Reglamento interno de seguridad y salud en el trabajo

For most multi-atlas segmentation methods, the dependence on image registration can be prob- lematic as inaccurate alignment adversely affects the performance of the segmentation. Addi- tionally, finding suitable (fixed) registration parameters that yield accurate non-linear corre- spondences on different images can be a challenge on its own, particularly for anatomies that are highly variable. Furthermore, the range of atlases available may not always fully accom- modate for the anatomical variability present between subjects, particularly as acquiring large datasets of atlases may be time consuming and expensive.

Patch-based methods for label propagation [47],[142] relax the dependence on registration ac- curacy and do not rely on explicit one-to-one correspondences between images. In general, these approaches label each voxel of a target image by comparing the image patch centred on the voxel with neighbouring patches from an atlas library and assigning the most likely label according to the closest matches (see Figure 2.10). Due to the relaxation of the required alignment between images, these methods are often able to use affine rather than non-rigid registration, yet still produce comparable results [142]. Patch-based methods for label fusion have also been shown to be effective for several applications in medical imaging [8], [179]. In contrast to previous MALP approaches, where atlas selection and label fusion is performed

Figure 2.10: Patch-based Segmentation: For each voxel, labels are propagated from the most similar patches in the atlas library, rather than propagating one-to-one, voxel-to-voxel from the atlases to the image like in MALP.

on a global voxel-to-voxel basis, the patch-based approach to segmentation can be conceptually described as a similar process but within local neighbourhoods around each voxel. For each voxel within an image, a patch is essentially a raw feature descriptor of the local area which surrounds that voxel. Selecting similar patches from atlases for patch-level label fusion is analogous to selecting atlases for label fusion in MALP. The key advantages of this local approach are:

1. Increased population size and reduced dimensionality. There are many more patches to select from than whole atlases. The dimensionality of each patch is also much smaller than a whole image, decreasing the possible combinations of intensity values. This means the data space is much more dense, so increasing the chances that the selection results have high statistical significance.

2. No assumption of a one-to-one mapping between images. MALP transfers labels from atlases to images on a one-to-one voxel basis, but this relationship may not always be present between images, even after registration. A patch-based approach does not assume an explicit one-to-one mapping between images and label transfer is not limited to a one- to-one relationship between images. Voxel-wise, labels can be transferred to any number of voxels on the target image. This can overcome problems for multi-atlas segmentation where the anatomical variability cannot be fully accounted with the available atlases. This also relaxes the required accuracy of the registration algorithms, reducing the amount of manual input and bespoke customization needed.

2.3. Image Segmentation 69

Nonlocal Means Based Label Propagation

Many existing patch-based approaches [47, 142, 61, 191] apply a label fusion method based on the nonlocal means method [34] which was original proposed for patch-based denoising. When applied to label fusion, this approach derives a weighting for each label according to the intensity distances of the most similar patches. At each voxel location, x, in the target image, let P (x) be the patch extraction operator at x and let Nx be a surrounding neighbourhood of

x and yL,i ∈ Nx represent voxels from the atlas library for label L which have similar patches

to x. A weighting for each label at voxel x is then determined as:

wL(x) = P yL,i∈Nxw(x, yL,i) P L∈LA P yL,i∈Nxw(x, yL,i) (2.22)

where w(x, y) is the weight of each patch and is determined by:

w(x, y) = e−||P (y) − P (y)||

2 2

h2_(x) (2.23)

h2(x) is a decay parameter to control the level of influence of patches as the distance increases. In [47], an automatic estimation of this is calculated for each voxel based on the minimum distance between patch P (x) and the relevant patches from the atlas library, {P (yi) : yi ∈ Nx}:

h2(x) = min{||P (x) − P (yi)||22} (2.24)

In approaches based on [47, 142], L is determined as the final label if wL(x) is greater than

a predefined threshold t, otherwise the label defaults to the background label. For binary labelling, t is often simply defined as 0.5, which is equivalent to determining the final label by majority voting. Additionally in these methods, a sliding window approach is used to define Nx, and only patches from within this window are used for label fusion. In [47], a structural

from for label fusion. This is defined as: ss = 2µxµy µxµy × 2σxσy σxσy (2.25)

where µ and σ are the means and standard deviation of the intensities of the patches around voxel x in the target image and voxel y from the atlas. Only patches with structural similarities greater than a predefined threshold are used for label fusion. This was used to reduce the computational time, since heat maps of the means and standard deviations can be produced offline. In [47] and [61] only patches with ss > 0.95 were used.

Joint Label Fusion

In addition to nonlocal means derived methods, other alternative patch-based approaches have also been proposed, although not always explicitly described as such. One particular approach, called joint label fusion [179], was proposed to combine labels whilst evaluating the performance of the atlases together rather than independently as the other multi-atlas approaches have done so far. By doing so, it aims to take into account similar errors which can occur with different atlases and minimise the expected total labelling error. To do this, the pairwise dependency between atlases is modelled as a joint probability of two atlases making an error at each voxel. This is approximated by looking at the intensity similarities between each pair of atlases and the target image in a local neighbourhood, similarly to [7] and as shown in (2.21). Thereafter, the aim is to choose a set of weights w∗_x for the atlases that minimise the error between the true segmentation and the consensus segmentation. This can be represented as:

w∗_x= arg min wx wT_xMxwx subject to N X i=1

wx(i) = 1 and wx(i) ≥ 0 (2.26)

where wx is a vector of weights [w1(x), ..., wN(x)] for each atlas and Mx is a pairwise depen-

dency matrix with Mx(i, j) being the probability atlas i and atlas j both produce the wrong