o :ήc6@sfdZddlZddlmZmZmZddlmZ dddZdd Z d d Z dd d dddddddZ dS)z Port of Manuel Guizar's code from: http://www.mathworks.com/matlabcentral/fileexchange/18401-efficient-subpixel-image-registration-by-cross-correlation N)fftnifftnfftfreq)_masked_phase_cross_correlationc Cst|ds |g|j}n t||jkrtd|dur"dg|j}n t||jkr-tddtj}tt|j||}|dddD]/\}}}t ||dddft ||} t | | } | j |j dd } tj| |d d }qB|S) a Upsampled DFT by matrix multiplication. This code is intended to provide the same result as if the following operations were performed: - Embed the array "data" in an array that is ``upsample_factor`` times larger in each dimension. ifftshift to bring the center of the image to (1,1). - Take the FFT of the larger array. - Extract an ``[upsampled_region_size]`` region of the result, starting with the ``[axis_offsets+1]`` element. It achieves this result by computing the DFT in the output array without the need to zeropad. Much faster and memory efficient than the zero-padded FFT approach if ``upsampled_region_size`` is much smaller than ``data.size * upsample_factor``. Parameters ---------- data : array The input data array (DFT of original data) to upsample. upsampled_region_size : integer or tuple of integers, optional The size of the region to be sampled. If one integer is provided, it is duplicated up to the dimensionality of ``data``. upsample_factor : integer, optional The upsampling factor. Defaults to 1. axis_offsets : tuple of integers, optional The offsets of the region to be sampled. Defaults to None (uses image center) Returns ------- output : ndarray The upsampled DFT of the specified region. __iter__zSshape of upsampled region sizes must be equal to input data's number of dimensions.NrzJnumber of axis offsets must be equal to input data's number of dimensions.y@Fcopy)rr)axes)hasattrndimlen ValueErrornppilistzipshapearangerexpastypedtype tensordot) dataupsampled_region_sizeupsample_factor axis_offsetsim2pidim_propertiesn_itemsups_size ax_offsetkernelr$T/tmp/pip-target-vg8gfxp4/lib/python/skimage/registration/_phase_cross_correlation.py_upsampled_dft s$ & r&cCst|j|jS)a Compute global phase difference between the two images (should be zero if images are non-negative). Parameters ---------- cross_correlation_max : complex The complex value of the cross correlation at its maximum point. )rarctan2imagreal)cross_correlation_maxr$r$r%_compute_phasediffQs r+cCs(d||||}tt|S)a Compute RMS error metric between ``src_image`` and ``target_image``. Parameters ---------- cross_correlation_max : complex The complex value of the cross correlation at its maximum point. src_amp : float The normalized average image intensity of the source image target_amp : float The normalized average image intensity of the target image g?)conjrsqrtabs)r*src_amp target_amperrorr$r$r%_compute_error^s r2r)Tg333333?phase)rspace return_errorreference_mask moving_mask overlap_ratio normalizationcCs|dus|durt|||||S|j|jkrtd|dkr%|} |} n|dkr4t|} t|} ntd| j} | | } |dkr[t| jj j } | t t | d| } n|durctdt | }ttt ||j}td d | D}| jj }t|j|d d }|||kt| ||k8<|d kr|rtt| | }|| j}tt| | }|| j}||}notj||d}t|||}t|d}t|d}|||}t| |||}ttt ||j}||}t|j|d d }||8}|||7}|r9tt| | }tt| | }t| jD]}| |d krKd||<q>|rqt|sbt|sbt|rftd|t|||t|fS|S)uEfficient subpixel image translation registration by cross-correlation. This code gives the same precision as the FFT upsampled cross-correlation in a fraction of the computation time and with reduced memory requirements. It obtains an initial estimate of the cross-correlation peak by an FFT and then refines the shift estimation by upsampling the DFT only in a small neighborhood of that estimate by means of a matrix-multiply DFT [1]_. Parameters ---------- reference_image : array Reference image. moving_image : array Image to register. Must be same dimensionality as ``reference_image``. upsample_factor : int, optional Upsampling factor. Images will be registered to within ``1 / upsample_factor`` of a pixel. For example ``upsample_factor == 20`` means the images will be registered within 1/20th of a pixel. Default is 1 (no upsampling). Not used if any of ``reference_mask`` or ``moving_mask`` is not None. space : string, one of "real" or "fourier", optional Defines how the algorithm interprets input data. "real" means data will be FFT'd to compute the correlation, while "fourier" data will bypass FFT of input data. Case insensitive. Not used if any of ``reference_mask`` or ``moving_mask`` is not None. return_error : bool, optional Returns error and phase difference if on, otherwise only shifts are returned. Has noeffect if any of ``reference_mask`` or ``moving_mask`` is not None. In this case only shifts is returned. reference_mask : ndarray Boolean mask for ``reference_image``. The mask should evaluate to ``True`` (or 1) on valid pixels. ``reference_mask`` should have the same shape as ``reference_image``. moving_mask : ndarray or None, optional Boolean mask for ``moving_image``. The mask should evaluate to ``True`` (or 1) on valid pixels. ``moving_mask`` should have the same shape as ``moving_image``. If ``None``, ``reference_mask`` will be used. overlap_ratio : float, optional Minimum allowed overlap ratio between images. The correlation for translations corresponding with an overlap ratio lower than this threshold will be ignored. A lower `overlap_ratio` leads to smaller maximum translation, while a higher `overlap_ratio` leads to greater robustness against spurious matches due to small overlap between masked images. Used only if one of ``reference_mask`` or ``moving_mask`` is not None. normalization : {"phase", None} The type of normalization to apply to the cross-correlation. This parameter is unused when masks (`reference_mask` and `moving_mask`) are supplied. Returns ------- shifts : ndarray Shift vector (in pixels) required to register ``moving_image`` with ``reference_image``. Axis ordering is consistent with numpy (e.g. Z, Y, X) error : float Translation invariant normalized RMS error between ``reference_image`` and ``moving_image``. phasediff : float Global phase difference between the two images (should be zero if images are non-negative). Notes ----- The use of cross-correlation to estimate image translation has a long history dating back to at least [2]_. The "phase correlation" method (selected by ``normalization="phase"``) was first proposed in [3]_. Publications [1]_ and [2]_ use an unnormalized cross-correlation (``normalization=None``). Which form of normalization is better is application-dependent. For example, the phase correlation method works well in registering images under different illumination, but is not very robust to noise. In a high noise scenario, the unnormalized method may be preferable. When masks are provided, a masked normalized cross-correlation algorithm is used [5]_, [6]_. References ---------- .. [1] Manuel Guizar-Sicairos, Samuel T. Thurman, and James R. Fienup, "Efficient subpixel image registration algorithms," Optics Letters 33, 156-158 (2008). :DOI:`10.1364/OL.33.000156` .. [2] P. Anuta, Spatial registration of multispectral and multitemporal digital imagery using fast Fourier transform techniques, IEEE Trans. Geosci. Electron., vol. 8, no. 4, pp. 353–368, Oct. 1970. :DOI:`10.1109/TGE.1970.271435`. .. [3] C. D. Kuglin D. C. Hines. The phase correlation image alignment method, Proceeding of IEEE International Conference on Cybernetics and Society, pp. 163-165, New York, NY, USA, 1975, pp. 163–165. .. [4] James R. Fienup, "Invariant error metrics for image reconstruction" Optics Letters 36, 8352-8357 (1997). :DOI:`10.1364/AO.36.008352` .. [5] Dirk Padfield. Masked Object Registration in the Fourier Domain. IEEE Transactions on Image Processing, vol. 21(5), pp. 2706-2718 (2012). :DOI:`10.1109/TIP.2011.2181402` .. [6] D. Padfield. "Masked FFT registration". In Proc. Computer Vision and Pattern Recognition, pp. 2918-2925 (2010). :DOI:`10.1109/CVPR.2010.5540032` Nzimages must be same shapefourierr)z*space argument must be "real" of "fourier"r3dz*normalization must be either phase or NonecSsg|] }t|dqS))rfix).0 axis_sizer$r$r% sz+phase_cross_correlation..Fr r)rg?g@rzNaN values found, please remove NaNs from your input data or use the `reference_mask`/`moving_mask` keywords, eg: phase_cross_correlation(reference_image, moving_image, reference_mask=~np.isnan(reference_image), moving_mask=~np.isnan(moving_image)))rrrlowerrr,rfinfor)repsmaximumr.r unravel_indexargmaxarraystackrsumsizeroundceilr=r&ranger isnanr2r+)reference_image moving_imagerr4r5r6r7r8r9src_freq target_freqr image_productrCcross_correlationmaxima midpoints float_dtypeshiftsr/r0CCmaxrdftshiftsample_region_offsetdimr$r$r%phase_cross_correlationpsj     "    $ r])rN) __doc__numpyr scipy.fftrrrrr&r+r2r]r$r$r$r%s  E