|
| 1 | +"""Point-set structures |
| 2 | +
|
| 3 | +Imaging data are sampled at points in space, and these points |
| 4 | +can be described by coordinates. |
| 5 | +These structures are designed to enable operations on sets of |
| 6 | +points, as opposed to the data sampled at those points. |
| 7 | +
|
| 8 | +Abstractly, a point set is any collection of points, but there are |
| 9 | +two types that warrant special consideration in the neuroimaging |
| 10 | +context: grids and meshes. |
| 11 | +
|
| 12 | +A *grid* is a collection of regularly-spaced points. The canonical |
| 13 | +examples of grids are the indices of voxels and their affine |
| 14 | +projection into a reference space. |
| 15 | +
|
| 16 | +A *mesh* is a collection of points and some structure that enables |
| 17 | +adjacent points to be identified. A *triangular mesh* in particular |
| 18 | +uses triplets of adjacent vertices to describe faces. |
| 19 | +""" |
| 20 | +from __future__importannotations |
| 21 | + |
| 22 | +importmath |
| 23 | +importtypingasty |
| 24 | +fromdataclassesimportdataclass,replace |
| 25 | + |
| 26 | +importnumpyasnp |
| 27 | + |
| 28 | +fromnibabel.castingimportable_int_type |
| 29 | +fromnibabel.filesliceimportstrided_scalar |
| 30 | +fromnibabel.spatialimagesimportSpatialImage |
| 31 | + |
| 32 | +ifty.TYPE_CHECKING:# pragma: no cover |
| 33 | +fromtyping_extensionsimportSelf |
| 34 | + |
| 35 | +_DType=ty.TypeVar('_DType',bound=np.dtype[ty.Any]) |
| 36 | + |
| 37 | + |
| 38 | +classCoordinateArray(ty.Protocol): |
| 39 | +ndim:int |
| 40 | +shape:tuple[int,int] |
| 41 | + |
| 42 | +@ty.overload |
| 43 | +def__array__(self,dtype:None= ...,/)->np.ndarray[ty.Any,np.dtype[ty.Any]]: |
| 44 | + ...# pragma: no cover |
| 45 | + |
| 46 | +@ty.overload |
| 47 | +def__array__(self,dtype:_DType,/)->np.ndarray[ty.Any,_DType]: |
| 48 | + ...# pragma: no cover |
| 49 | + |
| 50 | + |
| 51 | +@dataclass |
| 52 | +classPointset: |
| 53 | +"""A collection of points described by coordinates. |
| 54 | +
|
| 55 | + Parameters |
| 56 | + ---------- |
| 57 | + coords : array-like |
| 58 | + (*N*, *n*) array with *N* being points and columns their *n*-dimensional coordinates |
| 59 | + affine : :class:`numpy.ndarray` |
| 60 | + Affine transform to be applied to coordinates array |
| 61 | + homogeneous : :class:`bool` |
| 62 | + Indicate whether the provided coordinates are homogeneous, |
| 63 | + i.e., homogeneous 3D coordinates have the form ``(x, y, z, 1)`` |
| 64 | + """ |
| 65 | + |
| 66 | +coordinates:CoordinateArray |
| 67 | +affine:np.ndarray |
| 68 | +homogeneous:bool=False |
| 69 | + |
| 70 | +# Force use of __rmatmul__ with numpy arrays |
| 71 | +__array_priority__=99 |
| 72 | + |
| 73 | +def__init__( |
| 74 | +self, |
| 75 | +coordinates:CoordinateArray, |
| 76 | +affine:np.ndarray|None=None, |
| 77 | +homogeneous:bool=False, |
| 78 | + ): |
| 79 | +self.coordinates=coordinates |
| 80 | +self.homogeneous=homogeneous |
| 81 | + |
| 82 | +ifaffineisNone: |
| 83 | +self.affine=np.eye(self.dim+1) |
| 84 | +else: |
| 85 | +self.affine=np.asanyarray(affine) |
| 86 | + |
| 87 | +ifself.affine.shape!= (self.dim+1,)*2: |
| 88 | +raiseValueError(f'Invalid affine for{self.dim}D coordinates:\n{self.affine}') |
| 89 | +ifnp.any(self.affine[-1, :-1]!=0)orself.affine[-1,-1]!=1: |
| 90 | +raiseValueError(f'Invalid affine matrix:\n{self.affine}') |
| 91 | + |
| 92 | +@property |
| 93 | +defn_coords(self)->int: |
| 94 | +"""Number of coordinates |
| 95 | +
|
| 96 | + Subclasses should override with more efficient implementations. |
| 97 | + """ |
| 98 | +returnself.coordinates.shape[0] |
| 99 | + |
| 100 | +@property |
| 101 | +defdim(self)->int: |
| 102 | +"""The dimensionality of the space the coordinates are in""" |
| 103 | +returnself.coordinates.shape[1]-self.homogeneous |
| 104 | + |
| 105 | +def__rmatmul__(self,affine:np.ndarray)->Self: |
| 106 | +"""Apply an affine transformation to the pointset |
| 107 | +
|
| 108 | + This will return a new pointset with an updated affine matrix only. |
| 109 | + """ |
| 110 | +returnreplace(self,affine=np.asanyarray(affine) @self.affine) |
| 111 | + |
| 112 | +def_homogeneous_coords(self): |
| 113 | +ifself.homogeneous: |
| 114 | +returnnp.asanyarray(self.coordinates) |
| 115 | + |
| 116 | +ones=strided_scalar( |
| 117 | +shape=(self.coordinates.shape[0],1), |
| 118 | +scalar=np.array(1,dtype=self.coordinates.dtype), |
| 119 | + ) |
| 120 | +returnnp.hstack((self.coordinates,ones)) |
| 121 | + |
| 122 | +defget_coords(self,*,as_homogeneous:bool=False): |
| 123 | +"""Retrieve the coordinates |
| 124 | +
|
| 125 | + Parameters |
| 126 | + ---------- |
| 127 | + as_homogeneous : :class:`bool` |
| 128 | + Return homogeneous coordinates if ``True``, or Cartesian |
| 129 | + coordiantes if ``False``. |
| 130 | +
|
| 131 | + name : :class:`str` |
| 132 | + Select a particular coordinate system if more than one may exist. |
| 133 | + By default, `None` is equivalent to `"world"` and corresponds to |
| 134 | + an RAS+ coordinate system. |
| 135 | + """ |
| 136 | +ident=np.allclose(self.affine,np.eye(self.affine.shape[0])) |
| 137 | +ifself.homogeneous==as_homogeneousandident: |
| 138 | +returnnp.asanyarray(self.coordinates) |
| 139 | +coords=self._homogeneous_coords() |
| 140 | +ifnotident: |
| 141 | +coords= (self.affine @coords.T).T |
| 142 | +ifnotas_homogeneous: |
| 143 | +coords=coords[:, :-1] |
| 144 | +returncoords |
| 145 | + |
| 146 | + |
| 147 | +classGrid(Pointset): |
| 148 | +r"""A regularly-spaced collection of coordinates |
| 149 | +
|
| 150 | + This class provides factory methods for generating Pointsets from |
| 151 | + :class:`~nibabel.spatialimages.SpatialImage`\s and generating masks |
| 152 | + from coordinate sets. |
| 153 | + """ |
| 154 | + |
| 155 | +@classmethod |
| 156 | +deffrom_image(cls,spatialimage:SpatialImage)->Self: |
| 157 | +returncls(coordinates=GridIndices(spatialimage.shape[:3]),affine=spatialimage.affine) |
| 158 | + |
| 159 | +@classmethod |
| 160 | +deffrom_mask(cls,mask:SpatialImage)->Self: |
| 161 | +mask_arr=np.bool_(mask.dataobj) |
| 162 | +returncls( |
| 163 | +coordinates=np.c_[np.nonzero(mask_arr)].astype(able_int_type(mask.shape)), |
| 164 | +affine=mask.affine, |
| 165 | + ) |
| 166 | + |
| 167 | +defto_mask(self,shape=None)->SpatialImage: |
| 168 | +ifshapeisNone: |
| 169 | +shape=tuple(np.max(self.coordinates,axis=0)[:self.dim]+1) |
| 170 | +mask_arr=np.zeros(shape,dtype='bool') |
| 171 | +mask_arr[tuple(np.asanyarray(self.coordinates)[:, :self.dim].T)]=True |
| 172 | +returnSpatialImage(mask_arr,self.affine) |
| 173 | + |
| 174 | + |
| 175 | +classGridIndices: |
| 176 | +"""Class for generating indices just-in-time""" |
| 177 | + |
| 178 | +__slots__= ('gridshape','dtype','shape') |
| 179 | +ndim=2 |
| 180 | + |
| 181 | +def__init__(self,shape,dtype=None): |
| 182 | +self.gridshape=shape |
| 183 | +self.dtype=dtypeorable_int_type(shape) |
| 184 | +self.shape= (math.prod(self.gridshape),len(self.gridshape)) |
| 185 | + |
| 186 | +def__repr__(self): |
| 187 | +returnf'<{self.__class__.__name__}{self.gridshape}>' |
| 188 | + |
| 189 | +def__array__(self,dtype=None): |
| 190 | +ifdtypeisNone: |
| 191 | +dtype=self.dtype |
| 192 | + |
| 193 | +axes= [np.arange(s,dtype=dtype)forsinself.gridshape] |
| 194 | +returnnp.reshape(np.meshgrid(*axes,copy=False,indexing='ij'), (len(axes),-1)).T |