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### Maximally Stable Extremal Regions and Extensions

Medical Image Processing Course

Loris Bazzani, PhD Student

Department of Computer Science,

University of Verona, Italy,

VIPS Lab.

Supervisor: Prof. Vittorio Murino

Introduction

- Maximally Stable Extremal Region
- Maximally Stable Volume: 3D Extension
- Segmentation of volumes
- Maximally Stable Colour Region: RGB Extension
- Objects of interest modeling
- Conclusions

Outline

- Maximally Stable Extremal Region
- Maximally Stable Volume
- Maximally Stable Colour Region
- Conclusions

Maximally Stable Extremal Region(MSER) [Matas2002]

- Set of all thresholdings of to a binary img:
- MSER = connected region in with little size change across several thresholdings
- Margin = the number of thresholds for which the region is stable

Outline

- Maximally Stable Extremal Region
- Maximally Stable Volume
- Maximally Stable Colour Region
- Conclusions

Maximally Stable Volumes (MSV) [Donoser2006]

New interpretation/formulation of MSER (2D):

- Find the level sets of a connected, weighted graph
- Node: pixel
- Edge: connection relationship (e.g. 4-neghborhood)
- Weight: pixel intensity
- contains a set of nodes that have a weight above a given threshold
- Build a component tree from a connected, weighted graph
- Nodes: the connected components of
- Edges: inclusion relationship between and

MSV (1)

Extension to the third dimension: spatial or temporal

- Find the level sets of a connected, weighted graph
- Node: voxel
- Edge: 3D connection relationship (e.g. 6-neghborhood)
- Weight: voxel intensity
- contains a set of nodes that have a weight above a given threshold
- Build a component tree from a connected, weighted graph
- Nodes: the connected volumes of
- Edges: inclusion relationship between and

MSV (2)

- A connected volume fulfills:
- is the set of all boundary voxels of a volume
- A connected volume is son of iff
- i.e., an inclusion relationship between connected volumes

MSV (3)

- MSVs are identified as the connected volumes with high stability:
- Local minimum along the path to the root of the tree
- Computation of the tree:
- number of edges + nodes
- inverse Ackermann function

3D segmentation (1)

- Applied to simulated brain MR images
- Size: , with different noise

MSV detection result of brain segmentation.

Images from [Donoser2006]

3D segmentation (2)

3D visualization of human brain,

which was detected as a single MSV

Images from [Donoser2006]

3D segmentation (3)

- Applied to paper fiber network images
- Sequences of cross-sectional images with max resolution of

Images from [Donoser2006]

Outline

- Maximally Stable Extremal Region
- Maximally Stable Volume
- Maximally Stable Colour Region
- Conclusions

Maximally Stable Colour Region (MSCR) [Forssen2007]

- Novel colour-based affine covariant region detector
- Extension of the MSER to colour
- Look at successive time-steps of an aggloramerative clustering of image pixel, based on proximity and similarity on colour
- Modelling of the distribution of edge magnitudes
- Novel edge significance measure based on a Poisson image noise model
- Perform better than MSER and other state-of-the-art blob detectors
- Applications: 3D object recognition and view matching

Original set of images

MSCR representation

MSCR (1)

- Evolution process over the image that successively clusters neighbouring pixels with similar colours
- For each time step , the evolution is a map of labels
- Any two positions are connected by a path of distances which are smaller than

MSCR (2)

Evolution Process with agglomerative clustering

- is all zeroes
- is constructed from by assigning new regions to all pair of pixel with
- If one pixel of the pair already belongs to a region, the non-assigned pixel is appended to the region
- If both pixels belong to regions the corresponding regions are merged

MSCR (3)

- How the distance is defined:
- Sensors count the number of photons
- Noise follows the discrete Poisson distribution
- For high , good approximation is a Gaussian:
- Measure of edge significance: probability that a pixel has a larger mean than its neighbour:

Chi-squared distance

MSCR (4)

- Dynamically adapt the threshold :
- Linearly increasing: very fast image evolution in the beginning and very slow at the end of the evolution
- Change according to the inverse Cumulative Distribution Function (CDF)
- Observation: edge significance measure follows a Chi-squared distribution:
- Evolution thresholds:

MSCR (5)

- Detecting stable regions:
- For each region in the label image, we store the area and the distance threshold
- When the area increases more than a threshold

, and are re-initialized

- The slope of the area and distance function is used for the detection

if is the best (smallest), the region is stored

MSCR (6)

- Descriptor for the MSCRs:
- Region area
- Centroid
- Inertia Matrix
- Average colour
- These measures define an approximating ellipse for the detected region as:

Tracking-by-detection (1)

- Tracking: spatial and temporal localization of a mobile object in an environment monitored by sensor(s)
- Multi-target (MTT): keeping the identity of different targets
- Reliable: insensible to noise and occlusions
- Detection: identify all the objects of interest into the image
- Tracking-by-detection:
- targets are detected for every frame
- IDs are associated from frame (t-1) to frame (t), with a data association process

Tracking-by-detection (2)

- Tracking-by-detection using the MSCR descriptor
- Our method extracts the MSCR from the foreground of the detected objects
- We define a distance measurement in order to compare the objects at time (t-1) with the objects at time (t)
- For each pair of blobs, we have:
- Color distance:
- y distance:
- Distance between the objects :

Euclidean distance

Quantitative Results

Tagging error

Rate for each t

Tagging error Rate

for each N of ped

Total Tagging

Success Rate

Person Re-identification (1)

- Multi-camera scenario with (non-)overlapping fields of View (FoV)
- Objective: recognize an object, when it is being seen in different FoV
- Challenging problem with non-overlapping FoV
- Idea:
- Keep a database of all the history of the seen objects
- Once a new object enters in the scene, the method retrieves the IDs of the object from the database (if it is being seen before)
- If the object is not in the database, a new ID is given to it and it is added to the database

Person Re-identification (2)

- The method is the same used for tracking-by-detection problem
- Compute the distance
- Extraction of part-based HSV histogram
- Divide the image in three parts: legs, torso, head
- Compare the hist. of each part using the Bhattacharyya distance
- MSCR and HSV hist. distance are combined:

Quantitative Results (1)

- Evaluation in term of:
- Cumulative Matching Characteristic (CMC): represents the expectation of finding the correct match in the top n matches
- Synthetic Recognition Rate (SRR): represents the probability that any of the m best matches is correct
- Using challenging publicly available datasets: VIPeR and iLIDS Dataset
- pose variation and shape deformation
- illumination changes, camera movement, and occlusions
- noise and blurring

Conclusions

- Two extensions of the MSER feature had been discussed
- MSV that deals with 3D segmentation and modeling of medical images
- MSCR that deals with hard problems in very different applications: tracking-by-detection, and person re-identification
- MSER and extensions seem to be good features for representing and segmenting of object of interest in different kind of application

Thanks!Questions?

References

[Matas2002] J. Matas, O. Chum, M. Urban and T. Pajdla, Robust Wide Baseline Stereo from Maximally Stable Extremal Regions, In BMVC, 2002.

[Donoser2006] M. Donoser and H. Bischrof, 3D Segmentation by Maximally Stable Volumes (MSVs), In ICPR, 2006.

[Forssen2007] P. Forssen, Maximally Stable Colour Regions for Recognition and Matching, In CVPR, 2007.

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