computer vision - wordpress.com · 2020. 2. 5. · computer vision image geometry and...

Computer VisionImage geometry and implementation

Juan Irving Vasquez

Consejo Nacional de Ciencia y Tecnologıa

5 de febrero de 2020

J. Irving Vasquez (jivg.org) Computer Vision 5 de febrero de 2020 1 / 29

Image geometry

The pinhole model


Image geometry

There are two parts of the image formation:

Geometry. Determines where in the image plane a point of the realworld will be shown.Intensity of light. Determines the amount of brightness that a point inthe image will have.


Image geometry (inverted)


Image geometry


Image geometry

Let us write,f

z=

r ′

r

x ′

x=

y ′

y=

r ′

r

Prove that (activity),

x ′ =f

zx

y ′ =f

zy


What is an image?

A function.f (x , y) : R2 → R (1)

But computers are not so capable, then

I (i , j) : [a, b]× [c , d ]→ [min,max ] (2)


Samplig and quantization

A discrete image

I (i , j) : [a, b]× [c , d ]→ [min,max ]

Samplig. The amount of pixels in the image.e.g. 640× 480 pixels

Quantization. The possibles values for each pixel.e.g. binary, 8 bits, or float (HDRI)


Implementation

Figura: Gray scale imageJ. Irving Vasquez (jivg.org) Computer Vision 5 de febrero de 2020 9 / 29

Color images

A vector valued function or ”stacked”

f (x , y) =

r(x , y)g(x , y)b(x , y)


Implementation

Figura: Color imageJ. Irving Vasquez (jivg.org) Computer Vision 5 de febrero de 2020 11 / 29

OpenCV

OpenCV

The Open Source Computer Vision Library is an open source computervision and machine learning software library.

Provides a common infrastructure for computer vision application

Accelerates the use of machine perception in the commercial products

BSD-licensed product


Implementation

Create an image (matrix).

Mat a= Mat ( S i z e ( 5 , 5 ) , CV 32F ) ;

Data types

CV 8UC1CV 8UC3CV 8UC4CV 32FC1CV 32FC3CV 32FC4


Data types

(Check by yourself)

Mat

Vec

Scalar

Point

Size

Rect

RotatedRect


Lets go to code!!

Repository:

OpenCV Exampleshttps://github.com/irvingvasquez/vision_programas.git

Primer programa: leer y mostrar una imagen.

01_operaciones_basicas.ipynb


https://github.com/irvingvasquez/vision_programas.git

Basic operations

Addition, C = A + Bci ,j = ai ,j + bi ,j (3)

Substraction, C = A− B

ci ,j = ai ,j − bi ,j (4)

Multiplication, C = AB. If A is an m × n matrix and B is an n × pmatrix,

ci ,j =n∑

k=1

ai ,kbk,j (5)

Element-wise multiplication

ci ,j = ai ,jbi ,j (6)


Suma

Programa 03

Mat ImGray= imread ( ” . . / l e n a . j p g ” , 0 ) ;Mat ImGray2 = imread ( ” . . / monkey . j p g ” , 0 ) ;

Mat sum = Mat ( ImGray . s i z e ( ) , t y p e ) ;sum = ImGray + ImGray2 ;

imshow (”Suma” , sum ) ;


Addition

Figura: Addition. Is this ok?


Suma (Weighted)

Programa 04

Mat ImGray= imread ( ” . . / l e n a . j p g ” , 0 ) ;Mat ImGray2 = imread ( ” . . / monkey . j p g ” , 0 ) ;

Mat sum = Mat ( ImGray . s i z e ( ) , t y p e ) ;

f l o a t a l p h a = 0 . 5 ;sum = a l p h a ∗ ImGray + (1− a l p h a ) ∗ ImGray2 ;

imshow (” wighted sum ” , sum ) ;


Suma (Weighted)

Figura:J. Irving Vasquez (jivg.org) Computer Vision 5 de febrero de 2020 20 / 29

Region of Interest

A ROI allow us to work with certain parts of an image.

Figura: Regions of interest.


Crop an image

// Read imagesMat ImGray= imread ( ” . . / l e n a . j p g ” , 0 ) ;Mat ImCropped ;

// x , yRect window ( 0 , 0 , ImGray . c o l s , 0 . 5∗ ImGray . rows ) ;

ImCropped = ImGray ( window ) ;


Histograma

Muestra la frecuencia con la que aparece cada valor.

Una funcionf (i)

que cuenta cuantos pixeles tienen igual intensidad o en el intervalo i .


Histogram

Figura: Red channel’s histogram


Histogramas

Histograma normalizado

g(i) = f (i)/m

Histograma acumulado

g(i) =i∑

j=1

f (i)


Histogram Modification

Histogram equalization.

Defines a mapping of gray levels p into gray levels q such that thedistribution of gray levels q is uniform.


Equalizacion de histograma

Mapping


Miniproject 1

Read this paper:BENDIG, Juliane, et al. Combining UAV-based plant height from crop surface

models, visible, and near infrared vegetation indices for biomass monitoring in

barley. International Journal of Applied Earth Observation and Geoinformation,

2015, vol. 39, p. 79-87.

Download this imagehttps://jivg.org/2016/10/05/mapa-del-campo-escom/

Compute the following idices:

GRVIMGRVI or RGBVI

Display your results


computer vision - wordpress.com · 2020. 2. 5. · computer vision image geometry and...

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