Active shape models with adaptive weights
Improvement of active shape models dealing with noisy and blured images of objects is developed. Results are tested on a set of radiographic images of welds. Improvement of performance of the proposed modified active shape models for radiographic images compared to conventional ones was shown basing...
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Фізико-механічний інститут ім. Г.В. Карпенка НАН України
2009
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| Цитувати: | Active shape models with adaptive weights / T.S. Mandziy // Відбір і оброб. інформації: Міжвід. зб. наук. пр. — 2009. — Вип. 30(106). — С. 133-137. — Бібліогр.: 7 назв. — англ. |
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Mandziy, T.S. 2011-02-04T17:10:47Z 2011-02-04T17:10:47Z 2009 Active shape models with adaptive weights / T.S. Mandziy // Відбір і оброб. інформації: Міжвід. зб. наук. пр. — 2009. — Вип. 30(106). — С. 133-137. — Бібліогр.: 7 назв. — англ. 0474-8662 https://nasplib.isofts.kiev.ua/handle/123456789/16083 004.932 Improvement of active shape models dealing with noisy and blured images of objects is developed. Results are tested on a set of radiographic images of welds. Improvement of performance of the proposed modified active shape models for radiographic images compared to conventional ones was shown basing on experimental results comparison. Удосконалено моделі активних форм для зашумлених зображень та зображень з нечіткими границями об'єктів. Результати протестовано на наборі рентгенографічних зображень зварних швів. Покращання функціонування вдосконалених моделей активних форм порівняно з класичними продемонстровано на порівнянні експериментальних результатів для рентгенографічних зображень. en Фізико-механічний інститут ім. Г.В. Карпенка НАН України Обробка зображень та розпізнавання образів Active shape models with adaptive weights Моделі активних форм з адаптивними вагами Article published earlier |
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| title |
Active shape models with adaptive weights |
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Active shape models with adaptive weights Mandziy, T.S. Обробка зображень та розпізнавання образів |
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Active shape models with adaptive weights |
| title_full |
Active shape models with adaptive weights |
| title_fullStr |
Active shape models with adaptive weights |
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Active shape models with adaptive weights |
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active shape models with adaptive weights |
| author |
Mandziy, T.S. |
| author_facet |
Mandziy, T.S. |
| topic |
Обробка зображень та розпізнавання образів |
| topic_facet |
Обробка зображень та розпізнавання образів |
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2009 |
| language |
English |
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Фізико-механічний інститут ім. Г.В. Карпенка НАН України |
| format |
Article |
| title_alt |
Моделі активних форм з адаптивними вагами |
| description |
Improvement of active shape models dealing with noisy and blured images of objects is developed. Results are tested on a set of radiographic images of welds. Improvement of performance of the proposed modified active shape models for radiographic images compared to conventional ones was shown basing on experimental results comparison.
Удосконалено моделі активних форм для зашумлених зображень та зображень з нечіткими границями об'єктів. Результати протестовано на наборі рентгенографічних зображень зварних швів. Покращання функціонування вдосконалених моделей активних форм порівняно з класичними продемонстровано на порівнянні експериментальних результатів для рентгенографічних зображень.
|
| issn |
0474-8662 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/16083 |
| citation_txt |
Active shape models with adaptive weights / T.S. Mandziy // Відбір і оброб. інформації: Міжвід. зб. наук. пр. — 2009. — Вип. 30(106). — С. 133-137. — Бібліогр.: 7 назв. — англ. |
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AT mandziyts activeshapemodelswithadaptiveweights AT mandziyts modelíaktivnihformzadaptivnimivagami |
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2025-11-25T23:09:09Z |
| last_indexed |
2025-11-25T23:09:09Z |
| _version_ |
1850578981097570304 |
| fulltext |
ISSN 0474-8662. . 2009. . 30 (106) 133
004.932
T. S. Mandziy
ACTIVE SHAPE MODELS WITH ADAPTIVE WEIGHTS
Improvement of active shape models dealing with noisy and blured images of objects is developed.
Results are tested on a set of radiographic images of welds. Improvement of performance of the
proposed modified active shape models for radiographic images compared to conventional ones was
shown basing on experimental results comparison.
.
. -
-
.
Representation of images containing objects, whose shape can vary, is a necessary
and challenging task. Examples of such objects can be images of human faces or
magnetic resonance brain sections. Models called to deal with such type of object
images have very wide practical application. They are able to handle various types of
tasks, such as object shape modeling, objects tracking, feature localization, image
segmentation etc. They also can be used for object state recognition, like recognition of
human emotions. Those models are very important for tasks of image segmentation
where correct segmentation is impossible without relying on shape information due to
its low signal to noise ratio or texture inconsistency. Such model application is very
important and successful in medicine and industry for radiographic, magnetic
resonance and ultrasonic image segmentation.
There were proposed many models to handle aforementioned tasks. Probably, the
first attempt to deal with images of varying objects were active contours [1]. They are
able to track changes in shape, but they are shape free models and initially were not
able to respond to the particular shapes. There exist some improvements of the model
to make it sensitive to the particular user defined shapes [2, 3].
Proposed by T. Cootes Active Shape Models (ASM) (also known as smart snakes)
[4] were designed especially for handling shape variations of object images. The ASM
is relying on statistical model of shape variation. Shape in this model is represented as
a set of landmarks (set of points placed on a statistically significant object image parts).
Relative variations of landmarks are constrained by a Point Distribution Models (PDM)
captured from a training set of shapes. Matching model to image is made by iterative
technique. A new landmark point locations are obtained by nearby search around
current landmark point locations, aiming to find the best texture model match, expected
at the landmark position, with the image area around current landmarks. After new
landmark point locations are found, parameters of a model are adjusted to the best
match of these new locations to model generated ones. Since T. Cootes original paper
was published there were made a lot of efforts to improve the ASM: double contours
ASM [5], ASM with bifurcation contours handling [6], non-linear multi-view ASM [7]
etc.
The following reveals mathematical basis of ASM, gives the examples of cases
where conventional ASM is failed to show a consistent result, proposes an
improvement of the model to deal with those hard cases and compares obtained results
to those obtained with conventional ASM.
T. S. Mandziy, 2009
ISSN 0474-8662. Information Extraction and Proces. 2009. Issue 30 (106)134
Active shape model formulation. Model building. ASM is built based on
training set of annotated images (images with placed ground truth landmarks) of
modeled object. There are two main stages in model building. The first is building
statistical model of shape. This step uses only coordinates of landmarks as an input and
disregards images. The second is a landmark local texture descriptions building. This
step utilizes images and landmark position information.
Active shape models represent an object shape by a fixed size set of key points
that correspond to particular previously selected interest regions of the object (e.g.
those points are usually placed along the contours of significant object parts, such as
nose, mouth, eyes etc., if images of human faces are considered).
Point distribution model (PDM) [4] is a statistical tool for modeling variations of
object shape. The set of all possible shapes is assumed to form a Gaussian distribution
around some mean point 1 1( ,..., , ,... )n nx x x y y in shape space. PDM is inferred, based
on training set composed of possible shape variations examples. After the training data
are collected all training shapes must be aligned in minimum of mean squared error
sense (1):
min ( )( )Ti i
i
x x x x , (1)
where x is the mean shape and ix is an ith shape from training set. Interested readers
are referred to [4] for introduction with technique of aligning two similar shapes by
removing relative translation, rotation and scale between them. To build a compact
shape model (i.e. to build model with possible smallest model parameters set) principal
component analysis (PCA) is applied. After mean shape x and PCA transform is known
arbitrary shape x similar to shapes in training set can be generated by equation (2):
x x Pb , (2)
where P is a matrix composed of t largest eigenvectors (eigenvectors with largest
corresponding eigenvalues) and b is a vector of model parameters.
The model also should build an average description of image local texture,
surrounding every key point. These descriptions of landmark local texture are required
for the model to be able to locate landmark positions on new image of modeled object.
Determination of such descriptions is very important for further model performance. In
[3] it was proposed to use normalized intensity gradient n
ijdg of gray-level profiles
along normal to contour tangent:
ijn
ij
ijl
k
dg
dg
dg
. (3)
where ijdg is a thj landmark intensity gradient profile of thi shape and ijldg is a thl
component of ijdg . Average description of local texture around thj landmark is
computed as following:
i
1
j ijdg dg
N
, where N is a train set size.
Thus, output model consists of mean shape x , matrix P and a set of landmark
local texture descriptors jdg .
Model utilization. Due to possible variations of object image shape, model should
be able to tune its parameters to match those shape variations. To match given image of
object with obtained model in addition to model parameters b we should also
determine scale s, translation (tx, ty) and rotation of the shape generated by model (1).
ISSN 0474-8662. . 2009. . 30 (106) 135
Initial guess about the model parameters b and position ( , , , )x ys t t should be
made for satisfactory final convergence of the model to a given new image (in present
paper the initialization of the ( , , , )x ys t t is out of consideration and assumed to be
known). After the initial model (i.g. model consisted of mean shape x , zero vector
parameter b and initial guess for translation, rotation and scale parameters) is placed
on new image the search procedure begins. It can be divided on three steps:
1. Search for a new locations newx of key points.
2. Fix b and determine ( , , , )x ys t t that minimize ( ) ( )T
new cur new curx x W x x .
3. Fix ( , , , )x ys t t and find b that minimizes ( ) ( )T
new cur new curx x W x x ,
where W is a weighting diagonal matrix (4), which is used to give more significance to
those landmark points that have more stability in their displacements with respect to all
other landmark points presented in a given shape.
1 0
0 n
w
W
w
, (4)
where wk is a weight of kth landmark computed as following:
1
k km
m
w V , (5)
where Vkm is a variance of distance between kth and mth landmark points in training set.
In step 1, determination of new locations newx of key points is made by nearby
search around current positions of key points. It aims to find better match of average
normalized gradient profile jdg (inferred from training images) and normalized
gradient profile n
jdg of input image (computed by (3)) for every landmark j. In this
work, search of new locations xnew is made by similar procedure to that described in [4].
In step 2, having newx and fixing b we try to align currentx to newx by finding
( , , )x ys t t that minimizes ( ) ( )T
new cur new curx x W x x . This is done by similar
procedure as for training shapes alignment.
In step 3, after ( , , )x ys t t is determined and fixed we compute new values of
model parameters newb trying to minimize ( ) ( )T
new cur new curx x W x x . Such
minimization with respect to model parameters b is provided by the following:
1( )new newb P x x . (6)
The above three steps are repeated until convergence is reached.
Thus, for testing we should provide the model with a new image of modeled
object and initial guess for model parameters b and position ( , , , )x ys t t . After model
converges, it provides as with a set of output parameters: final model parameters
finalb (that describe shape of modeled object) and final position parameters
( , , , )final final final final
x ys t t (that describe relative scale, translation and rotation of
shape of object depicted on input image and shape generated by (2) with finalb as
model parameters).
ISSN 0474-8662. Information Extraction and Proces. 2009. Issue 30 (106)136
Active shape model with adaptive weights. Considering ASM applied to
radiographic images (that can be characterized as noisy with fuzzy edges of objects)
more attention should be paid to building characteristics of image area around every
key point. Due to fuzzy nature of radiographic images it can be sometimes difficult to
determine the true location of the landmarks. It can cause some landmark point
locations to be remote from their true positions on the image. Consequently the whole
model can converge in a wrong way, especially when points with big weight values are
localized at false positions.
Usage of adaptive weights kw that allow ASM to avoid problems that could
appear with misdetected key points locations, is proposed in this paper. The idea of
adaptive weights consist of making weight magnitude dependent on matching rate of
average normalized profiles jdg (inferred from training set) and normalized profiles
n
jdg of input image. Such dependence makes it possible to reduce the influence of
mislocated points having big weights on final convergence.
Expression (7) is used by conventional ASM to compute the similarity between
n
jdg , that characterize texture of input image around thj landmark point and jdg ,
inferred from training set:
1( ) ( ) ( )n n n T
j j j j j jf dg dg dg dg dg , (7)
where ( )n
jf dg is a Mahalanobis distance and j is a covariance matrix of all
normalized gradients n
ijdg that belongs to thj landmark. Thus to make weights
adaptable we propose to scale the weights kw by the ( )n
jf dg (7). Consequently the
scaled weights (5) are computed by the following:
( )n
k k jw w f dg . (8)
With adaptive weights kw model becomes less sensitive to wrongly located during
search procedure key points. Even if some landmarks have kw with large magnitude
and are misplaced from its true location, the further scaling by (8) will reduce the
magnitude of that weight with respect to all other weights, preventing the model
convergence to a false shape.
Experimental results and conclusions. Proposed model performance evaluation
and all experimental results were obtained by training and testing it on a set of radio-
graphic images of pipe welds. An example of that type of images is shown at Fig. 1a.
For model building a set of 22 manually annotated images was used. After the
training, model containing only a small set of significant model parameters (in the
given case vector b contains only three parameters) were obtained. Despite of that
small number of parameters the model is able to reproduce about 99% of training data
variation.
After the input image is given, initial model (in our case model with zero parameter
vector b and guess for scale, rotation and translation parameters provided by user)
should be placed on it. An example of initial model placed on input image is shown at Fig.
1b. Two model performances were tested when given the same initialization (Fig. 1b)
of the model. First model was conventional ASM. As depicted at Fig. 1c the
convergence of the model is not satisfactory for a given initialization. Bad convergence
was caused by the misslocation of key points with big weights. In contrast to
conventional ASM, proposed adaptive weights ASM converged to plausible final
convergence. The result of adaptive weights ASM performance is shown at Fig. 1d.
ISSN 0474-8662. . 2009. . 30 (106) 137
Fig. 1. Convergence results of conventional ASM and ASM
with adaptive weights:
a – original input image;
b – original input image with initial shape model;
c – result of conventional ASM search;
d – result of ASM with adaptive weights search.
Experiments show that even though 85...95% of key points are located in proper
way the model still can be lead to a wrong convergence by the small amount of key
points with a big weights values. This drawback of conventional ASM can be avoided
by using adaptive weights values witch are able to change during optimization stage.
This approach also can be used for occlusion handling. For instance, it can be
usefull in situations when modeled object tend to appear in cluttered environment
where some of its parts are occluded.
Obtained results show the advantage of the adaptive weights ASM utilization over
conventional ASM for images with fuzzy edges of modeled objects.
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H. V. Karpenko Physico-Mechanical Institute NAS of Ukraine Received
24. 05.2008
УДК 004.932
T. S. Mandziy
ACTIVE SHAPE MODELS WITH ADAPTIVE WEIGHTS
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