Page 127 - Artificial Intelligence for Computational Modeling of the Heart

Chapter 3 Learning cardiac anatomy 99

tinguish points on the object surface from points that are not on
the surface, one can estimate the K coefficients at runtime and
thereby obtain a surface segmentation of the object.

3.2.1.2 Traditional feature engineering
Based on this formulation, Zheng et al. [31] proposed to use the
Probabilistic Boosting Tree (PBT) [203] as discriminative learner.
In terms of feature computation, 3D Haar wavelets [259]were
extracted and used to encode the image information for transla-
tion estimation. Haar wavelets can be computed very efficiently
and can easily generalize to high dimensions. However, their ap-
plication is limited for capturing orientation and scale informa-
tion. The extension requires a pre-alignment of the volume and
the wavelet sampling pattern, which is very tedious and time-
consuming for a 3D learning problem.
A fast alternative, that comes at the expense of missing global
information, is the selection of local image intensity features. In
this context, steerable features were proposed [31]. The idea of
steerable features is to use a flexible sampling pattern to deter-
mine the image points at which local features are computed. For
a given hypothesis (x,y,z,φ x ,φ y ,φ z ,s x ,s y ,s z ) the sampling pat-
tern is centered at position (x,y,z), rotated by the correspond-
ing angles (φ x ,φ y ,φ z ) and anisotropically scaled with the factors
(s x ,s y ,s z ). Assuming that N local features are computed over a pat-
tern of P sampling points, the complete feature pool will contain
P × N features. With this strategy, Zheng et al. [31] demonstrate
that one can effectively capture both global and local information
and by steering the pattern, also incorporate orientation and scale
information.

3.2.1.3 Sparse adaptive deep neural networks
An alternative to handcrafted features was proposed in [258].
The proposed classifier is based on a modern deep neural network
architecture that supports the implicit learning of image features
for image classification directly from the raw image signal. The
application of standard deep neural network architectures is not
feasible in the volumetric setting, mainly due to the complexity
of the sampling operation under the considered object transfor-
mations. To address this challenge, Ghesu et al. [258] propose to
enforce sparsity in the network architecture to significantly accel-
erate the sampling operation. The derived architecture is called:
sparse adaptive deep neural networks, or SADNNs (see Fig. 3.1).
Given a fully-connected network architecture, the aim is to find
asparsitymap s for the network weights w,suchthatover T train-