ó  ‰\c@sÙddlZddlZddlmZddlmZd„Zd„Zd„Z de fd „ƒYZ d e fd „ƒYZ d e fd „ƒYZ de fd„ƒYZd„Zdddejdddd„ZdS(iÿÿÿÿN(toptimizei(tcheck_random_statecCs9|jdks"|jd|kr5td|ƒ‚ndS(Niis#Input data must have shape (N, %d).(tndimtshapet ValueError(tdatatdim((s2lib/python2.7/site-packages/skimage/measure/fit.pyt_check_data_dims"cCs5|jdks"|jddkr1tdƒ‚ndS(NiisInput data must be at least 2D.(RRR(R((s2lib/python2.7/site-packages/skimage/measure/fit.pyt_check_data_atleast_2D s"cCstjtjd||ƒƒS(sFNumPy < 1.8 does not support the `axis` argument for `np.linalg.norm`.sij,ij->i(tnptsqrtteinsum(txtaxis((s2lib/python2.7/site-packages/skimage/measure/fit.pyt_norm_along_axisst BaseModelcBseZd„ZRS(cCs d|_dS(N(tNonetparams(tself((s2lib/python2.7/site-packages/skimage/measure/fit.pyt__init__s(t__name__t __module__R(((s2lib/python2.7/site-packages/skimage/measure/fit.pyRst LineModelNDcBsJeZdZd„Zdd„Zddd„Zdd„Zdd„ZRS(sŽTotal least squares estimator for N-dimensional lines. In contrast to ordinary least squares line estimation, this estimator minimizes the orthogonal distances of points to the estimated line. Lines are defined by a point (origin) and a unit vector (direction) according to the following vector equation:: X = origin + lambda * direction Attributes ---------- params : tuple Line model parameters in the following order `origin`, `direction`. Examples -------- >>> x = np.linspace(1, 2, 25) >>> y = 1.5 * x + 3 >>> lm = LineModelND() >>> lm.estimate(np.array([x, y]).T) True >>> tuple(np.round(lm.params, 5)) (array([ 1.5 , 5.25]), array([ 0.5547 , 0.83205])) >>> res = lm.residuals(np.array([x, y]).T) >>> np.abs(np.round(res, 9)) array([ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]) >>> np.round(lm.predict_y(x[:5]), 3) array([ 4.5 , 4.562, 4.625, 4.688, 4.75 ]) >>> np.round(lm.predict_x(y[:5]), 3) array([ 1. , 1.042, 1.083, 1.125, 1.167]) cCsÙt|ƒ|jddƒ}||}|jddkry|d|d}tjj|ƒ}|dkrÆ||:}qÆnM|jddkrºtjj|dtƒ\}}}|d}n tdƒ‚||f|_ t S(sEstimate line model from data. This minimizes the sum of shortest (orthogonal) distances from the given data points to the estimated line. Parameters ---------- data : (N, dim) array N points in a space of dimensionality dim >= 2. Returns ------- success : bool True, if model estimation succeeds. R iiit full_matricessAt least 2 input points needed.( RtmeanRR tlinalgtnormtsvdtFalseRRtTrue(RRtorigint directionRt_tv((s2lib/python2.7/site-packages/skimage/measure/fit.pytestimate@s   !  cCs t|ƒ|dkr"|j}n|dk s4t‚t|ƒdkrUtdƒ‚n|\}}||tj|||ƒdtjf|}t |ddƒS(sDetermine residuals of data to model. For each point, the shortest (orthogonal) distance to the line is returned. It is obtained by projecting the data onto the line. Parameters ---------- data : (N, dim) array N points in a space of dimension dim. params : (2, ) array, optional Optional custom parameter set in the form (`origin`, `direction`). Returns ------- residuals : (N, ) array Residual for each data point. is!Parameters are defined by 2 sets..R iN( RRRtAssertionErrortlenRR tdottnewaxisR(RRRRRtres((s2lib/python2.7/site-packages/skimage/measure/fit.pyt residualses    (icCs¯|dkr|j}n|dk s*t‚t|ƒdkrKtdƒ‚n|\}}||dkrztd|ƒ‚n|||||}||dtjf|}|S(smPredict intersection of the estimated line model with a hyperplane orthogonal to a given axis. Parameters ---------- x : (n, 1) array Coordinates along an axis. axis : int Axis orthogonal to the hyperplane intersecting the line. params : (2, ) array, optional Optional custom parameter set in the form (`origin`, `direction`). Returns ------- data : (n, m) array Predicted coordinates. Raises ------ ValueError If the line is parallel to the given axis. is!Parameters are defined by 2 sets.isLine parallel to axis %s.N(RRR#R$RR R&(RR R RRRtlR((s2lib/python2.7/site-packages/skimage/measure/fit.pytpredictƒs   cCs/|j|ddd|ƒdd…df}|S(s¤Predict x-coordinates for 2D lines using the estimated model. Alias for:: predict(y, axis=1)[:, 0] Parameters ---------- y : array y-coordinates. params : (2, ) array, optional Optional custom parameter set in the form (`origin`, `direction`). Returns ------- x : array Predicted x-coordinates. R iRNi(R*(RtyRR ((s2lib/python2.7/site-packages/skimage/measure/fit.pyt predict_xªs+cCs/|j|ddd|ƒdd…df}|S(s¤Predict y-coordinates for 2D lines using the estimated model. Alias for:: predict(x, axis=0)[:, 1] Parameters ---------- x : array x-coordinates. params : (2, ) array, optional Optional custom parameter set in the form (`origin`, `direction`). Returns ------- y : array Predicted y-coordinates. R iRNi(R*(RR RR+((s2lib/python2.7/site-packages/skimage/measure/fit.pyt predict_yÁs+N( RRt__doc__R"RR(R*R,R-(((s2lib/python2.7/site-packages/skimage/measure/fit.pyRs " % ' t CircleModelcBs,eZdZd„Zd„Zdd„ZRS(s¿Total least squares estimator for 2D circles. The functional model of the circle is:: r**2 = (x - xc)**2 + (y - yc)**2 This estimator minimizes the squared distances from all points to the circle:: min{ sum((r - sqrt((x_i - xc)**2 + (y_i - yc)**2))**2) } A minimum number of 3 points is required to solve for the parameters. Attributes ---------- params : tuple Circle model parameters in the following order `xc`, `yc`, `r`. Examples -------- >>> t = np.linspace(0, 2 * np.pi, 25) >>> xy = CircleModel().predict_xy(t, params=(2, 3, 4)) >>> model = CircleModel() >>> model.estimate(xy) True >>> tuple(np.round(model.params, 5)) (2.0, 3.0, 4.0) >>> res = model.residuals(xy) >>> np.abs(np.round(res, 9)) array([ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]) cCs®t|ddƒ|dd…df}|dd…df}|d|d}tj|ƒ}tj|ƒ}tj||ƒ}tjtj|dƒ||g|tj|dƒ|g||tt|ƒƒggƒ}tjtj||ƒtj||ƒtj|ƒggƒj} tjj|ƒj | ƒ\} } } | d| d| d} } } | d} | d}tj d| | d| dƒd}| ||f|_ t S(s/Estimate circle model from data using total least squares. Parameters ---------- data : (N, 2) array N points with ``(x, y)`` coordinates, respectively. Returns ------- success : bool True, if model estimation succeeds. RiNiii( RR tsumtarraytfloatR$tTRtpinvR%R RR(RRR R+tx2y2tsum_xtsum_ytsum_xytm1tm2tatbtctxctyctr((s2lib/python2.7/site-packages/skimage/measure/fit.pyR"ýs(!$   'cCsst|ddƒ|j\}}}|dd…df}|dd…df}|tj||d||dƒS(sfDetermine residuals of data to model. For each point the shortest distance to the circle is returned. Parameters ---------- data : (N, 2) array N points with ``(x, y)`` coordinates, respectively. Returns ------- residuals : (N, ) array Residual for each data point. RiNii(RRR R (RRR>R?R@R R+((s2lib/python2.7/site-packages/skimage/measure/fit.pyR(&s cCsy|dkr|j}n|\}}}||tj|ƒ}||tj|ƒ}tj|d|dfd|jƒS(sÂPredict x- and y-coordinates using the estimated model. Parameters ---------- t : array Angles in circle in radians. Angles start to count from positive x-axis to positive y-axis in a right-handed system. params : (3, ) array, optional Optional custom parameter set. Returns ------- xy : (..., 2) array Predicted x- and y-coordinates. .R N(.N(.N(RRR tcostsint concatenateR(RttRR>R?R@R R+((s2lib/python2.7/site-packages/skimage/measure/fit.pyt predict_xy@s   N(RRR.R"R(RRE(((s2lib/python2.7/site-packages/skimage/measure/fit.pyR/Ùs" ) t EllipseModelcBs,eZdZd„Zd„Zdd„ZRS(sjTotal least squares estimator for 2D ellipses. The functional model of the ellipse is:: xt = xc + a*cos(theta)*cos(t) - b*sin(theta)*sin(t) yt = yc + a*sin(theta)*cos(t) + b*cos(theta)*sin(t) d = sqrt((x - xt)**2 + (y - yt)**2) where ``(xt, yt)`` is the closest point on the ellipse to ``(x, y)``. Thus d is the shortest distance from the point to the ellipse. The estimator is based on a least squares minimization. The optimal solution is computed directly, no iterations are required. This leads to a simple, stable and robust fitting method. The ``params`` attribute contains the parameters in the following order:: xc, yc, a, b, theta Attributes ---------- params : tuple Ellipse model parameters in the following order `xc`, `yc`, `a`, `b`, `theta`. Examples -------- >>> xy = EllipseModel().predict_xy(np.linspace(0, 2 * np.pi, 25), ... params=(10, 15, 4, 8, np.deg2rad(30))) >>> ellipse = EllipseModel() >>> ellipse.estimate(xy) True >>> np.round(ellipse.params, 2) array([ 10. , 15. , 4. , 8. , 0.52]) >>> np.round(abs(ellipse.residuals(xy)), 5) array([ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]) cCs5t|ddƒ|dd…df}|dd…df}tj|d|||dgƒj}tj||tjt|ƒƒgƒj}tj|j|ƒ}tj|j|ƒ}tj|j|ƒ}tjdddgdddgdddggƒ} yGtjj | ƒj|tj|tjj |ƒƒj|jƒƒ} Wntjj k r`t SXtjj | ƒ\} } d tj | ddd…f| ddd…fƒtj| ddd…fdƒ} | dd…| dkf}d|jkst|jƒƒd krt S|jƒ\}}}tjtjj |ƒ |jƒj|ƒ}|jƒ\}}}|d:}|d:}|d:}|||||d||}|||||d||}||d||d||dd||||||}tj||dd |dƒ}|d|||||}|d||| ||}tjd||ƒ}tjd||ƒ}d tjd|||ƒ}||krÜ|d tj7}ntj|||||gƒjƒ|_g|jD]}ttj|ƒƒ^q |_tS( sfEstimate circle model from data using total least squares. Parameters ---------- data : (N, 2) array N points with ``(x, y)`` coordinates, respectively. Returns ------- success : bool True, if model estimation succeeds. References ---------- .. [1] Halir, R.; Flusser, J. "Numerically stable direct least squares fitting of ellipses". In Proc. 6th International Conference in Central Europe on Computer Graphics and Visualization. WSCG (Vol. 98, pp. 125-132). RiNiigg@gð¿iigà?(RR tvstackR3tonesR$R%R1Rtinvt LinAlgErrorRteigtmultiplytpowerRtravelR tarctantpit nan_to_numttolistRR2trealR(RRR R+tD1tD2tS1tS2tS3tC1tMteig_valsteig_vecstcondta1R;R<R=ta2tdtftgtx0ty0t numeratorttermt denominator1t denominator2twidththeighttphi((s2lib/python2.7/site-packages/skimage/measure/fit.pyR"„sP'*353#'+   ""B# '.csLt|ddƒ|j\‰‰‰‰}tj|ƒ‰tj|ƒ‰|dd…df}|dd…df}|jd}‡‡‡‡‡‡fd†}tj|fdtjƒ}tj |ˆ|ˆƒ|}xot |ƒD]a} || } || } t j ||| d| | fƒ\} } tj || | | ƒƒ|| R?(s2lib/python2.7/site-packages/skimage/measure/fit.pytfuns tdtypetargs(RRRlRARBRR temptytdoubletarctan2trangeRtleastsqR (RRtthetaR R+tNRuR(tt0tiRmRnRDR ((R;R<RsRtR>R?s2lib/python2.7/site-packages/skimage/measure/fit.pyR(ãs    (#cCsÉ|dkr|j}n|\}}}}}tj|ƒ}tj|ƒ} tj|ƒ} tj|ƒ} ||| ||| | } ||| ||| | } tj| d| dfd|jƒS(sÂPredict x- and y-coordinates using the estimated model. Parameters ---------- t : array Angles in circle in radians. Angles start to count from positive x-axis to positive y-axis in a right-handed system. params : (5, ) array, optional Optional custom parameter set. Returns ------- xy : (..., 2) array Predicted x- and y-coordinates. .R N(.N(.N(RRR RARBRlRCR(RRDRR>R?R;R<R}RoRpRsRtR R+((s2lib/python2.7/site-packages/skimage/measure/fit.pyRE!s  N(RRR.R"R(RRE(((s2lib/python2.7/site-packages/skimage/measure/fit.pyRF[s' _ >cCs¶|dkrtjSd|}|dkr0tjS|t|ƒ}d||}|dkr^dS|dkrqtjStj|ƒ}tj|ƒ}|dkrŸdSttj||ƒƒS(sDetermine number trials such that at least one outlier-free subset is sampled for the given inlier/outlier ratio. Parameters ---------- n_inliers : int Number of inliers in the data. n_samples : int Total number of samples in the data. min_samples : int Minimum number of samples chosen randomly from original data. probability : float Probability (confidence) that one outlier-free sample is generated. Returns ------- trials : int Number of trials. ii(R tinfR2tlogtinttceil(t n_inlierst n_samplest min_samplest probabilitytnomt inlier_ratiotdenom((s2lib/python2.7/site-packages/skimage/measure/fit.pyt_dynamic_max_trialsCs       idiic Cs¦d} d} tj} d}t| ƒ} |dkrBtdƒ‚n|dkr]tdƒ‚n| dksu| dkr„tdƒ‚nt|tƒ r°t|tƒ r°|g}nt|ƒ}|djd}xt |ƒD]s}g}| j d||ƒ}x|D]}|j ||ƒqW|dk r<||Œ r<qÚn|ƒ}|j |Œ}|dk ro|soqÚqon|dk r‘|||Œ r‘qÚntj |j|Œƒ}||k}tj|dƒ}tj|ƒ}|| ksû|| krÚ|| krÚ|} |} |} |}| |ksF| |ksF|t| ||| ƒkrMPqMqÚqÚW|dk rœx,t t|ƒƒD]}|||||= stop_probability``, depending on the current best model's inlier ratio and the number of trials. This requires to generate at least N samples (trials): N >= log(1 - probability) / log(1 - e**m) where the probability (confidence) is typically set to a high value such as 0.99, and e is the current fraction of inliers w.r.t. the total number of samples. random_state : int, RandomState instance or None, optional If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. Returns ------- model : object Best model with largest consensus set. inliers : (N, ) array Boolean mask of inliers classified as ``True``. References ---------- .. [1] "RANSAC", Wikipedia, http://en.wikipedia.org/wiki/RANSAC Examples -------- Generate ellipse data without tilt and add noise: >>> t = np.linspace(0, 2 * np.pi, 50) >>> xc, yc = 20, 30 >>> a, b = 5, 10 >>> x = xc + a * np.cos(t) >>> y = yc + b * np.sin(t) >>> data = np.column_stack([x, y]) >>> np.random.seed(seed=1234) >>> data += np.random.normal(size=data.shape) Add some faulty data: >>> data[0] = (100, 100) >>> data[1] = (110, 120) >>> data[2] = (120, 130) >>> data[3] = (140, 130) Estimate ellipse model using all available data: >>> model = EllipseModel() >>> model.estimate(data) True >>> np.round(model.params) # doctest: +SKIP array([ 72., 75., 77., 14., 1.]) Estimate ellipse model using RANSAC: >>> ransac_model, inliers = ransac(data, EllipseModel, 20, 3, max_trials=50) >>> abs(np.round(ransac_model.params)) array([ 20., 30., 5., 10., 0.]) >>> inliers # doctest: +SKIP array([False, False, False, False, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True], dtype=bool) >>> sum(inliers) > 40 True Robustly estimate geometric transformation: >>> from skimage.transform import SimilarityTransform >>> np.random.seed(0) >>> src = 100 * np.random.rand(50, 2) >>> model0 = SimilarityTransform(scale=0.5, rotation=1, ... translation=(10, 20)) >>> dst = model0(src) >>> dst[0] = (10000, 10000) >>> dst[1] = (-100, 100) >>> dst[2] = (50, 50) >>> model, inliers = ransac((src, dst), SimilarityTransform, 2, 10) >>> inliers array([False, False, False, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True], dtype=bool) is'`min_samples` must be greater than zeros&`max_trials` must be greater than zerois*`stop_probability` must be in range [0, 1]iN(RR RRRt isinstancetlistttupleRR{trandinttappendR"tabsR(R0RŒR$(Rt model_classR‡tresidual_thresholdt is_data_validtis_model_validt max_trialststop_sample_numtstop_residuals_sumtstop_probabilityt random_statet best_modeltbest_inlier_numtbest_inlier_residuals_sumt best_inlierst num_samplest num_trialstsamplest random_idxsR`t sample_modeltsuccesstsample_model_residualstsample_model_inlierstsample_model_residuals_sumtsample_inlier_numR€((s2lib/python2.7/site-packages/skimage/measure/fit.pytransacksh                      (RltnumpyR tscipyRt _shared.utilsRRRRtobjectRRR/RFRŒRRRª(((s2lib/python2.7/site-packages/skimage/measure/fit.pyts     ½‚è )