

Neighborhood

Processing

•

_Introduction

Basic Image Processing

Operations

• _{Neighborhood processing}

• _{process the pixel with its neighbors} • _{Point operations}

Point Processing

Original

Original Darken_Darken

Invert

Invert Lighten_Lighten

Lower Contrast

Lower Contrast

Raise Contrast

Raise Contrast Nonlinear Lower _ContrastNonlinear Lower _Contrast

Nonlinear Raise Contrast

Point Processing

Original

Original Darken_Darken

Invert

Invert Lighten_Lighten

Lower Contrast

Lower Contrast

Raise Contrast

Raise Contrast Nonlinear Lower ContrastNonlinear Lower _Contrast

Nonlinear Raise Contrast

Nonlinear Raise Contrast

x + 128 x * 2

255 - x ((x / 255.0) ^2) * 255.0

x - 128 x / 2

Neighborhood operations

Image Edge detection Blur

• _{Deteksi tepi ( Edge detection ) adalah operasi yang dijalankan untuk}

mendeteksi garis tepi (edges) yang membatasi dua wilayah citra homogen yang memiliki tingkat kecerahan yang berbeda

• _{Tujuannya adalah untuk mengubah citra 2D menjadi bentuk kurva}

Neighborhood Processing

3x3 Mask

Output derives from multiplying all elements in the mask

by corresponding elements in the neighborhood and

Filter

• _{A rule or procedure for processing an image} • _{Combination of mask and function}

• _{Goal: separating/attenuating a desired component of an} observed image

• _Type:

• _{Linear (function), Nonlinear (function)}

Steps of

Linear Spatial

Filtering

• _{Position the mask over the current pixel.}

• _{Form all products of filter elements with the corresponding}

elements of the neighborhood.

• _{Add all products.}

• _{Other names for mask:}

Linear Spatial Filter: Example

Linear Spatial Filter: Example

20/9 0/9

10/9

Linear Spatial Filter: Example

(3)

15/9 20/9

10/9 15/9

10/9 10/9

Add all products for output.

15/9 + 10/9 + 20/9 +

0/9 + 10/9 + 15/9 +

20/9 + 10/9 + 10/9

= 12.22

Output intensity of blue pixel

= 12.22

Correlation and

Convolution

Correlation

• _{Sum of the product of mask and intensity on each point.}

Example: Correlation (2)

Multiply and sum all products.

10



1 +15



2 +10



3

+10



2 +20



3

+15



4 +5



3 +0



4

+0



5

Exercise: Correlation

Convolution

• _{Sum of the response on each point}

Example: Convolution (2)

Multiply and sum all products.

10



5 +15



4 +10



3

+10



4 +20



3

+15



2 +5



3 +0



2

+0



1

Exercise: Convolution

Example: HPF (2)

Filtered Image

10 20 10 15 5

5 0 20 -10 0

20 -40 25 15 5

10 5 -35 0 10

Edges of The Image

• _{A linear filter is represented as a matrix, e.g., the 3 x 3 averaging}

filter.

• _{Edges of the Image}

• _{There are a number of different approaches to dealing with this problem.}

• _{Ignore the edges: The mask is applied to all pixels except the edges and}

results in an output image that is smaller than the original. If the mask is very large, a significant amount of information may be lost.

• _{Pad with zeros: We assume that all necessary values outside the image are}

zero. It will return an output image of the same size as the original, but may have the effect of introducing unwanted artifacts, e.g., edges, around the image.

1/9

1/9

1/9 1/9 1/9

1/9 1/9 1/9

Edges of The Image

Batas atau tepi citra (edges of the image)

•_{hal yang harus diselesaikan dalam operasi filtering}

•_{misalnya, bagaimana jika sebagian “mask” berada di luar}

Edges of The Image (1)

Tidak mempedulikan batas atau tepi citra

•_{“mask” hanya diaplikasikan pada piksel-piksel citra dimana}

seluruh “mask” berada dalam citra.

•_{Pendekatan ini menghasilkan citra output yang ukurannya} lebih kecil daripada citra input.

•_{Jika ukuran “mask” sangat besar, akan menyebabkan sejumlah}

Edges of The Image (2)

Tambahkan piksel-piksel dengan nilai 0 (Pad with zeroes)

•_{Dalam pendekatan ini, diasumsikan bahwa semua piksel yang}

berada di luar citra mempunyai nilai grey-level nol.

•_{Pendekatan ini menghasilkan citra output yang ukurannya sama}

Filtering in MATLAB

• _Command: filter2

• _Syntax: filter2(filter, image, shape); filter2(filter, image);

• shape:

• ‘same’: pad edge with zeros. Size unchanged. (default)

• ‘valid’: apply mask only to inside pixel. Size smaller.

Filter Construction in

MATLAB

• _Command: fspecial

• _Syntax: fspecial(type, parameter); fspecial(type);

• type: type of the filter

• ‘average’ : average filter • ‘gaussian’ : Gaussian filter • ‘laplacian’ : Laplacian filter …

• parameter: _{parameter of the filter (size, sigma, …). Default varies}

Filter on Frequency Domain

• _{Low-pass filter (LPF): filter that allows only the low-frequency}

components and reduces or eliminates the high-frequency components.

• _{E.g. Gaussian, average}

• _{High-pass filter (HPF): filter that allows only the high-frequency}

components and reduces or eliminates the low-frequency components.

• _{E.g. Laplacian, Prewitt, Sobel}

• _{Spatial data (intensity) transformed by Fourier transform.} • _{Simplified version:}

• _{high-frequency indicates the abrupt changes in intensity}  edges.

Computing Consideration

•

_{Filter may lead to the value outside [0,255]}

•

_{Solution 1: Make negative values positive (use}

absolute value)



good when there are few negative

values and the negative values are close to zero

•

_{Solution 2: Clip values}

_{. Values larger than 255 become}

255 and values less than 0 become 0.



not good if

there are many values outside the range.

•

_{Solution 3: Scaling transformation}

_{. Rescale the range}

Rescaling Intensity

Rescaled value (y)

1. Map

g

_L

to 0.

2. Map

g

_H

to 255.

3. Interpolate for

the remaining

Rescaling: MATLAB

• _Manual:

>> gH = max(filtered_image(:));

>> gL = min(filtered_image(:));

>> scaled = (image – gmin)/(gmax – gmin);

Rescaling: MATLAB (2)

• _Command: mat2gray

• _Syntax: mat2gray(double_image); What this command do?

• _{scale the value in} double_image _{to displayable value. Output is} double type.

Low Pass Filter

Averaging

Low Pass Filter

• _{Useful for reducing noise and eliminating small details.} • _{The elements of the mask must be positive.}

• _{Sum of mask elements is 1 (after normalization).}

Filter Average

• _{Filter average penting dalam permasalahan-permasalahan di}

mana aspek citra yang menjadi perhatian adalah bukan detail citra

• _{objek pengamatan :}

berapa jumlah objek yang ada pada citra

luas daerah gelap dan daerah terang pada citra.

Low Pass Filter : Averaging

• _{Mask size determines the degree of smoothing (loss of detail).}

3x3 5x5 7x7

15x15 25x25

Low Pass Filter : Averaging

• _{Mask size determines the degree of smoothing (loss of detail).}

Low Pass Filter : Gaussian

• _{1D Gaussian filter:}

• _{2D Gaussian filter:}

Low Pass Filter : Gaussian

• _{σ (sigma) controls the amount of smoothing}

• _{As σ increases, more samples must be obtained to represent}

• _{the Gaussian function accurately.}

σ = 3

Low Pass Filter : Gaussian

Filter Gaussian

•_{Implementasinya : membangun filter Gaussian, mengalikannya}

dengan matriks hasil transformasi Fourier, dan menginversikan hasilnya.

•_{Filter Gaussian merupakan jenis filter yang “paling smooth” dan}

Benefits of Gaussian Filter

•

_{They are}

_{mathematically very well behaved}

_{. The}

Fourier transform

of a Gaussian filter is

another

Gaussian

.

•

_{There are rotationally symmetric, so are very}

good starting points for

some edge-detection

algorithms

.

•

_{They are separable in}

_x

_and

_y

_{axes. This can lead}

to

very fast implementations

.

•

_The

_{convolution of two Gaussians}

_{is another}

Low Pass Filter : Gaussian

• _{Effect of Gaussian filter = blurring} • _larger leads to more blur.

50

Averaging vs Gaussian Smoothing

Averaging

Gaussian Filter: MATLAB

• _{Construction of Gaussian filter:}

• _command: fspecial(‘gaussian’, size, gamma);

size _{: size of the filter [row column], default [3 3]} gamma _: , default 0.5.

>>gaussian1 = fspecial(‘gaussian’, [5 5], 5);

_{Create the 55 Gaussian filter with the  value of 5.}

>>gaussian2 = fspecial(‘gaussian’, 3, 0.75);

 Create the 33 Gaussian filter with the  value of 0.75.

High Pass Filter

Useful for

highlighting fine details

.

The elements of the mask contain both

positive

and

negative

weights.

Sum of mask elements is 0.

1st _derivative

of Gaussian

2nd _derivative

Edge Sharpening

• _{Also known as edge enhancement, edge crispening, unsharp} masking.

• _{Process to make the edge slightly sharper (tajam) and crisper}

(tegas).

• _{E.g. linear edge sharpening, unsharp masking, high boost} filtering

• _{High pass filter (HPF)}

High Pass Filter : MATLAB

• _Command: filter2

• _Syntax: filter2(filter, image, shape); filter2(filter, image);

• shape:

• ‘same’: pad edge with zeros. Size unchanged. (default)

• ‘valid’: apply mask only to inside pixel. Size smaller.

• ‘full’: pad edge with zeros and applying the filter at all places on and around the image where the mask intersects the image matrix. Size larger.

LPF - HPF

• _{LPF = perbedaan warna rendah}

• _{HPF = perbedaan warna tinggi atau signifikan}

Unsharp Masking

and High Boost

Unsharp Masking

•

_{Obtain a}

_{sharp image}

_by

_subtracting

_{a lowpass filtered}

(i.e., smoothed) image

from

the

original

image:

-

₌

[unsharp_image] = [input] – (a [filter]  [input])

= (I* – a [filter]) _ [input]

= [unsharp_filter]  [input]

I* : matrix whose center member is 1 and the others are zero.

E.g. for 3  3 matrix I* =

• _{For 3}3 matrix, after some rearranging term:

[unsharp_filter] =

Unsharp Filter: MATLAB

• _Command: fspecial

• _Syntax: fspecial(‘unsharp’, alpha);

• alpha : alpha value for unsharp filter

• _{Size of the filter is fixed to 3}  3

Effect of Unsharp Masking

BEFORE AFTER

High Boost Filter

Image sharpening emphasizes edges but low frequency components are lost. (menekankan ketajaman)

High boost filter: amplify input image, then subtract a lowpass image.

Best result when 3/5  A  5/6

• _{Used in dark image.}

• _{Boost the intensity of the original image.}

Effect of High Boost Filter

High Boost Filter : MATLAB

Image Derivatives

•

_{How can we differentiate a}

_digital

_{image F[x,y]?}

–

_{Option 1: reconstruct a continuous image,}

_f,

_then

compute the derivative

–

_{Option 2: take discrete derivative (finite difference)}

1 -1

How would you implement this as a linear filter?

-1

1

Image Gradient

The gradient points in the direction of most rapid increase in intensity

•

_The

_gradient

_{of an image:}

The edge strength is given by the gradient magnitude (besar gradient):

The gradient direction is given by:

Metode Robert

• _{adalah teknik differensial pada arah horisontal dan differensial}

Image Gradient

•

_{A different approximation of the gradient:}

•We can implement and using the following masks:

*

(x+1/2,y+1/2)

Metode Prewitt

• _{Metode Prewitt merupakan pengembangan metode robert}

dengan menggunakan filter HPF yang diberi satu angka nol

Metode Sobel

• _{Metode ini mengambil prinsip dari fungsi laplace dan gaussian}

Image Gradient : MATLAB

• _Command: fspecial • _Syntax:

• fspecial(‘prewitt’);

• fspecial (‘sobel’);