moving object detection

Moving Object Detection

04/12/2023DSG, CEERI Pilani2

Tracking Tracking is the problem of estimating the

trajectory of an object in the image plane as it moves around a scene.


What is Motion Tracking…?• Technologies that collect data on human movement

(input) used to control sounds, music, recorded or projected text, video art, stage lighting (output) via performer actions / gestures / movements / bio-data.


What is Motion Tracking…?• other uses:

• Animation modeling (motion capture)

• Scientific research (musicology, semantics, ergonomics, medicine, sports medicine, architecture)

• Therapy for physically and mentally handicapped


Motion tracking vs. Motion captureMotion capture

• Tracks location of fixed positions on body

• Highly accurate, expensive ($200k-2m)

• Generally not realtime

• Used for data collection (research) and for making human or animal motion in animations (films, games, etc.) more realistic

Motion tracking

• less equipment, less data,

• less cost ($1k-2k)

• concerned with motion qualities like dynamic, direction of motion

• real time

• used for live applications: installation art, dance, theater and music


Motion capture Motion capture is defined as "The creation of a 3D

representation of a live performance." Tracks location of fixed positions on body with reflective

markers 12-24 cameras, each lens is ringed with infrared lights


Motion capture Motion capture is used to be considered a tool

for creating animation.


Motion capture Typical uses

Human movement research (sports, musicology, ergonomics, medicine,...)

Film and Animation -- often used with 3-D animation (modeling) programs to make animations

maya (http://www.animationarena.com)

houdini (http://www.sidefx.com)

http://www.animationarena.com/

http://www.sidefx.com/


Motion capture

Vicon is a leading company in motion capture


Motion tracking

input

physical

human action

media output

sounds,

music, text,

projections,

lighting


Motion tracking

input

physical

human action

computersensor

(e.g. video camera)

output device (e.g. loud speakers)

media output

sounds,

music, text,

projections,

lighting

analogue to digital

conversion

digital to analogue

conversion


Digital vs. Analogue Analogue data

• hard to reproduce• "rich data" (infinite values)• very high resolution• more details• contaminated data (becomes noisy, but rarely fails completely)

Digital data

• easy to reproduce• lower resolution, less human-feel.• easy to store• easy to process• contaminated data remains clean (errors can be filtered) or signal fails altogether


What you need to track motion Computer needs video input

Digital video (Firewire, USB2)

+ digital cameras (camcorder, webcams)

+ low noise

+ works with laptops

- latency issues

- image resolution issues (smaller chip sizes)

- limited cable length

Analog video

+ "unlimited" cable length

+ lower latency

+ even digital cams usually have analog output

- cost more (although many older cameras work quite well)

- works less well with laptops i.e. need an external or internal framegrabber


Palindrome Intermedia Performance Group Krisztina de Chatel Igloo Ventura Dance (Pablo Ventura) Robert Lepage André Werner Marlon Barrios Solano La la la Human Steps Georg Hobmeier Leine Roebana Dans Kompanie Troika Ranch Blue Man Group you

Who is using motion tracking?

The Problem in Motion Tracking Given a set of images in time which are similar

but not identical, derive a method for identifying the motion that has occurred (in 2d) between different images.

Motion Detection and Estimation in Literature

Image differencing based on the threshold difference of successive images difficult to reconstruct moving areas

Background subtraction foreground objects result by calculating the difference

between an image in the sequence and the background image (previously obtained)

remaining task: determine the movement of these foreground objects between successive frames

Block motion estimation Calculates the motion vector between frames for sub-

blocks of the image mainly used in image compression too coarse

What Is Optical Flow? Optical flow is the displacement field for

each of the pixels in an image sequence.

For every pixel, a velocity vector is found which says:

how quickly a pixel is moving across the image

the direction of its movement.

dt

dy

dt

dx,


Optical Flow Examples

Image #1 Optical Flow Field Image #2

Optical Flow ExamplesTranslation Rotation Scaling


Estimation of the optical flow Sequences of ordered images allow the

estimation of motion as either instantaneous image velocities or discrete image displacements.

The optical flow methods try to calculate the motion between two image frames which are taken at times

t and t + δt at every voxel position.


Voxel Position A voxel (volumetric pixel or Volumetric Picture

Element) is a volume element, representing a value on a regular grid in three dimensional space.

A series of voxels in a stack with a single voxel highlighted


Estimation of the optical flow Optical Flow methods are called differential since

they are based on local Taylor series approximations of the image signal; that is, they use partial derivatives with respect to the spatial and temporal coordinates.

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.


Taylor series The Taylor series of a real or complex function ƒ(x) that is

infinitely differentiable in a neighborhood of a real or complex number a is the power series

which can be written in the more compact sigma notation as

where n! denotes the factorial of n and ƒ (n)(a) denotes the nth derivative of ƒ evaluated at the point a. The zeroth derivative of ƒ is defined to be ƒ itself and (x − a)0 and 0! are both defined to be 1. In the case that a = 0, the series is also called a Maclaurin series.


Estimation of the optical flow For a 2D+t dimensional case (3D or n-D cases are similar) a

voxel at location (x,y,t) with intensity I(x,y,t) will have moved by δx, δy and δt between the two image frames, and the following image constraint equation can be given:

I(x,y,t) = I(x + δx,y + δy,t + δt)

Assuming the movement to be small, the image constraint at I(x,y,t) with Taylor series can be developed to get:

H.O.T

(higher-order terms)


Estimation of the optical flow


Estimation of the optical flowwhere Vx,Vy are the x and y components of the velocity or optical flow of I(x,y,t) and are the derivatives of the image at (x,y,t) in the

corresponding directions. Ix,Iy and It can be written for the derivatives in the following.

Thus: IxVx + IyVy = − It

or

This is an equation in two unknowns and cannot be solved as such. This is known as the aperture problem of the optical flow algorithms. To find the optical flow another set of equations is needed, given by some additional constraint. All optical flow methods introduce additional conditions for estimating the actual flow.

Our Solution Optical flow: maximum one pixel large

movements

Optical flow: larger movements

Morphological filter

Contour detection (demo purposes)

Optical Flow: maximum one pixel large movements

The optical flow for a pixel given 2 successive images and :

),(),( yxjimk

ji,k 1k

so that

),(),( 1 yjxiIjiI kk

is minimum for 11,11 yx

(1)

k k+1

Optical Flow: maximum one pixel large movements

More precision: consider a 3×3 window around the pixel:

Optical flow for pixel becomes: ji,

),(),( yxjimk so that

1

1

1

11

1

1

1

1

),(),(u v

ku v

k yvjxuiIvjuiI

is minimum for 11,11 yx

(2)

Optical Flow: larger movements Reduce the size of the image

=> reduced size of the movement

Solution: multi-resolution analysis of the images

Advantages: computing efficiency, stability

Multi-resolution Analysis Coarse to fine optical flow estimation:

Original image k Original image k+1

256×256

128×128

64×64

32×32

Optical Flow: Top-down StrategyAlgorithm (1/4 scale of resolution

reduction): Step 1: compute optical flow vectors for the

highest level of the pyramid l (smallest resolution)

Step 2: double the values of the vectors Step 3: first approximation: optical flow vectors

for the (2i, 2j), (2i+1, 2j), (2i, 2j+1), (2i+1, 2j+1) pixels in the l-1 level are assigned the value of the optical flow vector for the (i,j) pixel from the l level

Level l Level l-1

Optical Flow: Top-down Strategy Step 4:

adjustment of the vectors of the l-1(one) level in the pyramid

method: detection of maximum one pixel displacements around the initially approximated position

Step 5:

smoothing of the optical flow field (Gaussian filter)

Filtering the Size of the Detected Regions

Small isolated regions of motion detected by the optical flow method are classified as noise and are eliminated with the help of morphological operations:

Step 1: Apply the opening:

Step 2: Apply the closing: BBXBX

BBXBX

Contour Detection For demonstration purposes, the contours of the

moving regions detected are outlined Method: the Sobel edge detector:

Compute the intensity gradient:

using the Sobel masks:

Compute the magnitude of the gradient:

if then edge pixel

else non-edge pixel

yx ffy

f

x

fyxf ,,,

(5)

121

000

121

4

1,

101

202

101

4

1yx GG (6)

22,, yx ffyxfyxM (7)

thresholdyxM ,

A Block Diagram of the System

Conclusions What we did:

We managed to estimate the motion with a certain level of accuracy

The results might be good enough for some applications, while other applications might require better accuracy

What remains to be done: Reduce computational complexity

use the computed background image to separate foreground objects

Parallelism of the algorithms Experiment with specific problems, calibrate

the parameters of the algorithms


Thanks

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