Download - Detection theory and industrial applications
![Page 1: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/1.jpg)
Detection theory and industrial applications
Jean-Michel Morel [email protected]
With contributions of:
Agnès Desolneux, Lionel Moisan, Rafael Grompone, Thibaud Ehret,
Gregory Randall, Jérémy Jakubowicz, Yiqing Wang, Mauricio Delbracio,
Pablo Musé, Tina Nikoukhah, Marina Gardella, Miguel Colom, José
Lezama
![Page 2: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/2.jpg)
“Detection ” is the most frequent request made by researchers, industrials,
police, press, defence for exploiting images, images series, video among other
data.
“Detection ” means that an automatic decision must be made. A wrong decision
may entail costs and false alerts if it is falsely positive, and worse costs, accidents
and disasters if it is falsely negative.
Therefore Detection requests a general decision theory controlling the “number
of false alarms” and giving tight detection thresholds
This theory exists, it uses simple (but sometimes subtle) probability arguments,
mixed with a fine control of image and video features
![Page 3: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/3.jpg)
Skolnik, M. I. (1962). Introduction to radar. Radar handbook, 2, 21.
LSD: a Line Segment Detector (2012), www.ipol.im
Rafael Grompone von Gioi, Jérémie Jakubowicz, J.M.M., Gregory Randall
An Unsupervised Point Alignment Detection Algorithm (2015), www.ipol.im
José Lezama, Gregory Randall, J.M.M., Rafael Grompone von Gioi
Cloud Detection by Luminance and Inter-band Parallax Analysis for Pushbroom Satellite Imagers
(2020), www.ipol.im
Tristan Dagobert, Rafael Grompone von Gioi, Carlo de Franchis, J.M.M., Charles Hessel
Local JPEG Grid Detector via Blocking Artifacts, a Forgery Detection Tool (2020), www.ipol.im
2020-05-21 · Tina Nikoukhah, Miguel Colom, J.M.M., Rafael Grompone von Gioi
How to Reduce Anomaly Detection in Images to Anomaly Detection in Noise, www.ipol.im
2019-12-08 · Thibaud Ehret, Axel Davy, Mauricio Delbracio, J.M.M.
Agnès Desolneux, Lionel Moisan, & J.M.M. (2007). From gestalt theory to image analysis: a probabilistic
approach (Vol. 34). Springer Science & Business Media.
References
![Page 4: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/4.jpg)
Example 1: Playing Roulette with Dostoievski
![Page 5: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/5.jpg)
Example 1: Playing Roulette with Dostoevski
Extract from the novel « The gambler »:
That time, as if on purpose, a circumstance arose which, incidentally,
recurs rather frequently in gambling. Luck sticks, for example, with red and
does not leave it for ten or even fifteen turns. Only two days before, I had
heard that red had come out twenty two times in a row in the previous
week. One could never recall a similar case at roulette and it was
spoken of with astonishment.
![Page 6: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/6.jpg)
Number of false alarms = expected number of occurrences of the event =
(number of tests) x (probability of the rare event)
![Page 7: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/7.jpg)
Number of false alarms = expected number of occurrences of the event =
(number of tests) x (probability of the rare event)
![Page 8: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/8.jpg)
Example 2: birthdays in a class
![Page 9: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/9.jpg)
Example 2: birthdays in a class
![Page 10: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/10.jpg)
Example 2: birthdays in a class
![Page 11: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/11.jpg)
Birthdays in a class: first the classic approach
Take home message: for the detection of rare events, the computation of the expectation of the event, or
Number of False Alarms is much easier than the computation of its probability of appearing, and it brings
more information.
![Page 12: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/12.jpg)
![Page 13: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/13.jpg)
An aparte: Statistics in the wild, or how to fight illusory detections
![Page 14: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/14.jpg)
Observations made by Dr Gastaldi and two other doctors (June 2020):
"For the past few weeks, all three of us have been prescribing this treatment to all our patients with
coronavirus. For my part, this represents more than 200 patients. I have only had two serious cases that
required hospitalization and have since been discharged. Obviously, this is not a multi-center,
randomized study, but these are very interesting results. Based on the known data on the disease, out
of at least 200 cases, we should have had at least two deaths and about 40 hospitalizations.”
Exercise: finding on the internet the mortality rate among symptomatic patients and the number of
medical doctors in France, compute the NFA of this event (> 200 saved patients and no death) and
deduce how many such medical « discoveries » may have been done.
https://www.femmeactuelle.fr/sante/news-sante/coronavirus-trois-medecins-generalistes-pensent-avoir-
trouve-un-traitement-contre-le-covid-19-2093814
Statistics in the wild, or how to fight illusory detections
![Page 15: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/15.jpg)
Solution by Florian Laborde
![Page 16: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/16.jpg)
Danger of ignoring the number of tests to evaluate a number of false alarms (NFA), (also called per family
error rate (PFER))
Neglecting this fact leads to discover crabs on Mars!
16/49
Perception analysis implies making statistics « in the wild » (a
posteriori design of the testing set)
Mars Exploration Rover
![Page 17: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/17.jpg)
Danger of ignoring the
number of tests to evaluate
a number of false alarms
(NFA), (also called per family
error rate (PFER))
Neglecting this fact leads to
discover gods in the ocean!
17/49
The image by photographer
Mathieu Rivrin taken on
January 30, 2021 shows the
storm Justine with a face that
could be that of the god of
Greek mythology Poseidon
(Neptune for the Romans).
Statistics in the wild, or how to fight illusory detections
![Page 18: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/18.jpg)
First real example : image forgery detection
(Fake news debunking, work in collaboration with Agence France Presse)
![Page 19: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/19.jpg)
Forgery detection
![Page 20: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/20.jpg)
The cue to forgery detection is the number of zeros in a JPEG bloc.
Each digital image is divided in 8x8 blocs. The high frequencies in
each bloc are put to zero by JPEG: this allows one to retrieve the
position of the blocs and therefore the original JPEG grid.
But if the image has been manipulated in parts, the JPEG grid will
generally be shifted. Thus forgery detection amounts to find clusters
of blocs where the grid is not aligned with the general grid.
![Page 21: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/21.jpg)
![Page 22: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/22.jpg)
Selecting the grid by the number of zeros
The number of zeros is larger
when a 8x8 block is aligned
with a previous JPEG
compression grid
![Page 23: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/23.jpg)
The tail of the binomial law
![Page 24: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/24.jpg)
The tail of the binomial law
![Page 25: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/25.jpg)
The tail of the binomial law
![Page 26: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/26.jpg)
![Page 27: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/27.jpg)
![Page 28: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/28.jpg)
NFA= 2.E-86
![Page 29: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/29.jpg)
![Page 30: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/30.jpg)
Test the method here:
https://ipolcore.ipol.im/demo/clientApp/demo.html?id=77777000073
![Page 31: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/31.jpg)
Real example 2: LSD, Line Segment Detector
![Page 32: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/32.jpg)
![Page 33: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/33.jpg)
![Page 34: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/34.jpg)
![Page 35: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/35.jpg)
![Page 36: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/36.jpg)
![Page 37: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/37.jpg)
Read the paper, have the code and test the online
demo on any image here
LSD: a Line Segment Detector
2012-03-24 · Rafael Grompone von Gioi, Jérémie
Jakubowicz, Jean-Michel Morel, Gregory Randall
![Page 38: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/38.jpg)
Real example 3: Detection of dot alignments
![Page 39: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/39.jpg)
Real example 3: Detection of dot alignments:
Using first LSD and then alignment of lines (which are dots in the dual
space) leads to the detection of vanishing points and of the horizon
![Page 40: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/40.jpg)
![Page 41: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/41.jpg)
![Page 42: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/42.jpg)
![Page 43: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/43.jpg)
![Page 44: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/44.jpg)
![Page 45: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/45.jpg)
![Page 46: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/46.jpg)
![Page 47: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/47.jpg)
![Page 48: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/48.jpg)
Read the paper, have the code and test the online demo on any
image here
An Unsupervised Point Alignment Detection Algorithm (2015), www.ipol.im
José Lezama, Gregory Randall, J.M.M., Rafael Grompone von Gioi
![Page 49: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/49.jpg)
Theory:
A general definition of NFA
How to estimate the binomial tail
The interpretation of multiple detections : nonmaxima suppression
![Page 50: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/50.jpg)
A general definition of NFA
[73] A-contrario detectability of spots in textured backgrounds B Grosjean, L Moisan
Journal of Mathematical Imaging and Vision 33 (3), 313-337
![Page 51: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/51.jpg)
A general definition of NFA
![Page 52: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/52.jpg)
A general definition of NFA
![Page 53: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/53.jpg)
![Page 54: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/54.jpg)
Estimating the binomial tail
![Page 55: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/55.jpg)
Estimating the binomial tail
![Page 56: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/56.jpg)
Non maxima suppression of multiple detections
Noisy square, meaningful alignments, maximal meaningful alignments
![Page 57: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/57.jpg)
An Analysis of the Viola-Jones Face Detection Algorithm, Yiqing Wang IPOL
Non maxima suppression of multiple detections
![Page 58: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/58.jpg)
An Analysis of the Viola-Jones Face Detection Algorithm, Yiqing Wang IPOL
Non maxima suppression of multiple detections
![Page 59: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/59.jpg)
An Analysis of the Viola-Jones Face Detection Algorithm, Yiqing Wang IPOL
Non maxima suppression of multiple detections
![Page 60: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/60.jpg)
How to Reduce Anomaly Detection in Images to Anomaly Detection in Noise
2019-12-08 · Thibaud Ehret, Axel Davy, Mauricio Delbracio, Jean-Michel Morel
Anomaly detection in any image
![Page 61: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/61.jpg)
“Novelty (or anomaly) detection is the task of classifying test data that differ in some respect
from the data that are considered “normal”. This may be seen as “one-class classification”, in
which a model is constructed to describe “normal” data. The novelty detection approach is
necessary because the quantity of available “abnormal” data is insufficient to construct explicit
models for non-normal classes. Detection must work even in a single image with a single
anomaly.”
A review of novelty detection (2014) Marco A.F. Pimentel, David A. Clifton, Lei Clifton, Lionel Tarassenko 61/49
Anomaly detection in any image
![Page 62: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/62.jpg)
Examples of industrial images with anomalies to detect. From left to right a suspicious
mammogram, an undersea mine, a defective textile pattern and a defective wheel
“Novelty (or anomaly) detection is the task of classifying test data that differ in some respect
from the data that are considered “normal”. This may be seen as “one-class classification”, in
which a model is constructed to describe “normal” data. The novelty detection approach is
necessary because the quantity of available “abnormal” data is insufficient to construct explicit
models for non-normal classes. Detection must work even in a single image with a single
anomaly.”A review of novelty detection (2014) Marco A.F. Pimentel, David A. Clifton, Lei Clifton, Lionel Tarassenko
62/49
Anomaly detection in any image
![Page 63: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/63.jpg)
63/49
![Page 64: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/64.jpg)
Self-similar part scale 0
64/49
Anomaly detection in any image
![Page 65: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/65.jpg)
Non self-similar residue scale 0
65/49
Anomaly detection in any image
![Page 66: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/66.jpg)
Detections in « noise », scale 0, min (log NFA) = -11,7
66/49
Anomaly detection in any image
![Page 67: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/67.jpg)
Self-similar part scale 1
67/49
Anomaly detection in any image
![Page 68: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/68.jpg)
Non self-similar residue scale 1
68/49
Anomaly detection in any image
![Page 69: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/69.jpg)
Detections in « noise » scale 1, min (log NFA) = -26,2
69/49
Anomaly detection in any image
![Page 70: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/70.jpg)
Self-similar part scale 2
70/49
Anomaly detection in any image
![Page 71: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/71.jpg)
Non self-similar residue scale 2
71/49
Anomaly detection in any image
![Page 72: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/72.jpg)
Detections in « noise » scale 2, min (log NFA) = -11,7
72/49
Anomaly detection in any image
![Page 73: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/73.jpg)
Detections in « noise » scale 3 , min (log NFA) = -19,9
73/49
Anomaly detection in any image
![Page 74: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/74.jpg)
Sanity check 1 : No detection in
white noise!
Scale 0
Minimum log10NFA region = 1.03
-----------------------
Scale 1
Minimum log10NFA region = 0.04
-----------------------
Scale 2
Minimum log10NFA region = 2.66
-----------------------
Scale 3
Minimum log10NFA region = -0.11
74/49
![Page 75: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/75.jpg)
Sanity check 2: No detection in homogeneous texture
ORIGINAL SELF-SIMILAR PART
75/49
![Page 76: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/76.jpg)
B. Grosjean and L. Moisan. A-contrario detectability of spots in textured backgrounds. Journal of Mathematical
Imaging and Vision, 33(3):313–337, 2009.
Sanity check 3: working on the residual increases the « NFA gap » between false alarms and
detectionsmammography with tumor new detection (log NFA=-12) Detections in [14]: log NFA = 0
76/49
![Page 77: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/77.jpg)
Left: Picture of textile, right: The residual for pixels and the detections. All the textile impurities are highlighted on the
residual.
Example on a real scene with no ground truth
77/49
![Page 78: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/78.jpg)
Left: Input image, Right: detections with pixels. The method successfully detects a tank hidden in the landscape. This example is one of the examples
provided by Itti et al.
L. Itti and C. Koch. A saliency-based search mechanism for overt and covert shifts of visual attention. Vision research, 2000.
78/49
Example on a real scene with no ground truth
![Page 79: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/79.jpg)
Anomaly detection in industrial parts
![Page 80: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/80.jpg)
Anomaly detection in industrial parts
![Page 81: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/81.jpg)
Thank you, questions?
![Page 82: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/82.jpg)
![Page 83: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/83.jpg)
Local Image Comparison
Cloud detection in time series of satellite images
![Page 84: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/84.jpg)
Cloud detection in time series of satellite images
![Page 85: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/85.jpg)
A contrario formulation
Cloud detection in time series of satellite images
![Page 86: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/86.jpg)
Cloud detection in time series of satellite images
![Page 87: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/87.jpg)
Cloud detection in time series of satellite images
![Page 88: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/88.jpg)
Polyominoes
![Page 89: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/89.jpg)
![Page 90: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/90.jpg)
Matteoli, S. ; Diani, M. ; Corsini, G., A tutorial overview of anomaly detection in hyperspectral images
I. S. Reed, X.(iaoli) Yu, Adaptive Multiple-Band CFAR Detection of An Optical Pattern with Unknown Spectral
Distribution, IEEE Trans. Acoust. Speech Signal Process., 38(10) (1990) 1760-1770.
Anomaly detection theory: Gaussian models and background subtraction
![Page 91: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/91.jpg)
![Page 92: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/92.jpg)
![Page 93: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/93.jpg)
![Page 94: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/94.jpg)
![Page 95: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/95.jpg)
Matteoli, S. ; Diani, M. ; Corsini, G., A tutorial overview of anomaly detection in hyperspectral images
I. S. Reed, X.(iaoli) Yu, Adaptive Multiple-Band CFAR Detection of An Optical Pattern with Unknown Spectral
Distribution, IEEE Trans. Acoust. Speech Signal Process., 38(10) (1990) 1760-1770.
Anomaly detection in hyperspectral images
![Page 96: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/96.jpg)
Matteoli, S. ; Diani, M. ; Corsini, G., A tutorial overview of anomaly detection in hyperspectral images
I. S. Reed, X.(iaoli) Yu, Adaptive Multiple-Band CFAR Detection of An Optical Pattern with Unknown Spectral
Distribution, IEEE Trans. Acoust. Speech Signal Process., 38(10) (1990) 1760-1770.
Anomaly detection in hyperspectral images
![Page 97: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/97.jpg)
Matteoli, S. ; Diani, M. ; Corsini, G., A tutorial overview of anomaly detection in hyperspectral images
I. S. Reed, X.(iaoli) Yu, Adaptive Multiple-Band CFAR Detection of An Optical Pattern with Unknown Spectral
Distribution, IEEE Trans. Acoust. Speech Signal Process., 38(10) (1990) 1760-1770.
Anomaly detection in hyperspectral images
![Page 98: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/98.jpg)
Matteoli, S. ; Diani, M. ; Corsini, G., A tutorial overview of anomaly detection in hyperspectral images
I. S. Reed, X.(iaoli) Yu, Adaptive Multiple-Band CFAR Detection of An Optical Pattern with Unknown Spectral
Distribution, IEEE Trans. Acoust. Speech Signal Process., 38(10) (1990) 1760-1770.
Anomaly detection in hyperspectral images
![Page 99: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/99.jpg)
Matteoli, S. ; Diani, M. ; Corsini, G., A tutorial overview of anomaly detection in hyperspectral images
I. S. Reed, X.(iaoli) Yu, Adaptive Multiple-Band CFAR Detection of An Optical Pattern with Unknown Spectral
Distribution, IEEE Trans. Acoust. Speech Signal Process., 38(10) (1990) 1760-1770.
Graphical representation of the detection of a local anomaly that is not anomalous in the whole scene. (a) spatial domain. (b)
simplified two-dimensional spectral domain. The scene reported contains a forest and a locally isolated tree. The RX sliding window
is represented in red. The samples captured by this window are pixels of a homogeneous background of grass, and hence the
locally isolated tree is detected even if it is not anomalous in the scene.
Anomaly detection in hyperspectral images
![Page 100: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/100.jpg)
Matteoli, S. ; Diani, M. ; Corsini, G., A tutorial overview of anomaly detection in hyperspectral images
J. C. Harsanyi, C-I. Chang, Hyperspectral Image Classification and Dimensionality Reduction: An Orthogonal
Subspace Projection Approach, IEEE Trans. Geosci. Remote Sens., 32(4) (1994) 779-785.
Anomaly detection in hyperspectral images
![Page 101: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/101.jpg)
Matteoli, S. ; Diani, M. ; Corsini, G., A tutorial overview of anomaly detection in hyperspectral images
J. C. Harsanyi, C-I. Chang, Hyperspectral Image Classification and Dimensionality Reduction: An Orthogonal
Subspace Projection Approach, IEEE Trans. Geosci. Remote Sens., 32(4) (1994) 779-785.
![Page 102: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/102.jpg)
Anomaly detection in RGB images by background subtraction and final detection in noise
How to Reduce Anomaly Detection in Images to Anomaly Detection in Noise
2019-12-08 · Thibaud Ehret, Axel Davy, Mauricio Delbracio, Jean-Michel Morel
![Page 103: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/103.jpg)
![Page 104: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/104.jpg)
![Page 105: Detection theory and industrial applications](https://reader033.vdocuments.site/reader033/viewer/2022050604/62730814c6a9de68cd44c810/html5/thumbnails/105.jpg)
Anomaly detectors address the difficult problem of detecting automatically exceptions in a background image,
that can be as diverse as a fabric or a mammography. Detection methods have been proposed by the
thousands because each problem requires a different background model.
Anomaly detection cannot be formulated in a Bayesian framework: this would require to simultaneously learn
a model of the anomaly, and a model of the background.
(In the case where there are plenty of examples of the background and for the object to be detected, neural
networks may provide a practical answer, but without explanatory power). In the case of anomalies, we often
dispose of only one image as unique informer on the background, and of no example at all for the anomaly.
The problem can be reduced to detecting anomalies in residual images (extracted from the target image) in
which noise and anomalies prevail. Hence, the general and impossible background modeling problem is
replaced by a simple noise model, and allows the calculation of rigorous detection thresholds.
Our approach is therefore unsupervised and works on arbitrary images. The residual images can favorably be
computed on dense features of neural networks. Our detector is powered by the a contrario detection theory,
which avoids over-detection by fixing detection thresholds taking into account the multiple tests.