0-Ph~ddlZddlmZddlZddlmZddlmZm Z ej dZ dZ dZ Gdd ZGd d eZGd d eZGddeZdZdddejddddfdZdS)N)warn)inv)optimizespatialcd|jdks|jd|krtd|ddS)NrzInput data must have shape (N, z).ndimshape ValueError)datadims S/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/skimage/measure/fit.py_check_data_dimr s? yA~~A#--B3BBBCCC.-c\|jdks|jddkrtddS)Nr rzInput data must be at least 2D.r )rs r_check_data_atleast_2Drs4 y1}} 1 )):;;;*)rceZdZdZdS) BaseModelcd|_dSN)params)selfs r__init__zBaseModel.__init__s  rN)__name__ __module__ __qualname__rrrrrs#rrc8eZdZdZdZd dZd dZd dZd dZdS) LineModelNDauTotal 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.stack([x, y], axis=-1)) True >>> tuple(np.round(lm.params, 5)) (array([1.5 , 5.25]), array([0.5547 , 0.83205])) >>> res = lm.residuals(np.stack([x, y], axis=-1)) >>> 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]) ct||d}||z }|jddkr<|d|dz }tj|}|dkr||z}nA|jddkr.tj|d\}}}|d}ndS||f|_dS)aEstimate 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. raxisr rF) full_matricesT)rmeanr nplinalgnormsvdr)rrorigin directionr)_vs restimatezLineModelND.estimate?s t$$$""f} :a=A  Q$q')I9>>),,DqyyT! Z]Q  immDm>>GAq!!II5y) trNc4t|||jtd|j}t|dkrtd|\}}||z ||z |zdtjf|zz }tj|dS)aDetermine residuals of data to model. For each point, the shortest (orthogonal) distance to the line is returned. It is obtained by projecting the data onto the line. Parameters ---------- data : (N, dim) array N points in a space of dimension dim. params : (2,) array, optional Optional custom parameter set in the form (`origin`, `direction`). Returns ------- residuals : (N,) array Residual for each data point. NParameters cannot be Noner !Parameters are defined by 2 sets..rr#)rrr lenr'newaxisr(r))rrrr+r,ress r residualszLineModelND.residualsds$ t$$$ >{" !<===[F v;;!  @AA A" f}$-9!< O! !y~~c~***rrc*||jtd|j}t|dkrtd|\}}||dkrtd||||z ||z }||dtjf|zz}|S)alPredict intersection of the estimated line model with a hyperplane orthogonal to a given axis. Parameters ---------- x : (n, 1) array Coordinates along an axis. axis : int Axis orthogonal to the hyperplane intersecting the line. params : (2,) array, optional Optional custom parameter set in the form (`origin`, `direction`). Returns ------- data : (n, m) array Predicted coordinates. Raises ------ ValueError If the line is parallel to the given axis. Nr1r r2rzLine parallel to axis .)rr r3r'r4)rxr$rr+r,lrs rpredictzLineModelND.predicts. >{" !<===[F v;;!  @AA A" T?a  s r predict_yzLineModelND.predict_yr@rr)rN) rrr__doc__r/r6r:r?rBrrrr!r!s!!F###J++++@&&&&P.rr!c&eZdZdZdZdZddZdS) CircleModelaMTotal 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`. Notes ----- The estimation is carried out using a 2D version of the spherical estimation given in [1]_. References ---------- .. [1] Jekel, Charles F. Obtaining non-linear orthotropic material models for pvc-coated polyester via inverse bubble inflation. Thesis (MEng), Stellenbosch University, 2016. Appendix A, pp. 83-87. https://hdl.handle.net/10019.1/98627 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.]) ctt|dtj|jtj}||d}|d}||z }|}|tj|j krtdtddS||z}tj |dztj |jdd f| d }tj|dzd }tj||d \}}} }| d krtddS|dd} t%j| |} tjtj| dz} | |z} | |z} | |z } t+| | fz|_dS)a/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. r rFcopyrr#zUStandard deviation of data is too small to estimate circle with meaningful precision.category stacklevelrdtypeN)rcondz6Input does not contain enough significant data points.T)rr' promote_typesrNfloat32astyper&stdfinfotinyrRuntimeWarningappendonesr sumr(lstsqrminkowski_distancesqrttupler) rr float_typer+scaleAfCr-rankcenter distancesrs rr/zCircleModel.estimate s !$$$$%dj"*== {{:E{22""f}  28J'', , , 4'      5   IdQhA(:* M M MTU V V V F47 # # # 1D99 1dA 199 I J J J51Q3.vt<< GBGIqL)) * * % U &Fmmqd* trct|d|j\}}}|dddf}|dddf}|tj||z dz||z dzzz S)aeDetermine residuals of data to model. For each point the shortest distance to the circle is returned. Parameters ---------- data : (N, 2) array N points with ``(x, y)`` coordinates, respectively. Returns ------- residuals : (N,) array Residual for each data point. r rGNrr)rrr'r])rrxcycrgr8r>s rr6zCircleModel.residualsCsp" !$$$$K B AJ AJ27AFq=AFq=89999rNc||j}|\}}}||tj|zz}||tj|zz}tj|d|df|jS)aPredict 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. N.Nr#)rr'cossin concatenater )rtrrirjrgr8r>s r predict_xyzCircleModel.predict_xy]sk" >[F B RVAYY  RVAYY ~q|Qy\:HHHHrrrrrrCr/r6rqrrrrErEsX++Z888t:::4IIIIIIrrEc&eZdZdZdZdZddZdS) EllipseModelaLTotal 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, 8, 4, np.deg2rad(30))) >>> ellipse = EllipseModel() >>> ellipse.estimate(xy) True >>> np.round(ellipse.params, 2) array([10. , 15. , 8. , 4. , 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.]) ct|dt|dkrtdtddSt j|jtj}||d}| d }||z }| }|t j |j krtd tddS||z}|d d df}|d d d f}t j |dz||z|dzgj}t j ||t j|gj}|j|z} |j|z} |j|z} t jgd gdgdg} t#| | | t#| z| jzz z} n#tjj$rYdSwxYwtj| \}}dt j|dd d f|dd d fzt j|d d d fdz }|d d |dkf}d|jvs%t|dkrdS|\}}}t#|  | jz|z}|\}}}|dz}|dz}|dz}||z||zz |dz||zz z }||z||zz |dz||zz z }||dzz||dzzz||dzzzd|z|z|zz ||z|zz }t j||z dzd|dzzz}|dz||zz |||zz z}|dz||zz | ||zz z}t jd|z|z }t jd|z|z } dt jd|z||z z z}!||kr|!dtjzz }!|| kr| |} }|!tjdz z }!|!tjz}!t j|||| |!gj}"|"d dxx|zcc<|"d dxx|z cc<t=d|"D|_dS)agEstimate ellipse 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). r rGz3Need at least 5 data points to estimate an ellipse.rJFrHrr#zVStandard deviation of data is too small to estimate ellipse with meaningful precision.Nr)rw@)rwgrw)rxrwrwrPrxg?c34K|]}t|VdSr)float).0ps r z(EllipseModel.estimate..$s(55E!HH555555rT) rr3rrWr'rQrNrRrSr&rTrUrVvstackT ones_likearrayrr( LinAlgErroreigmultiplypowerr ravelr]arctanpi nan_to_numrealr^r)#rrr_r+r`r8r>D1D2S1S2S3C1Meig_valseig_vecsconda1abca2drbgx0y0 numeratorterm denominator1 denominator2widthheightphirs# rr/zEllipseModel.estimates0 !$$$$ t99q== E'     5%dj"*== {{:E{22""f}  28J'', , , 5'      5   AJ AJY1a!eQT* + + - Y1bl1oo. / / 1TBY TBY TBYX(8(8(8///J K K B2SWW rt 334AAy$   55   Y]]1--(2;x111~x111~>>> QTNAB B  aaa$(m $ ==C OOq005((**1a"ggX_r !((**1a S S S!ea!em3Q /!ea!em3Q /1Hq1a4x'!ad(2QUQY]BQUQYN wA!|a!Q$h.//1q1u Q8 1q1u $!a%9 I 455Y566BIsQw1q51222 q55 3; C 6>>"E6E 2519 C ru Bvs;<<Arr e rr f 55f55555 ts -F88GGcFt|d|j\}tj|tj||dddf}|dddf}|jd}fd}t j|ft j}t j |z |z |z }t|D]V} || } || } tj ||| | | f\} } t j || | | || <W|S) afDetermine residuals of data to model. For each point the shortest distance to the ellipse is returned. Parameters ---------- data : (N, 2) array N points with ``(x, y)`` coordinates, respectively. Returns ------- residuals : (N,) array Residual for each data point. r rGNrrctjtj|}tjtj|}  z|zz z|zz }  z|zz z|zz}||z dz||z dzzS)Nr )mathrmr'squeezern) rpxiyictstxtytrrcthetasthetarirjs rfunz#EllipseModel.residuals..funEs"*Q--((B"*Q--((Ba&j2o%F R7Ba&j2o%F R7BG>R"WN2 2rrM)args)rrrrmrnr r'emptyfloat64arctan2rangerleastsqr])rrthetar8r>Nrr6t0irrrpr-rrrrrirjs @@@@@@rr6zEllipseModel.residuals(sU" !$$$$"kB1e%% AJ AJ JqM 3 3 3 3 3 3 3 3 3 3$HaT444 ZBB ' '% /q 3 3A1B1B#CAb"X>>>DAq733q"b>>22IaLLrNcf||j}|\}}}}}tj|}tj|} t j|} t j|} ||| z|zz|| z| zz } ||| z|zz|| z| zz} tj| d| df|jS)aPredict x- and y-coordinates using the estimated model. Parameters ---------- t : array Angles in circle in radians. Angles start to count from positive x-axis to positive y-axis in a right-handed system. params : (5,) array, optional Optional custom parameter set. Returns ------- xy : (..., 2) array Predicted x- and y-coordinates. Nrlr#)rr'rmrnrror )rrprrirjrrrrrrrr8r>s rrqzEllipseModel.predict_xyfs$ >[F$B1e VAYY VAYY%% Vb 1v:? 2 Vb 1v:? 2~q|Qy\:HHHHrrrrrrrrtrtxs\&&PEEEN<<<|IIIIIIrrtc`|dkrdS|dkr tjS||z }d|z }d||zz }tj|tdtz }tj|tdtz }tjtj|tj|z S)aDetermine 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. rr)a_mina_max)r'infclip_EPSILONceillog) n_inliers n_samples min_samples probability inlier_rationomdenoms r_dynamic_max_trialsrs(aqA~~v y(L k/C k) )E '#XQ\ : : :C GEX > > >E 726#;;. / //rdc d} tj} g|du}|du}tj| } t |t t fs|f}t|d}d|cxkr|ksntd|d|dkrtd|dkrtdd| cxkrdksntd| 6t| |kr#td t| d |d | | n| ||d |}d}||kr|dz }fd|D}| ||d |r||s9|j |}||sH|r ||g|RsTtj |j |}||k}| |}tj|}|| ks || kr9|| kr3|} |} |t|t!| ||| }| |ks| |krn||kt#r3fd|D}|j ||r||g|Rst%dnd}dt%d|fS)aFit a model to data with the RANSAC (random sample consensus) algorithm. RANSAC is an iterative algorithm for the robust estimation of parameters from a subset of inliers from the complete data set. Each iteration performs the following tasks: 1. Select `min_samples` random samples from the original data and check whether the set of data is valid (see `is_data_valid`). 2. Estimate a model to the random subset (`model_cls.estimate(*data[random_subset]`) and check whether the estimated model is valid (see `is_model_valid`). 3. Classify all data as inliers or outliers by calculating the residuals to the estimated model (`model_cls.residuals(*data)`) - all data samples with residuals smaller than the `residual_threshold` are considered as inliers. 4. Save estimated model as best model if number of inlier samples is maximal. In case the current estimated model has the same number of inliers, it is only considered as the best model if it has less sum of residuals. These steps are performed either a maximum number of times or until one of the special stop criteria are met. The final model is estimated using all inlier samples of the previously determined best model. Parameters ---------- data : [list, tuple of] (N, ...) array Data set to which the model is fitted, where N is the number of data points and the remaining dimension are depending on model requirements. If the model class requires multiple input data arrays (e.g. source and destination coordinates of ``skimage.transform.AffineTransform``), they can be optionally passed as tuple or list. Note, that in this case the functions ``estimate(*data)``, ``residuals(*data)``, ``is_model_valid(model, *random_data)`` and ``is_data_valid(*random_data)`` must all take each data array as separate arguments. model_class : object Object with the following object methods: * ``success = estimate(*data)`` * ``residuals(*data)`` where `success` indicates whether the model estimation succeeded (`True` or `None` for success, `False` for failure). min_samples : int in range (0, N) The minimum number of data points to fit a model to. residual_threshold : float larger than 0 Maximum distance for a data point to be classified as an inlier. is_data_valid : function, optional This function is called with the randomly selected data before the model is fitted to it: `is_data_valid(*random_data)`. is_model_valid : function, optional This function is called with the estimated model and the randomly selected data: `is_model_valid(model, *random_data)`, . max_trials : int, optional Maximum number of iterations for random sample selection. stop_sample_num : int, optional Stop iteration if at least this number of inliers are found. stop_residuals_sum : float, optional Stop iteration if sum of residuals is less than or equal to this threshold. stop_probability : float in range [0, 1], optional RANSAC iteration stops if at least one outlier-free set of the training data is sampled with ``probability >= 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, e is the current fraction of inliers w.r.t. the total number of samples, and m is the min_samples value. rng : {`numpy.random.Generator`, int}, optional Pseudo-random number generator. By default, a PCG64 generator is used (see :func:`numpy.random.default_rng`). If `rng` is an int, it is used to seed the generator. initial_inliers : array-like of bool, shape (N,), optional Initial samples selection for model estimation Returns ------- model : object Best model with largest consensus set. inliers : (N,) array Boolean mask of inliers classified as ``True``. References ---------- .. [1] "RANSAC", Wikipedia, https://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]) >>> rng = np.random.default_rng(203560) # do not copy this value >>> data += rng.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)) # doctest: +SKIP array([20., 30., 10., 6., 2.]) >>> 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 RANSAC can be used to robustly estimate a geometric transformation. In this section, we also show how to use a proportion of the total samples, rather than an absolute number. >>> from skimage.transform import SimilarityTransform >>> rng = np.random.default_rng() >>> src = 100 * rng.random((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) >>> ratio = 0.5 # use half of the samples >>> min_samples = int(ratio * len(src)) >>> model, inliers = ransac( ... (src, dst), ... SimilarityTransform, ... min_samples, ... 10, ... initial_inliers=np.ones(len(src), dtype=bool), ... ) # doctest: +SKIP >>> inliers # doctest: +SKIP 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]) rNz#`min_samples` must be in range (0, ]z.`residual_threshold` must be greater than zeroz&`max_trials` must be greater than zerorz*`stop_probability` must be in range [0, 1]z4RANSAC received a vector of initial inliers (length z+) that didn't match the number of samples (z). The vector of initial inliers should have the same length as the number of samples and contain only True (this sample is an initial inlier) and False (this one isn't) values.F)replacec g|] }| Srr)r|rspl_idxss r zransac..s---11X;---rc g|] }| Srr)r|r best_inlierss rrzransac..s666A,666rz8Estimated model is not valid. Try increasing max_trials.z"No inliers found. Model not fitted)r'rrandom default_rng isinstancer^listr3r choicer/absr6dot count_nonzerominranyr)r model_classrresidual_threshold is_data_validis_model_valid max_trialsstop_sample_numstop_residuals_sumstop_probabilityrnginitial_inliersbest_inlier_numbest_inlier_residuals_sumvalidate_model validate_data num_samplesmodel num_trialssamplessuccessr6inliers residuals_sum inliers_count data_inliersrrs @@rransacrsjO "L#4/N!-M )   $ $C dUDM * *wd1g,,K * * * *{ * * * *M{MMMNNNAIJJJA~~ABBB ! & & & &Q & & & &EFFF"s?';';{'J'J ?##  #        &  ZZ [%Z @ @  KMMEJ z ! !a .------::k;:FF  !8   %.'*  w    .."A"A"A"A  F?5?D122 00! i00 (11  O + +00!$===,O(5 %"L##[+?OJ ?22,0BBBi z ! !n < 36666666  %%  M.."F"F"F"F M K L L L  1222 , r)rwarningsrnumpyr' numpy.linalgrscipyrrspacingrrrrr!rErtrrrrrrrs ######## 2:a==DDD <<<  }}}}})}}}@ZIZIZIZIZI)ZIZIZIzMIMIMIMIMI9MIMIMI` 0 0 0PF ffffffr