2014 Visikom 04 Grayscale Image Analysis (1)

8/10/2019 2014 Visikom 04 Grayscale Image Analysis (1)

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GRAYSCALE IMAGANALYSIS

Kuliah Visi KomputerJurusan Teknik Inform2014


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Review Minggu 3: Summary

Images as 2-D signals

Linear and non-linear filters

Fourier Transform

Discrete Fourier Transform

Hybrid Images


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Single Pixel Manipulation

The value of g(x,y) depends directly on the vf(x, y)

This is a greyscale transformation or simplmapping

Common mapping functions:

Identity transformation Thresholding


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Common Mapping Functions

lightening increase contra


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Common Mapping Functions

enhance contrast in dark regions enhance contrast in


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Histogram Equalization

Ideally we want the im

spread uniformly over Image data squashed into asmall ran e of re values

stretch out the histogram to produce a more uniformdistribution


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A very noisy

image


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Using Neighborhood Pixels

So far we modified values of single pix What if we want to take neighborhood

account?

A common application of linear filtering

image smoothing using an averaging

or averaging maskor averaging kerne

Each oint in the smoothed ima e

The averaging filter is also known as the box filter.

Each pixel under the mask is multiplied by 1/9,

summed, and the result is placed in the output image

The mask is successively moved across the image.

That is, we convolvethe image with the mask.

1


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Example of 2-D Convolution

Convolution with box filters of size 1,5,15,3,9,35 (reading or


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0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 0 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 0 0 0 0 0 0 0

0 0 90 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 0 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 0 0 0 0 0 0 0

0 0 90 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

],[],[],[

,

lnkmflkgnmh

lk

[.,.]h[.,.]f

Image filtering . , . =

1 1 1

1 1 1

1 1 1

. , .

19


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0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 0 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 0 0 0 0 0 0 0

0 0 90 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 10

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 0 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 0 0 0 0 0 0 0

0 0 90 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

[.,.]h[.,.]f


1 1 1

1 1 1

1 1 1

. , .

19

],[],[],[

,

lnkmflkgnmh

lk

f l


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0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 0 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 0 0 0 0 0 0 0

0 0 90 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 10 20

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 0 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 0 0 0 0 0 0 0

0 0 90 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

[.,.]h[.,.]f


1 1 1

1 1 1

1 1 1

. , .

19

],[],[],[

,

lnkmflkgnmh

lk

fil i


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0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 0 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 0 0 0 0 0 0 0

0 0 90 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 10 20 30

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 0 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 0 0 0 0 0 0 0

0 0 90 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

[.,.]h[.,.]f


1 1 1

1 1 1

1 1 1

. , .

19

],[],[],[

,

lnkmflkgnmh

lk

I fil i


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0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 0 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 0 0 0 0 0 0 0

0 0 90 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 10 20 30 30

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 0 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 0 0 0 0 0 0 0

0 0 90 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

[.,.]h[.,.]f


1 1 1

1 1 1

1 1 1

. , .

19

],[],[],[

,

lnkmflkgnmh

lk

I filt i


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0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 0 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 0 0 0 0 0 0 0

0 0 90 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 10 20 30 30

?

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 0 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 0 0 0 0 0 0 0

0 0 90 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

[.,.]h[.,.]f


1 1 1

1 1 1

1 1 1

. , .

19

],[],[],[

,

lnkmflkgnmh

lk


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I filt i


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0 10 20 30 30 30

0 20 40 60 60 60

0 30 60 90 90 90

0 30 50 80 80 90

0 30 50 80 80 90

0 20 30 50 50 60

10 20 30 30 30 30

10 10 10 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 0 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 0 0 0 0 0 0 0

0 0 90 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 90 0 90 90 90 0 0

0 0 0 90 90 90 90 90 0 0

0 0 0 0 0 0 0 0 0 0

0 0 90 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

[.,.]h[.,.]f


1 1 1

1 1 1

1 1 1

. , .

19

],[],[],[

,

lnkmflkgnmh

lk


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Practice with Linear Filters

Original

?0 0 0

0 1 0

0 0 0


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0 0 0

0 1 0

0 0 0


Original Filtered

(no chang


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0 0 0

0 0 1

0 0 0


Original

?


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Original Shifted

By 1 pi

0 0 0

0 0 1

0 0 0


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Original

-(Note that filter sums to 1)1

9

1 1 1

1 1 1

1 1 1

0 0 0

0 2 0

0 0 0


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Original Sharpening filter

- Accentuates differenc

average

-19

1 1 1

1 1 1

1 1 1

0 0 0

0 2 0

0 0 0


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Sharpening


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Other Averaging Filters

One expects the value of a pixel to be more closely relatevalues of pixels close to it than to those further away

Accordingly it is usual to weight the pixels near the centremask more strongly than those at the edge

1 1 1

1 2 1

1 1 1


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Other Averaging Filters

One expects the value of a pixel to be more closely rthe values of pixels close to it than to those further a

Accordingly it is usual to weight the pixels near the cthe mask more strongly than those at the edge

1

10

1 1 1

1 2 11 1 1

Important filter: Gaussian


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0.003 0.013 0.02

0.013 0.059 0.09

0.022 0.097 0.15

0.013 0.059 0.09

0.003 0.013 0.02

5 x 5,

Slide credit: Christ

Important filter: Gaussian

Use Matlabsfspecial function to create a Gaussian filter.

is also know

Gaussian Filter

Smoothing with box filter


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Smoothing with box filter

Example Box Filter Smoothing

Smoothing with Gaussian filter


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Smoothing with Gaussian filter

Example Gaussian Smoothing


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Key Properties of Linear Filt

Linearity:filter(f1+ f2) = filter(f1) + filter(f2)

Shift invariance: same behavior regardless of pix

filter(shift(f)) = shift(filter(f))

Any linear, shift-invariant operator can be representedconvolution


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Key Properties of Linear Filt

Commutative:a* b= b* a Conceptually no difference between filter and signal

Associative:a* (b* c) = (a* b) * c Often apply several filters one after another: (((a* b1)

This is equivalent to applying one filter: a * (b1* b2* b

Distributes over addition: a* (b+ c) = (a* b) Scalars factor out: ka * b = a * kb = k (a* b)

Identity:unit impulse e= [0, 0, 1, 0, 0],a* e= a


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Gaussian Filters

Linear filters Remove high-frequency components

the image (low-pass filter)

Images become more smooth

Convolution of a Gaussian with a Gaus

another Gaussian

So can smooth with small-width kernel, re

and get same result as larger-width kerne

Separability of the Gaussian fil


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Separability of the Gaussian fil

Gaussian Filters


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Practical Matters

What about near the edge? The filter window falls off the

edge of the image

Need to extrapolate

Methods:

clip filter (black) wrap around

copy edge

reflect across edge


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Practical Matters

Methods (MATLAB): clip filter (black): imfilter(f, g, 0)

wrap around: imfilter(f, g, circ

copy edge: imfilter(f, g, repl

reflect across edge: imfilter(f, g, symm


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Practical Matters MATLAB: filter2(g, f, shape)

shape = full: output size is sum of sizes of fan shape = same: output size is same as f

shape = valid: output size is difference of sizes

f

gg

gg

f

gg

gg

g

g

full same


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Low-Pass Filtering

Removing all highspatial frequencies fsignal to retain only lowspatial frequen

called low-pass filtering.

Old Spectrum New Spectrum Low-Pass


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High-Pass Filtering

Removing all lowspatial frequencies frsignal to retain only highspatial freque

called high-pass filtering.

Old Spectrum New Spectrum High-Pass


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Low-Pass FilteringAn Exa


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Low-Pass FilteringAn Exa


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High-Pass FilteringAn Exa


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High-Pass FilteringAn Exa

S


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Filtering in the Spatial Doma

Low-pass filtering -> convolve the imagbox / Gaussian filter

High-pass filtering -> ?

Filt i i th S ti l D


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Filtering in the Spatial Doma Low-pass filtering -> convolve the image with a box / Gaussian

High-pass filtering ->

Since the sum of the weights is 0, the resulting signal will havevalue (i.e., the average value or the coefficient of the zero freqcomponent) .

To display the image you will need to take the absolute values.

-1/9 -1/9 -1/9

-1/9 8/9 -1/9

-1/9 -1/9 -1/9

N Li Filt i


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Non-Linear Filtering Neighbourhood averaging or Gaussian smoothing will tend to blur edges becaus

frequency components are attenuated

An alternative approach is to use median filtering. Here we set the grey level toof the pixel values in the neighbourhood

Example: pixel values in 3 3 neighbourhood

Sort the values 10 15 20 20 20 20 20 25 100

Pixels with outlying values are forced to become more like their neighbours

10 20 20

20 15 2020 25 100

20

median v

M di Filt i A E


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Median FilteringAn Examp

Medremo

Med

smoo

imagblurr

edge

Hi h B t Filt i


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High-Boost Filtering Here we take the original image and boost the high frequency compon

Can think of HighPass = OriginalLowPass. Thus

HighBoost = b*OriginalLowPass

= (b-1)*Original + OriginalLowPass

= (b-1)*Original + HighPass

bis the boosting factor.

When b=1, HighBoost = HighPass

High-boost filteringuseful for emphasizing high frequencies while low frequency components of the original image to aid in the interpretaimage

Hi h B t Filt i ( t )


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High Boost Filtering (cont.)

How can we perform high-boost filterinspatial domain? -1/9 -1/9 -1/9-1/9 w/9 -1/9

-1/9 -1/9 -1/9

where w = 9*b-

Original High Boosted

intermediate result

High Boost

contrast stretc

H hi Filt i


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Homomorphic Filtering

The brightness of an image point(, function of the illumination at that pointreflectance of the object at that point, i.

, = , (, )illumination0 , < reflectanc

0 ,

H hi Filt i ( t


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Homomorphic Filtering (cont

Let , = log , = log , + log ,

In the frequency domain, we have , = , + ,

Fourier transform

of log( , )

Fourier transform

of log( , )

If we apply a high

then we can supp

frequency illumina

components and

reflectance comp

Homomorphic Filtering (cont.


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FFTHigh-boost

filteringFFT-1(, ) log exp


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Smoothing and Sub samplin


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Smoothing and Sub-samplin

In many Computer Vision applications, sub-samplin

needed, e.g., to build an image pyramid, or

simply to reduce the resolution for efficient storage, trprocessing,


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Throw away every other row and

column to create a 1/2size image

Sub sampling Issues


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Sub-sampling Issues

Sub-sampling may be dangerous. WResample tcheckerboa

one sample

In the case

board, new

is reasonab

Top right als

reasonable

Bottom left

(dubious) a

has checks

big.

Aliasing in Videos


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Aliasing in Videos

Aliasing in Graphics


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Aliasing in Graphics


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Sampling and Aliasing

Top row shows the images, sampled at every second pixel to ge

bottom row shows the magnitude of frequency spectrum of thes

Anti aliasing


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Anti-aliasing

1. Sample more often

2. Get rid of all frequencies that are greater tthe new sampling frequency(Nyquistfrequency)

Will lose information

But its better than aliasing

Apply a smoothing filter

S li d Ali i


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Sampling and Aliasing

Sampling with smoothing. Top row shows the images. We get the nex

smoothing the image with a Gaussian with sigma 1 pixel, then samplin

pixel to get the next; bottom row shows the magnitude spectrum of the

Subsampling without Pre-filt


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Subsampling without Pre-filt

1/4 (2x zoom) 1/8 (41/2

Subsampling with Gaussian Prfiltering


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filtering

G 1/4 GGaussian 1/2

Slide by

Image Pyramids


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Image Pyramids

Key component of many

high level computer vision

tasks

How to create an image

pyramid?

Image Pyramids


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Image Pyramids


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The Correspondence Proble


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Basic assumptions:

Most scene points are visible in both ima

Corresponding image regions are similar

These assumptions hold if:

The distance of points from the cameras larger than the distance between camera



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Is a search problem:

Given an element in the left image, search focorresponding element in the right image.

We will typically need geometric constraints the size of the search space

We must choose: Elements to match

A similarity measure to compare elements


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Summary


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Single Pixel Operations

Histogram Equalization

Filtering in the Spatial Domain

Subsampling and Anti-aliasing

Template Matching


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Lab Work 4

Next Week: Edge detection


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Template Matching

Lab Work 3

Tugas 3


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Buatlah dua fungsi Matlab berikut:

1. function score = ssd(t, im)

2. function score = ncc(t, im)untuk gambar input im dan template t.

Setiap fungsi menghasilkan matriks score yang ukurannya sim.

Buatlah script untuk menguji kedua fungsi tsb yang menampinput, gambar template, dan matriks score. Beri keterangan

bagaimana menginterpretasikan matriks score yang ditampilKumpulkan dua file yang menguji dua pasang gambar dan teberbeda

Contoh gambar input dan template bisa didownload di elearn

2014 Visikom 04 Grayscale Image Analysis (1)

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Transcript of 2014 Visikom 04 Grayscale Image Analysis (1)