The document discusses the Lucas-Kanade template tracking method. It begins with a review of Lucas-Kanade optical flow, then describes how the same approach can be used to track larger image patches or templates by imposing the constraint that neighboring pixels have similar motion. It presents the derivation step-by-step, showing how a Taylor series approximation allows formulation as a least squares problem. An example Jacobian for affine motion models is provided. The algorithm iterates between warping the template, computing error, estimating motion parameters, and updating. State-of-the-art examples include tracking facial mesh models.
Gives a basic idea of Finite field theory and its uses in Elliptic cure cryptography. ECDLP and Diffie Helman key exchange and Elgamal Encryption with ECC.
In recent years due to advancement in video and image editing tools
it has become increasingly easy to modify the multimedia content. The
doctored videos are very difficult to identify through visual
examination as artifacts left behind by processing steps are subtle
and cannot be easily captured visually. Therefore, the integrity of
digital videos can no longer be taken for granted and these are not
readily acceptable as a proof-of-evidence in court-of-law. Hence,
identifying the authenticity of videos has become an important field
of information security.
In this thesis work, we present a novel approach to detect and
temporally localize video inpainting forgery based on optical flow
consistency. The proposed algorithm comprises of two stages. In the
first step, we detect if the given video is inpainted or authentic and
in the second step we perform temporal localization. Towards this, we
first compute the optical flow between frames. Further, we analyze the
goodness of fit of chi-square values obtained from optical flow
histograms using a Guassian mixture model. A threshold is then applied
to classify between authentic and inpainted videos. In the next step,
we extract Transition Probability Matrices (TPMs) by modelling the
optical flow as first order Markov process. SVM based classification
is then applied on the obtained TPM features to decide whether a block
of non-overlapping frames is authentic or inpainted thus obtaining
temporal localization. In order to evaluate the robustness of the
proposed algorithm, we perform the experiments against two popular and
efficient inpainting techniques. We test our algorithm on public
datasets like PETS and SULFA. The results show that the approach is
effective against the inpainting techniques. In addition, it detects
and localizes the inpainted frames in a video with high accuracy and
low false positives.
Gives a basic idea of Finite field theory and its uses in Elliptic cure cryptography. ECDLP and Diffie Helman key exchange and Elgamal Encryption with ECC.
In recent years due to advancement in video and image editing tools
it has become increasingly easy to modify the multimedia content. The
doctored videos are very difficult to identify through visual
examination as artifacts left behind by processing steps are subtle
and cannot be easily captured visually. Therefore, the integrity of
digital videos can no longer be taken for granted and these are not
readily acceptable as a proof-of-evidence in court-of-law. Hence,
identifying the authenticity of videos has become an important field
of information security.
In this thesis work, we present a novel approach to detect and
temporally localize video inpainting forgery based on optical flow
consistency. The proposed algorithm comprises of two stages. In the
first step, we detect if the given video is inpainted or authentic and
in the second step we perform temporal localization. Towards this, we
first compute the optical flow between frames. Further, we analyze the
goodness of fit of chi-square values obtained from optical flow
histograms using a Guassian mixture model. A threshold is then applied
to classify between authentic and inpainted videos. In the next step,
we extract Transition Probability Matrices (TPMs) by modelling the
optical flow as first order Markov process. SVM based classification
is then applied on the obtained TPM features to decide whether a block
of non-overlapping frames is authentic or inpainted thus obtaining
temporal localization. In order to evaluate the robustness of the
proposed algorithm, we perform the experiments against two popular and
efficient inpainting techniques. We test our algorithm on public
datasets like PETS and SULFA. The results show that the approach is
effective against the inpainting techniques. In addition, it detects
and localizes the inpainted frames in a video with high accuracy and
low false positives.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
2. Robert Collins
CSE486, Penn State
Two Popular Tracking Methods
• Mean-shift color histogram tracking (last time)
• Lucas-Kanade template tracking (today)
4. Robert Collins
CSE486, Penn State Review: Lucas-Kanade
• Brightness constancy
• One equation two unknowns
unknown flow vector
temporal gradient spatial gradient
• How to get more equations for a pixel?
– Basic idea: impose additional constraints
• one method: pretend the pixel’s neighbors have the same (u,v)
– If we use a 5x5 window, that gives us 25 equations per pixel!
* From Khurram Hassan-Shafique CAP5415 Computer Vision 2003
5. Robert Collins
CSE486, Penn State
Review: Lucas-Kanade (cont)
• Now we have more equations than unknowns
• Solution: solve least squares problem
– minimum least squares solution given by solution (in d) of:
– The summations are over all pixels in the K x K window
– This technique was first proposed by Lucas & Kanade (1981)
• described in Trucco & Verri reading
* From Khurram Hassan-Shafique CAP5415 Computer Vision 2003
6. Robert Collins
CSE486, Penn State
Lucas Kanade Tracking
Traditional Lucas-Kanade is typically run on small,
corner-like features (e.g. 5x5) to compute optic flow.
Observation: There’s no reason we can’t use the same
approach on a larger window around the object being
tracked.
80x50 pixels
7. Robert Collins
Basic LK Derivation for Templates
CSE486, Penn State
template
(model)
current frame
u,v = hypothesized location of
template in current frame
8. Robert Collins
Basic LK Derivation for Templates
CSE486, Penn State
First order approx
Take partial derivs and set to zero
Form matrix equation
solve via
least-squares
9. Robert Collins
CSE486, Penn State
One Problem with this...
Assumption of constant flow (pure translation) for
all pixels in a larger window is unreasonable for
long periods of time.
However, we can easily generalize Lucas-Kanade
approach to other 2D parametric motion models
(like affine or projective) by introducing a “warp”
function W.
generalize
x
[ I (W ([ x, y ]; P)) T ([ x, y ])]2
within image patch
y
10. Robert Collins
CSE486, Penn State
Step-by-Step Derivation
The key to the derivation is Taylor series approximation:
W
[ I (W ([ x, y ]; P P)) ~ [ I (W ([ x, y ]; P)) I
~ P
P
We will derive this step-by-step. First, we need two background formula:
11. Robert Collins
CSE486, Penn State
Step-by-Step Derivation
First consider the expansion for a single variable p
12. Robert Collins
CSE486, Penn State
Step-by-Step Derivation
Note that each variable parameter pi contributes a term of the form
13. Robert Collins
CSE486, Penn State
Step-by-Step Derivation
Now let’s rewrite the expression as a matrix equation. For each term,
we can rewrite:
So that we have:
14. Robert Collins
CSE486, Penn State
Step-by-Step Derivation
Further collecting the dw/dpi terms into a matrix, we can write:
which are the terms in the matrix equation:
~ W
[ I (W ([ x, y ]; P P)) ~ [ I (W ([ x, y ]; P)) I P
P
15. Robert Collins
Example: Jacobian of Affine Warp
CSE486, Penn State
Let W([x, y]; P) [Wx , Wy ]
general equation of Jacobian Wx Wx Wx Wx
W P P P P
1 2 3 n
P Wy Wy Wy Wy
P
1 P2 P3 P
n
affine warp function (6 parameters)
x xP yP3 P5
1
x W xP2 y yP4 P6
1 p1
W ([ x, y ]; P )
p3 p5
y
p6 P P
p2 1 p4 1
x 0 y 0 1 0
0 x 0 y 0 1
16. Source: “Lucas-Kanade 20 years on: A unifying framework” Baker and Mathews, IJCV 04
Robert Collins
CSE486, Penn State
Iterate Warp I to obtain I(W([x y];P))
Compute the error image T(x) – I(W([x y]; P))
Warp the gradient I with W([x y]; P)
W
Evaluate at ([x y]; P) (Jacobian)
P
W
Compute steepest descent images I
P
W T W
Compute Hessian matrix (I P
) (I
P
)
W T
Compute ( I P
) (T ( x, y ) I (W ([ x, y ]; P )))
Compute P
Update P P + P
Until P magnitude is negligible
Dr. Ng Teck Khim
17. Robert Collins
CSE486, Penn State Algorithm At a Glance
Source: “Lucas-Kanade 20 years on: A unifying framework” Baker and Mathews, IJCV 04
18. Robert Collins
State of the Art Lucas Kanade Tracking
CSE486, Penn State
Tracking facial mesh models (piecewise affine)
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Baker, Matthews, CMU