Method for detection and tracking of deformable objects

1. A method for detecting and tracking a deformable object having a sequentially changing behavior, comprising:

using imaging apparatus to perform the steps of:

developing a temporal statistical shape model of the sequentially changing behavior of an embedding function representing the object from prior motion, comprising:

developing a hand segmented image sequence showing training of the object and level set functions for each one of the shapes;

computing a sequence of shape vectors comprising principal component representations of the level set functions;

estimating a dynamical model of for the sequence of shape vectors; and

determining the one of the sequence of shape vectors having the maximum probability of matching the dynamical model; and

wherein the estimating of the dynamical model comprises approximating the shape vectors α t ≡α φ t of the sequence of level set functions by a Markov chain of order k, in accordance with α t =μ+A 1 α t−1 +A 2 α t−2 + . . . +A k α t−k +η, where η is zero-mean Gaussian noise with covariance Σ.

2. A method for detecting and tracking a deformable object having a sequentially changing behavior, comprising:

using imaging apparatus to perform the steps of:

developing a temporal statistical shape model of the sequentially changing behavior of an embedding function representing the object from prior motion, comprising:

developing a hand-segmented image sequence showing training shapes of the object and level set functions for each one of the shapes;

computing a sequence of shape vectors comprising principal component representations of the level set functions;

estimating a dynamical model of for the sequence of shape vectors; and

determining the one of the sequence of shape vectors having the maximum probability of matching the dynamical model and wherein the maximum probability determining comprises performing gradient descent on the negative logarithm of the conditional probability; and

wherein given consecutive images I t : Ω→R from an image sequence, and given the segmentations α 1:t−1 and transformations {circumflex over (θ)} 1:t−1 obtained on the previous images I 1:t−1 , the maximum probability determining comprises: maximizes a conditional probability

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11

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with respect to the shape vectors α t and transformation parameters θ t ;

wherein the conditional probability is modeled as:

P(α t ,θ t |α 1:t−1 ,θ 1:t−1 ),  (12)

which constitutes the probability for observing a particular shape α t and a particular transformation θ t at time t, conditioned on the parameter estimates for shape and transformation obtained on previous images.

3. A method for detecting and tracking a deformable object having a sequentially changing behavior, comprising:

using imaging apparatus to perform the step of:

developing a temporal statistical shape model of the sequentially changing behavior of an embedding function representing the object from prior motion, comprising:

developing a hand-segmented image sequence showing training shapes of the object and level set functions for each one of the shapes;

computing a sequence of shape vectors comprising principal component representations of the level set functions;

estimating a dynamical model of for the sequence of shape vectors; and

determining the one of the sequence of shape vectors having the maximum probability of matching the dynamical model and wherein the maximum probability determining comprises performing gradient descent on the negative logarithm of the conditional probability; and

wherein the performing of the gradient descent on the negative logarithm of the conditional probability comprises using a gradient descent strategy, leading to the following differential equations to estimate the shape vector α t :

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22

where τ denotes the artificial evolution time, as opposed to the physical time t.