Classifying Sows' Activity Types from Acceleration Patterns. An Application of the MultiProcess Kalman Filter
Final preprint (uncorrected proof) of article published in Applied Animal Behaviour Science. Please
cite as:
Cornou, C. and Lundbye-Christensen S., 2008. Classifying sows’ activity types from acceleration
patterns: An application of the Multi-Process Kalman Filter. Applied Animal Behaviour Science 111
(3-4), 262-237.
DOI: 10.1016/j.applanim.2007.06.021
Classifying Sows’ Activity Types from Acceleration
Patterns.
An Application of the Multi-Process Kalman Filter
Cécile Cornou a,∗ and Søren Lundbye-Christensen b
a Department
of Large Animal Sciences, Faculty of Life Sciences, University of
Copenhagen
Groennegaardsvej 2, 1870 Frederiksberg C. Copenhagen, Denmark
Tel. +4535283364 Fax. +4535283055
b Institute
of Mathematical Sciences, Center for SundhedStatistik, Aalborg University
Fredrik Bajers Vej 7G, 9220 Aalborg SØ, Denmark
Abstract
An automated method of classifying sow activity using acceleration measurements would
allow the individual sow’s behavior to be monitored throughout the reproductive cycle; applications for detecting behaviors characteristic of estrus and farrowing or to monitor illness and welfare can be foreseen. This article suggests a method of classifying five types of
activity exhibited by group-housed sows. The method involves the measurement of acceleration in three dimensions. The five activities are: feeding, walking, rooting, lying laterally
and lying sternally. Four time series of acceleration (the three-dimensional axes, plus the
length of the acceleration vector) are selected for each activity. Each time series is modeled
using a Dynamic Linear Model with cyclic components. The classification method, based
on a Multi-Process Kalman Filter (MPKF), is applied to a total of 15 times series of 120 observations, which involves 30 minutes for each activity. The results show that feeding and
lateral/sternal lying activities are best recognized; walking and rooting activities are mostly
recognized by a specific axis corresponding to the direction of the sow’s movement while
performing the activity (horizontal sidewise and vertical). Various possible improvements
of the suggested approach are discussed.
Key words: group-housed sows, body activity, Dynamic Linear Models, Multi-Process
Kalman Filter.
∗ Corresponding author.
Email addresses: [email protected] (Cécile Cornou), [email protected]
(Søren Lundbye-Christensen).
Preprint submitted to Applied Animal Behaviour Science
4 October 2013
1 Introduction
When sows are group-housed it can be difficult to gain access to individual animals.
Often this leads to serious management problems. The development of sensor technology (Eradus and Jansen, 1999) opens up new possibilities for monitoring single
animals within a group, and current automation systems aim to facilitate ’management by exception’ by drawing the farmer’s attention to particular individuals.
A large range of automation systems for animal husbandry are based on Dynamic
Linear Models and the Kalman Filter (Kalman, 1960). Thus in pig production it is
possible to monitor the condition of young pigs via their drinking behavior (Madsen et al., 2005); and in group-housed sows it is possible to monitor estrus via individual body activity (Cornou and Heiskanen, 2007). A similar approach has been
described for monitoring milk quality in dairy cattle (Thysen, 1993), and de Mol
et al. (1999) suggest a method of this kind for detecting estrus and diseases. Finally,
an application for use in poultry production is presented in Roush et al. (1992).
The behavior of the individual sow can be affected both by its physiological state
and by illness: body activity tends to increase at the onset of estrus (Cornou and
Heiskanen, 2007; Freson et al., 1998; Geers et al., 1995; Serlet, 2004); nest-building
behavior is performed at the approach of farrowing (Jensen, 1993) lameness mainly
influences the sow’s walking activity, while other diseases may affect specific behaviors such as feeding (Forbes, 1995). Automated monitoring of the activities of
an individual group-housed sow would therefore help the farmer to detect deviations from normal behavior and provide information about the specific state of the
animal.
The objective of this study is to develop a method for automatically classifying particular activities that group-housed sows perform. The method tracks acceleration
measurements. An accelerometer, fixed on individual sows, allows activity data to
be recorded at any time. The modeling of activity patterns could allow the individual animal to be monitored for the full duration of its reproductive cycle, i.e. from
the mating section to the farrowing house. Other applications, such as monitoring
animal welfare, can also be foreseen.
The following section describes the collection of acceleration measurements and
the five types of activity selected. Section 3 sets out the methods used to model and
classify the activity types. Section 4 presents and evaluates the results. Section 5
further discusses the results; it explores perspectives for improvement and suggests
new applications of the classification method presented.
2
2 Time series of accelerations and activity types
2.1
Collection of acceleration measurements
The time series of acceleration measurements referred to in this article are extracts
of data collected from 5 group-housed sows in a production herd in Sjælland, Denmark over a period of 20 days during March 2005. The sows were fed ad libitum;
they had access to two Electronic Sow Feeders (ESF) and three nipple drinkers.
Resting areas were straw-bedded and activity areas had plain or slatted floors. Acceleration data were measured in three dimensions using a digital accelerometer
(LIS3L02DS from STMicroelectronics) 4 times per second, 24 hours a day. A box
containing the accelerometer and the battery package was fitted on a neck collar
which was put on the experimental sow. The neck collars tended to loosen after few
days. However, the weight of the box ensured that it generally stayed in position
under the neck. Data were transferred to two PCs via an external Bluetooth dongle
which hung from the ceiling in the middle of the pen. Video recordings covering
a large proportion of the pen were also performed over 20 days, 24 hours a day
(four pictures being recorded per second). The experimental protocol is described
in detail in Cornou and Heiskanen (2007).
Acceleration is a vector quantity defining the rate at which the sow changes its
velocity. The sow is treated as accelerating if its velocity is changing. The initial
series included values for the three axes (x, y and z), measured in volts. Of these
axes, x corresponded to the vertical dimension; y corresponded to the horizontal
dimension, with the acceleration being measured sidewise, while z corresponded to
the horizontal dimension, with the acceleration being measured forwards. Before
further processing, the data were converted into the acceleration unit (g) and the
length of the acceleration vector was calculated as
acc =
q
acc2x + acc2y + acc2z
(1)
where accx , accy and accz are the acceleration values for the axes x, y and z. Acceleration values for the three axes ranged from 2 to 2. The values of the length of
the acceleration vector (acc) ranged from to 0 to 3.46, where 1 g corresponds to no
acceleration. When the accelerometer was placed immobile on a plane surface, the
acceleration values for the axes x, y and z, were respectively 1, 0 and 0 g (the first
value being due to the effect of gravity).
3
2.2
Selection of the activity types and time series associated
With the help of the video recordings, extracts of time series were associated with
five activity types. The activity types were: feeding (FE), rooting (RO), walking
(WA), lying sternally (LS) and lying laterally (LL). Figure 1 shows the raw values of the length of the acceleration vector (acc) for the five types of activity (4
measurements per second). It can be seen that each activity type displays a distinct
acceleration pattern.
acc, in g
FEEDING
3
2
1
0
0
1
2
3
4
5
6
7
8
9
6
7
8
9
6
7
8
9
7
8
9
7
8
WALKING
3
2
1
0
0
1
2
3
4
5
ROOTING
3
2
1
0
0
1
2
3
4
5
LYING STERNALLY
3
2
1
0
0
1
2
3
4
5
6
LYING LATERALLY
3
2
1
0
0
1
2
3
4
5
6
9
Time, in min
Fig. 1. Ten minutes selected extracts of the length of the acceleration vector (acc) for the
five activity types (four measurements per second); vertical axes indicate the value of acceleration, in g; horizontal axes indicate the duration of the extracts, in minutes.
Some of these activities are not exclusive. For example, sows can root and walk
at the same time. Since a walking sow may also pause and stand immobile more
or less frequently for a limited period of time, walking activity, when measured
over a sufficient time, will generally be associated with short periods of temporary
immobility.
The data sets selected for this study satisfied two criteria: i) the selected activities
fill the entire period; ii) the overlapping of activities are reduced to a minimum (e.g.
in extracts corresponding to the rooting activity the sows only root over a limited
area in order to limit the effects of the walking activity).
4
For the purpose of modeling and classifying the activities two data sets satisfying
the above criteria were used:
• Learning data set: 10 minutes of each activity type (presented in Figure 1); this
data set is used to estimate the model parameters for each activity type.
• Test data set: 10 × 2 minutes of each activity type; this data set is used in the
implementation of the classification method, after each activity type has been
modeled.
Each data set included 4 time series of acceleration measurements: axes x, y, z and
the length of the acceleration vector acc (referred to as the axis acc in the following
sections). The total duration of the data sets was 10 hours (30 min of each activity
type × 5 activity types × 4 axes). These data sets correspond to acceleration measurements collected for three different sows: sows 1, 3 and 5 for feeding, walking
and lying laterally; sow 5 for rooting; sows 1 and 3 for lying sternally. The activities of rooting and lying sternally were generally performed in the straw-bedded
resting areas. The videos only covered parts of these areas, which made it difficult
to associate these types of series with videos recordings. Hence, here, the number
of sows for both activities is limited, compared with the other types of activity.
The selected data sets are relatively short in length. This is, first, to satisfy the
criteria presented above (regarding the filling of an entire period and exclusivity).
Secondly, the experimental conditions hindered efforts to associate particular activity types for a longer period of time: more often than not the timestamps of the
video recordings and the accelerometers were unsynchronized. Therefore series
were selected around the time at which the sows visited the ESF; at this time correct timestamps were available. Furthermore, the shifting of the battery inside of
the accelerometer boxes may have resulted in axes inversions when the neck collar
was repositioned. The limited length of the series was also designed to provide an
assurance, during the development of this classification method, that the position
of each axis would remain identical.
3 Modeling of the acceleration patterns and classification of the activities
Modeling of the activity patterns was performed using time series from the learning
data set, previously averaged per second. As Figure 2 shows, the analysis of correlation, for the x axis, of the feeding series of the learning data set showed periodic
movement, with a period of 22 seconds.
In the learning data set, periodicity was only observed for this above series (1 out
of 20). In the test data set, periodicity in the range of 15-25 was observed in 12 of
the 200 series (10 series × 5 activities × 4 axes). The patterns are pseudo-cyclic,
with a smoothly changing wavelength; therefore, the suggested model includes a
5
correlation
axis x
1.0
0.8
0.6
0.4
0.2
0.0
0
5
10
15
20
25
lag, in sec
Lag
Fig. 2. Autocorrelation function for the x axis of the feeding series of the learning data set.
A periodicity of 22 seconds is observed.
gradually changing sinoid movement.
3.1
Model design
The general DLM is represented as a set of two equations (West and Harrison,
1997). The observation equation (2) defines the sampling distribution for the observation Yt conditional on an unobservable state vector θt . The system equation
(3) defines the time evolution of the state vector θt .
Yt = Ft′ θt + νt ,
θt = Gt θt−1 + ωt ,
νt ∼ N (0, V )
(2)
ωt ∼ N (0, Wt )
(3)
The error sequences νt and ωt are assumed to be internally and mutually independent. The DLM combined with a Kalman Filter (KF) (Kalman, 1960) estimates the underlying state vector θt by its conditional mean vector mt and its
variance-covariance matrix Ct (the model variance) given all previous observations Dt = {Y1 , . . . Yt } of the acceleration measurements. Thus, the conditional
distribution of θt is
(θt | Dt ) ∼ N (mt , Ct ).
(4)
The updating equations of the KF used for stepwise calculation of mt and Ct can
be found in West and Harrison (1997).
6
The suggested DLM includes a sine-cosine movement that follows the sinoid movement of the observation data: the state vector θt consists of a set of parameters
describing the model level (µt ) and the sine-cosine components (st , ct ) at time t,
i.e.

θt =

 µt 
 
 
 st 
 
 
(5)
ct
The systems matrices are defined in (6): Ft is labeled the design matrix; Gt is
labeled the system matrix, which is defined here as identity matrix.
Ft⊤ = 1, sin
2π
2π
t , cos
t
T
T
Gt = I
(6)
The period T is defined in the design matrix (6). However, the random variation
over time of the sine-cosine components of the state vector θt (5) allows the model
to adapt to periodic movements with periods varying near T .
The system variance Wt = W (3) is defined as:

W =
W


 0


µ
0

0 


W sc 0 


sc
0 0 W
(7)
The observation variance V (a scalar) and the parameters W µ and W sc of the
system variance W , characteristic of each axis of the respective activities, were
estimated using the EM algorithm (Dempster et al., 1977; Jørgensen et al., 1996;
Dethlefsen, 2001). The EM algorithm is an iterative algorithm used to estimate unknown parameters by maximum likelihood estimation; it uses the conditional mean
vector mt and the model variance Ct from the Kalman filtering and their respective smoothed components m̃t and C̃t obtained after Kalman smoothing (West and
Harrison, 1997).
c µ and W
c sc , for each axis of each
The estimated values for the parameters Vb , W
activity, converged after 200 iterations. These values are available on request.
7
3.2
Multi-Process Kalman Filter
Following the procedure set out in Section 3.1, 20 DLMs (5 activities × 4 axes)
were defined. Each DLM was described by the quadruple at each time t, denoted
by:
Mt : {F, G, V, W }t
(8)
In the Multi-Process model of class I, a single DLM (out of a range of possible
DLMs) is appropriate for describing the entire time series. However, there is uncertainty about the ’true’ value of the defining parameter vector α = α(i, j), where
α(i, j) is the set of parameters for the 20 possible DLMs, i.e. the five activity types
indexed by i (FE, WA, RO, LL, LS) and their respective axes j (x, y, z, acc).
Mt = Mt (α)
(t = 1, 2, . . .)
(9)
Each DLM Mt (α) was analyzed using the updating equations of the Kalman Filter.
At each observation time t, the model one-step forecast mean ft and its respective
variance Qt were calculated. The posterior probabilities (pt ) were estimated for
each DLM, as
pt (i) ∝ φt (i) × pt−1 (i),
(10)
where φt (i) is the predictive distribution of the observation given both the past
Dt−1 , and that model i is appropriate.
In practice, each DLM was analyzed using the parameters estimated from the learning data set; the value of the period T was set to 22. Initial values of the posterior
probabilities were set to 0.2, corresponding to a uniform initial distribution for the
five activity types. At each time t, the probabilities were updated for the 20 DLMs
according to (10).
4 Results
Figure 3 shows the evolution of posterior probabilities for two time series of 120
observations (two minutes of observation) corresponding to the walking activity.
The upper frame (a) corresponds to the y axis. The MPKF tends to indicate that
the sow is rooting. This indicates that walking and rooting activities have similar
movements in a horizontal sidewise direction. Where the axis z (lower frame) is
8
concerned, the MPKF recognizes the ’true’ activity type; the posterior probabilities
reach the value 1 after 40 observations.
Figure 4 shows the mean posterior probabilities (wide line) for each axis for the
five activity types. The parameters estimated from the learning data set are applied
to the respective activity type/axis of the test data set.
The feeding activity is best recognized, while the walking activity is recognized
only on one axis, i.e. the horizontal z axis measuring forwards acceleration; the
posterior probabilities exceed the value 0.5 after approximately 30 seconds. Lying
laterally is correctly recognized by the y axis (horizontal sidewise direction). Lying
sternally is also rapidly recognized. However, the results here should be regarded
with precaution, since both the learning and test data set are extracts of time series
from two sows only. The speed of recognition of the rooting activity is relatively
slow, and the posterior probabilities tend to stay around 0.5 for axes y and z; rooting
is best recognized by the x axis (vertical direction). Closer observation of the posterior probabilities of walking and rooting activities indicates that these activities
tend to be confused with each other: indeed for the walking activity, in 8 out of the
10 times series the posterior probabilities of the y axis tend to indicate that the sow
is rooting. Similarly, for the rooting activity, the posterior probabilities of the z axis
indicate that the sow is walking in 8 out of 10 series. Particular axes perform better
when used to classify specific activity types. These results are in keeping with the
types of movement that a sow performs for each activity type: sidewise movements
are very limited when a sow is lying laterally, so the activity is better recognized by
the horizontal sidewise y axis. Upwards and downwards movements are performed
while the sows is rooting, which may explain the better recognition on the vertical
x axis. The fact that a sow tends to walk while rooting may explain why neither of
these activities are clearly recognized.
In order to corroborate the results of the classification method, new parameters were
estimated from the test data set and applied on the learning data set, which had
previously been divided into 5 series of 2 minutes. Table 1 indicates the percentage
of posterior probabilities (pp) above 0.5 during the 2-minute time series. The left
panel shows the results from the test data set, where the DLMs were analyzed
using the parameters estimated from the learning data set. The right panel shows
the results from the learning data set, where the DLMs were analyzed using the
parameters estimated from the test data set.
The activities of feeding, rooting and lying sternally are well recognized on most
axes of both data sets. Walking activity is best recognized on the forward horizontal
z axis; when the MPKF is applied to the test data set, the very low percentage
of recognition for the y axis confirms the observation derived from Figure 3 (a):
the classification method tends to indicate that the sow is rooting. Where the acc
axis is concerned, results indicate that the sow is either rooting or lying sternally.
The activity of lying laterally is also very poorly recognized on the acc axis: the
9
1
0.8
0.6
0.4
0.2
0
0
1
0.8
0.6
0.4
0.2
0
30
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70
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70
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80
90
100
110
Rooting
10
20
30
40
50
60
Lying laterally
10
20
30
40
50
60
Lying sternally
pp
0
60
Walking
pp
0
1
0.8
0.6
0.4
0.2
0
20
pp
0
1
0.8
0.6
0.4
0.2
0
10
pp
0
1
0.8
0.6
0.4
0.2
0
Feeding
pp
10
20
30
40
50
60
Time, in seconds
(a)
1
0.8
0.6
0.4
0.2
0
0
1
0.8
0.6
0.4
0.2
0
30
40
50
10
20
30
40
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60
Rooting
10
20
30
40
50
60
Lying laterally
10
20
30
40
50
60
Lying sternally
pp
0
60
Walking
pp
0
1
0.8
0.6
0.4
0.2
0
20
pp
0
1
0.8
0.6
0.4
0.2
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pp
0
1
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0.6
0.4
0.2
0
Feeding
pp
10
20
30
40
50
60
70
Time, in seconds
(b)
10
Fig. 3. Evolution of the posterior probabilities for the five activity types, for two time series
of 120 observations corresponding to the walking activity (a) y axis and (b) z axis
pp
FE
1
0.8
0.6
0.4
0.2
0
WA
1
0.8
0.6
0.4
0.2
0
RO
1
0.8
0.6
0.4
0.2
0
LL
1
0.8
0.6
0.4
0.2
0
LS
1
0.8
0.6
0.4
0.2
0
0
X
20 40 60 80 100
pp
0
Y
pp
20 40 60 80 100
0
Z
20 40 60 80 100
pp
0
ACC
20 40 60 80 100
Time, in seconds
Fig. 4. Posterior probabilities for the axes x, y and z, and acc for the five types of activity.
Implementation of the classification method on the test data set. Mean of the 10 time series
(wide plain line) and 95% confidence intervals. The horizontal axes indicate the observation
time, in seconds (120 observations, i.e. 2 minutes)
percentages of posterior probabilities >0.5 are 12.7% and 2.5%, respectively, for
the test and learning data set, and the classification method tends to indicate that
the sow is feeding; results from the other three axes are in the range 56.2-97.9%.
Differences between the two panels observed here may be explained by the value
chosen for the threshold, i.e. 0.5. As shown in Figure 3 (a), some activities may
be partly recognized, but the values of the posteriors probabilities generally stay
below, and rarely exceed, the 0.5 threshold.
11
Table 1
Percentage of posterior probabilities where pp > 0.5 during the 2-minute windows for the
respective axes of each activity type. Left panel: application of the MPKF on the test data
set (1200 observations per result); right panel: application of the MPKF on the learning
data set (600 observations per result)
Test data set
Learning data set
x
y
z
acc
x
y
z
acc
FE
79.3
91.9
87.3
90.8
90.2
39.0
95.5
92.2
WA
22.8
05.0
81.9
00.0
49.2
42.3
66.2
49.3
RO
57.6
54.1
36.5
78.1
46.5
64.3
74.7
86.7
LL
77.9
97.9
65.6
12.7
85.3
97.3
56.2
02.5
LS
81.7
87.7
82.3
82.1
70.5
87.0
71.7
42.7
5 Discussion and Conclusion
The results of the classification method explored in this article show that all activity types can be recognized, either by using all axes or by focusing on a specific
axis. Both the three axes (x, y, z) and the length of the acceleration vector (acc)
were included. Reference to each of the three dimensions appears to be desirable;
this was especially seen in connection with the walking activity, where the z axis
(horizontal forward direction) showed the best results.
The results presented in Table 1 may be used as an indicator in an initial classification of the activity types. The choice of a 2-minute ’window’ is in accordance
with the average speed of recognition by the axis, which can take up to one minute
(as happens, for instance, with the x axis of rooting). Specific activities, such as
feeding, may be of short duration: in our experimental conditions the duration of
feeding activity was approximately 10 minutes per day, which corresponds to a sow
consuming her entire ration at once. This also supports the argument for classifying activities over a short time. In this study, a threshold of 0.5 was arbitrarily set
in order to evaluate the results of the classification method. As seen in Table 1, this
resulted in differences in the recognition of the same activity according to the data
sets. Other threshold values should be tested and optimized by mean of larger data
sets. Other methods, based on time-moving windows (Shasha and Zhu, 2004), may
be used to detect whether or not the sow is active, using the length of the acceleration vector. Class II Multi-Process models (West and Harrison, 1997, pp 443-456)
offer another kind of classification, over a shorter period of time. The interest of
this method appears, however, to be limited for two reasons. First, it is more complex: prior distributions for each activity type are defined according to the average
daily length of the activity, and this may vary from one sow to another. Second, it is
more demanding from a computational point of view, and this may limit its interest
so far as practical application is concerned.
12
Further developments of the method explored in this article may include combining
the three axes into a single multivariate model. For longer-term perspectives it may
be desirable to fit accelerometers to an ear tag. The use of an ear tag, rather than
fitting accelerometers to a neck collar, will generate more noise in the time series.
If that happens, the direction of each axis may become less clear, which will limit
their effectiveness as separate entities.
The five activity types were selected by associating acceleration patterns with specific activities observed in video recordings. The number and choice of activity
types depends on the practical application of the method being envisaged. In grouphoused sows fed by ESF the detection of feeding activity is less important, since
the ESF already registers the sow entering the feeding station. However, for grouphoused sows not being fed by ESF, or sows at any other stages (mating or farrowing
section), the monitoring of feeding activity may be used to detect, for example, illness: reduced feed intake is considered one of the first signs that an animal is ill
(Forbes, 1995). Some pairs of activities, such as standing and lying sternally, and
walking and rooting, may also present similar acceleration patterns, and may be difficult to distinguish one from another. The interest of detecting walking and rooting
separately is likely to be very limited, except in the detection of lameness; and in
that particular case a more detailed analysis of the walking pattern should be carried out. It can be argued that a larger number of activities will make acceleration
patterns more difficult to recognize and may, therefore, affect the performance and
reliability of the classification method. Types of activity may also be grouped and
reduced to two general categories: ’active behaviors’ (e.g. eating, walking, rooting)
and ’passive behaviors’ (e.g. lateral/sternal lying). These general categories could
be used, as indicators of general activity level, to detect estrus (Cornou and Heiskanen, 2007). Finally, the frequency of change in activity type, or posture, may be
used as an indicator of restlessness, in order to monitor, for example, parturition
(Harris and Gonyou, 1998; Hartsock and Barczewski, 1997).
In further experimentation, inter-pig and inter-pen variations need to be explored.
Particular behaviors, such as walking activity, may be influenced by the size of the
pen. However, the method presented in this article does not detect the daily distribution of the duration of an activity (which is needed in an MPKF of class II).
Differences may be observed more readily within the variance parameters, as a result of the speed of walking, for instance; this may nevertheless be due to inter-pig
variability. The data sets used in this study were obtained under ideal conditions: a
single activity type filled the whole period, and the activities were either not overlapping or such that overlapping was reduced to a minimum. This may have resulted
in overestimation of the performance of the method. More extensive data sets including several types of activity should now be tested. The use of a more complete
data set, covering a larger number of individuals and with optimal synchronization
between video recordings and acceleration measurements, may help researchers to
carry out these further analyzes.
13
The main interest of classifying activity types automatically is to supplement visual
observation with automatic registration. This makes it possible to monitor a larger
number of individuals at the same time, instantaneously, if the method performs
well. Development of a method of automatically classifying activity types is the
first step towards further automated methods designed to detect estrus, farrowing,
illness or welfare status.
In conclusion, then, the classification method presented in this article opens up new
possibilities for automatic monitoring of the types of activity an individual sow
performs. Further developments, involving the modeling each activity type, will
require larger data sets to be used. It will also be necessary to incorporate a method
of assessing inter-pig and inter-pen variation.
6 Acknowledgements
The authors gratefully acknowledge the Department of Computer Science, Copenhagen University, for assistance with data collection. Funding was provided by the
Danish Research Agency.
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