From 0afb00545da6abbb190f724c32316052caa0d7d2 Mon Sep 17 00:00:00 2001 From: Mateusz Baran Date: Fri, 30 Jun 2023 17:52:34 +0200 Subject: [PATCH 01/13] move hand-gestures to quarto --- docs/make.jl | 4 +- tutorials/hand-gestures.qmd | 109 ++++++++++++++++++++++++++++++++++++ 2 files changed, 111 insertions(+), 2 deletions(-) create mode 100644 tutorials/hand-gestures.qmd diff --git a/docs/make.jl b/docs/make.jl index 211b581203..398f6b0d97 100755 --- a/docs/make.jl +++ b/docs/make.jl @@ -17,7 +17,7 @@ if Base.active_project() != joinpath(@__DIR__, "Project.toml") end # (b) Did someone say render? Then we render! -if "--quarto" ∈ ARGS +if true || "--quarto" ∈ ARGS using CondaPkg CondaPkg.withenv() do @info "Rendering Quarto" @@ -87,7 +87,7 @@ makedocs( sitename="Manifolds.jl", pages=[ "Home" => "index.md", - "How to..." => ["🚀 Get Started with `Manifolds.jl`" => "tutorials/getstarted.md"], + "How to..." => ["🚀 Get Started with `Manifolds.jl`" => "tutorials/getstarted.md", "Hand gesture analysis" => "tutorials/hand-gestures.md"], "Manifolds" => [ "Basic manifolds" => [ "Centered matrices" => "manifolds/centeredmatrices.md", diff --git a/tutorials/hand-gestures.qmd b/tutorials/hand-gestures.qmd new file mode 100644 index 0000000000..dbfd29b4c8 --- /dev/null +++ b/tutorials/hand-gestures.qmd @@ -0,0 +1,109 @@ +--- +title: Hand gesture analysis +--- + +In this tutorial we will learn how to use Kendall's shape space to analyze hand gesture data. + +```{julia} +#| echo: false +#| code-fold: true +#| output: false +using Pkg; +cd(@__DIR__) +Pkg.activate("."); # for reproducibility use the local tutorial environment. +using Markdown +``` + + +```{julia} +using Manifolds +using CSV +using DataFrames +using Plots +using MultivariateStats + +function load_hands() + hands_url = "https://raw.githubusercontent.com/geomstats/geomstats/master/geomstats/datasets/data/hands/hands.txt" + hand_labels_url = "https://raw.githubusercontent.com/geomstats/geomstats/master/geomstats/datasets/data/hands/labels.txt" + + hands = Matrix(CSV.read(download(hands_url), DataFrame, header=false)) + hands = reshape(hands, size(hands, 1), 3, 22) + hand_labels = CSV.read(download(hand_labels_url), DataFrame, header=false).Column1 + return hands, hand_labels +end +``` + +Let's load dataset of hand gestures, described here: https://geomstats.github.io/notebooks/14_real_world_applications__hand_poses_analysis_in_kendall_shape_space.html +and plot a sample gesture as a 3D scatter plot of points. +```{julia} +hands, hand_labels = load_hands() +scatter3d(hands[1, 1, :], hands[1, 2, :], hands[1, 3, :]) +``` + +Each gesture is represented by 22 landmarks in ℝ³, so we use the appropriate Kendall's shape space +```{julia} +Mshape = KendallsShapeSpace(3, 22) +``` +Hands read from the dataset are projected to the shape space to remove translation +and scaling variability. Rotational variability is then handled using quotient +structure of KendallsShapeSpace +```{julia} +hands_projected = [project(Mshape, hands[i, :, :]) for i in axes(hands, 1)] +``` + +Now let's do tangent space PCA. This starts with computing a mean point and computing +logithmic maps at mean to each point in the dataset. +```{julia} +mean_hand = mean(Mshape, hands_projected) +hand_logs = [log(Mshape, mean_hand, p) for p in hands_projected] +``` + +For tangent PCA, we need coordinates in a basis. +Some libraries skip this step because the representation of tangent vectors +forms a linear subspace of an Euclidean space so PCA automatically detects +which directions have no variance but this is a more principled way to solve +this issue. +```{julia} +B = get_basis(Mshape, mean_hand, ProjectedOrthonormalBasis(:svd)) +hand_log_coordinates = [get_coordinates(Mshape, mean_hand, X, B) for X in hand_logs] +``` + +This code prepares data for MultivariateStats -- `mean=0` is set because we've centered +the data geometrically to `mean_hand` in the code above. +```{julia} + +red_coords = reduce(hcat, hand_log_coordinates) +fp = fit(PCA, red_coords; mean=0) +``` + +Now let's show explained variance of each principal component. +```{julia} + +plot(principalvars(fp), title="explained variance", label="Tangent PCA") + +``` +Also, let's look at how projections on the first two pricipal components look like. +```{julia} + + +fig = plot(; title="coordinates per gesture of the first two principal components") +for label_num in [0, 1] + mask = hand_labels .== label_num + cur_hand_logs = red_coords[:, mask] + cur_t = MultivariateStats.transform(fp, cur_hand_logs) + scatter!(fig, cur_t[1, :], cur_t[2, :], label="gesture " * string(label_num)) +end +xlabel!(fig, "principal component 1") +ylabel!(fig, "principal component 2") +fig +``` + +Now let's compute pairwise distances between gestures +we can use them for clustering, classification, etc. +```{julia} +hand_distances = [ + distance(Mshape, hands_projected[i], hands_projected[j]) for + i in eachindex(hands_projected), j in eachindex(hands_projected) +] +heatmap(hand_distances, aspect_ratio=:equal) +``` From ba00251f40ae8910fce689851881413a59f7da2d Mon Sep 17 00:00:00 2001 From: Mateusz Baran Date: Fri, 30 Jun 2023 18:10:19 +0200 Subject: [PATCH 02/13] fixing --- docs/Project.toml | 1 + docs/make.jl | 7 ++-- tutorials/hand-gestures.jl | 71 ------------------------------------- tutorials/hand-gestures.qmd | 11 ++++-- 4 files changed, 14 insertions(+), 76 deletions(-) delete mode 100644 tutorials/hand-gestures.jl diff --git a/docs/Project.toml b/docs/Project.toml index ed58b3d015..974042edbb 100644 --- a/docs/Project.toml +++ b/docs/Project.toml @@ -10,6 +10,7 @@ HybridArrays = "1baab800-613f-4b0a-84e4-9cd3431bfbb9" IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a" Manifolds = "1cead3c2-87b3-11e9-0ccd-23c62b72b94e" ManifoldsBase = "3362f125-f0bb-47a3-aa74-596ffd7ef2fb" +MultivariateStats = "6f286f6a-111f-5878-ab1e-185364afe411" OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" PythonPlot = "274fc56d-3b97-40fa-a1cd-1b4a50311bf9" diff --git a/docs/make.jl b/docs/make.jl index 398f6b0d97..0a823698a3 100755 --- a/docs/make.jl +++ b/docs/make.jl @@ -17,7 +17,7 @@ if Base.active_project() != joinpath(@__DIR__, "Project.toml") end # (b) Did someone say render? Then we render! -if true || "--quarto" ∈ ARGS +if "--quarto" ∈ ARGS using CondaPkg CondaPkg.withenv() do @info "Rendering Quarto" @@ -87,7 +87,10 @@ makedocs( sitename="Manifolds.jl", pages=[ "Home" => "index.md", - "How to..." => ["🚀 Get Started with `Manifolds.jl`" => "tutorials/getstarted.md", "Hand gesture analysis" => "tutorials/hand-gestures.md"], + "How to..." => [ + "🚀 Get Started with `Manifolds.jl`" => "tutorials/getstarted.md", + "Hand gesture analysis" => "tutorials/hand-gestures.md", + ], "Manifolds" => [ "Basic manifolds" => [ "Centered matrices" => "manifolds/centeredmatrices.md", diff --git a/tutorials/hand-gestures.jl b/tutorials/hand-gestures.jl deleted file mode 100644 index df5bd5151f..0000000000 --- a/tutorials/hand-gestures.jl +++ /dev/null @@ -1,71 +0,0 @@ -using Manifolds -using CSV -using DataFrames -using Plots -using MultivariateStats - -function load_hands() - hands_url = "https://raw.githubusercontent.com/geomstats/geomstats/master/geomstats/datasets/data/hands/hands.txt" - hand_labels_url = "https://raw.githubusercontent.com/geomstats/geomstats/master/geomstats/datasets/data/hands/labels.txt" - - hands = Matrix(CSV.read(download(hands_url), DataFrame, header=false)) - hands = reshape(hands, size(hands, 1), 3, 22) - hand_labels = CSV.read(download(hand_labels_url), DataFrame, header=false).Column1 - return hands, hand_labels -end - -function hand_analysis() - # Let's load dataset of hand gestures, described here: https://geomstats.github.io/notebooks/14_real_world_applications__hand_poses_analysis_in_kendall_shape_space.html - hands, hand_labels = load_hands() - - # This plots a sample gesture as a 3D scatter plot of points. - scatter3d(hands[1, 1, :], hands[1, 2, :], hands[1, 3, :]) - - # Each gesture is represented by 22 landmarks in ℝ³, so we use the appropriate - # Kendall's shape space - Mshape = KendallsShapeSpace(3, 22) - # Hands read from the dataset are projected to the shape space to remove translation - # and scaling variability. Rotational variability is then handled using quotient - # structure of KendallsShapeSpace - hands_projected = [project(Mshape, hands[i, :, :]) for i in axes(hands, 1)] - - # Now let's do tangent space PCA. This starts with computing a mean point and computing - # logithmic maps at mean to each point in the dataset. - mean_hand = mean(Mshape, hands_projected) - hand_logs = [log(Mshape, mean_hand, p) for p in hands_projected] - # For tangent PCA, we need coordinates in a basis. - # Some libraries skip this step because the representation of tangent vectors - # forms a linear subspace of an Euclidean space so PCA automatically detects - # which directions have no variance but this is a more principled way to solve - # this issue. - B = get_basis(Mshape, mean_hand, ProjectedOrthonormalBasis(:svd)) - hand_log_coordinates = [get_coordinates(Mshape, mean_hand, X, B) for X in hand_logs] - - # This code prepares data for MultivariateStats -- mean=0 is set because we've centered - # the data geometrically to mean_hand in the code above. - red_coords = reduce(hcat, hand_log_coordinates) - fp = fit(PCA, red_coords; mean=0) - # Now let's show explained variance of each principal component. - plot(principalvars(fp), title="explained variance", label="Tangent PCA") - - # Also, let's look at how projections on the first two pricipal components look like. - - fig = plot(; title="coordinates per gesture of the first two principal components") - for label_num in [0, 1] - mask = hand_labels .== label_num - cur_hand_logs = red_coords[:, mask] - cur_t = MultivariateStats.transform(fp, cur_hand_logs) - scatter!(fig, cur_t[1, :], cur_t[2, :], label="gesture " * string(label_num)) - end - xlabel!(fig, "principal component 1") - ylabel!(fig, "principal component 2") - fig - - # Now let's compute pairwise distances between gestures - # we can use them for clustering, classification, etc. - hand_distances = [ - distance(Mshape, hands_projected[i], hands_projected[j]) for - i in eachindex(hands_projected), j in eachindex(hands_projected) - ] - return heatmap(hand_distances, aspect_ratio=:equal) -end diff --git a/tutorials/hand-gestures.qmd b/tutorials/hand-gestures.qmd index dbfd29b4c8..4290346ce3 100644 --- a/tutorials/hand-gestures.qmd +++ b/tutorials/hand-gestures.qmd @@ -33,27 +33,30 @@ function load_hands() end ``` -Let's load dataset of hand gestures, described here: https://geomstats.github.io/notebooks/14_real_world_applications__hand_poses_analysis_in_kendall_shape_space.html +Let's load dataset of hand gestures, described [here](https://geomstats.github.io/notebooks/14_real_world_applications__hand_poses_analysis_in_kendall_shape_space.html) and plot a sample gesture as a 3D scatter plot of points. ```{julia} hands, hand_labels = load_hands() scatter3d(hands[1, 1, :], hands[1, 2, :], hands[1, 3, :]) ``` -Each gesture is represented by 22 landmarks in ℝ³, so we use the appropriate Kendall's shape space +Each gesture is represented by 22 landmarks in $ℝ³$, so we use the appropriate Kendall's shape space ```{julia} Mshape = KendallsShapeSpace(3, 22) ``` + Hands read from the dataset are projected to the shape space to remove translation and scaling variability. Rotational variability is then handled using quotient -structure of KendallsShapeSpace +structure of ``[`KendallsShapeSpace`](@ref)``{=commonmark} ```{julia} +#| output: false hands_projected = [project(Mshape, hands[i, :, :]) for i in axes(hands, 1)] ``` Now let's do tangent space PCA. This starts with computing a mean point and computing logithmic maps at mean to each point in the dataset. ```{julia} +#| output: false mean_hand = mean(Mshape, hands_projected) hand_logs = [log(Mshape, mean_hand, p) for p in hands_projected] ``` @@ -64,6 +67,7 @@ forms a linear subspace of an Euclidean space so PCA automatically detects which directions have no variance but this is a more principled way to solve this issue. ```{julia} +#| output: false B = get_basis(Mshape, mean_hand, ProjectedOrthonormalBasis(:svd)) hand_log_coordinates = [get_coordinates(Mshape, mean_hand, X, B) for X in hand_logs] ``` @@ -82,6 +86,7 @@ Now let's show explained variance of each principal component. plot(principalvars(fp), title="explained variance", label="Tangent PCA") ``` + Also, let's look at how projections on the first two pricipal components look like. ```{julia} From c1ffff6ab1f26d635f6167bd3cf5c371bdc44a52 Mon Sep 17 00:00:00 2001 From: Mateusz Baran Date: Fri, 30 Jun 2023 20:04:30 +0200 Subject: [PATCH 03/13] improve dependency organization --- docs/Project.toml | 1 - tutorials/Project.toml | 4 ++++ 2 files changed, 4 insertions(+), 1 deletion(-) diff --git a/docs/Project.toml b/docs/Project.toml index 974042edbb..ed58b3d015 100644 --- a/docs/Project.toml +++ b/docs/Project.toml @@ -10,7 +10,6 @@ HybridArrays = "1baab800-613f-4b0a-84e4-9cd3431bfbb9" IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a" Manifolds = "1cead3c2-87b3-11e9-0ccd-23c62b72b94e" ManifoldsBase = "3362f125-f0bb-47a3-aa74-596ffd7ef2fb" -MultivariateStats = "6f286f6a-111f-5878-ab1e-185364afe411" OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" PythonPlot = "274fc56d-3b97-40fa-a1cd-1b4a50311bf9" diff --git a/tutorials/Project.toml b/tutorials/Project.toml index 6ac1e0982a..d97ef56bac 100644 --- a/tutorials/Project.toml +++ b/tutorials/Project.toml @@ -1,8 +1,12 @@ [deps] +CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b" +DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0" IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a" Manifolds = "1cead3c2-87b3-11e9-0ccd-23c62b72b94e" ManifoldsBase = "3362f125-f0bb-47a3-aa74-596ffd7ef2fb" Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a" +MultivariateStats = "6f286f6a-111f-5878-ab1e-185364afe411" +Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" [compat] IJulia = "1" From 2dffec9b80c8a4cc6f2993f88911f5920475672b Mon Sep 17 00:00:00 2001 From: Mateusz Baran Date: Sat, 1 Jul 2023 15:20:39 +0200 Subject: [PATCH 04/13] trying working-in-charts quarto --- tutorials/working-in-charts.qmd | 174 ++++++++++++++++++++++++++++++++ 1 file changed, 174 insertions(+) create mode 100644 tutorials/working-in-charts.qmd diff --git a/tutorials/working-in-charts.qmd b/tutorials/working-in-charts.qmd new file mode 100644 index 0000000000..7622cb7eb4 --- /dev/null +++ b/tutorials/working-in-charts.qmd @@ -0,0 +1,174 @@ +--- +title: Working in charts +--- + +In this tutorial we will learn how to use Kendall's shape space to analyze hand gesture data. + +```{julia} +#| echo: false +#| code-fold: true +#| output: false +using Pkg; +cd(@__DIR__) +Pkg.activate("."); # for reproducibility use the local tutorial environment. +using Markdown +``` + +## Working in Charts: the embedded Torus + +There are two conceptually different approaches to working on a manifold: working in charts and chart-free representations. + +The first one, widespread in differential geometry textbooks, is based on defining an atlas on the manifold and performing computations in selected charts. This approach, while generic, is not ideally suitable in all circumstances. For example, working in charts that do not cover the entire manifold causes issues with having to switch charts when operating on a manifold. + +The second one is beneficital, if there exist a representation of points and tangent vectors for a manifold, which allow for efficient closed-form formulas for standard functions like the exponential map or Riemannian distance in this representation. These computations are then chart-free. `Manifolds.jl` supports both approaches, although the chart-free approach is the main focus of the library. + +In this tutorial we focus on chart-based computation. + +```{julia} +using Manifolds, RecursiveArrayTools, OrdinaryDiffEq, DiffEqCallbacks, BoundaryValueDiffEq +``` + +The manifold we consider is the `M` is the torus in form of the [`EmbeddedTorus`](https://juliamanifolds.github.io/Manifolds.jl/latest/manifolds/torus.html#Manifolds.EmbeddedTorus), that is the representation defined as a surface of revolution of a circle of radius 2 around a circle of radius 3. +The atlas we will perform computations in is its [`DefaultTorusAtlas`](https://juliamanifolds.github.io/Manifolds.jl/latest/manifolds/torus.html#Manifolds.DefaultTorusAtlas) `A`, consistting of a family of charts indexed by two angles, that specify the base point of the chart. + +We will draw geodesics time between `0` and `t_end`, and then sample the solution at multiples of `dt` and draw a line connecting sampled points. + +```{julia} +M = Manifolds.EmbeddedTorus(3, 2) +A = Manifolds.DefaultTorusAtlas() +``` + +## Setup + +We will first set up our plot with an empty torus. +`param_points` are points on the surface of the torus that will be used for basic surface shape in `Makie.jl`. +The torus will be colored according to its Gaussian curvature stored in `gcs`. We later want to have a color scale that has negative curvature blue, zero curvature white and positive curvature red so `gcs_mm` is the largest absolute value of the curvature that will be needed to properly set range of curvature values. + +In the documentation this tutorial represents a static situation (without interactivity). + +```{julia} +using GLMakie, Makie +GLMakie.activate!() + +""" + torus_figure() + +This function generates a simple plot of a torus and returns the new figure containing the plot. +""" +function torus_figure() + fig = Figure(resolution=(1400, 1000), fontsize=16) + ax = LScene(fig[1, 1], show_axis=true) + ϴs, φs = LinRange(-π, π, 50), LinRange(-π, π, 50) + param_points = [Manifolds._torus_param(M, θ, φ) for θ in ϴs, φ in φs] + X1, Y1, Z1 = [[p[i] for p in param_points] for i in 1:3] + gcs = [gaussian_curvature(M, p) for p in param_points] + gcs_mm = max(abs(minimum(gcs)), abs(maximum(gcs))) + pltobj = surface!( + ax, + X1, + Y1, + Z1; + shading=true, + ambient=Vec3f(0.65, 0.65, 0.65), + backlight=1.0f0, + color=gcs, + colormap=Reverse(:RdBu), + colorrange=(-gcs_mm, gcs_mm), + transparency=true, + ) + wireframe!(ax, X1, Y1, Z1; transparency=true, color=:gray, linewidth=0.5) + zoom!(ax.scene, cameracontrols(ax.scene), 0.98) + Colorbar(fig[1, 2], pltobj, height=Relative(0.5), label="Gaussian curvature") + return ax, fig +end +``` + + +## (Interactive) Values for the geodesic. + +`solve_for` is a helper function that solves a parallel transport along geodesic problem on the torus `M`. +`p0x` is the (ϴ, φ) parametrization of the point from which we will transport the vector. +We first calculate the coordinates in the embedding of `p0x` and store it as `p`, and then get the initial chart from atlas `A` appropriate for starting working at point `p`. +The vector we transport has coordinates `Y_transp` in the induced tangent space basis of chart `i_p0x`. +The function returns the full solution to the parallel transport problem, containing the sequence of charts that was used and solutions of differential equations computed using `OrdinaryDiffEq`. + +`bvp_i` is needed later for a different purpose, it is the chart index we will use for solving the logarithmic map boundary value problem in. + +Next we solve the vector transport problem `solve_for([θₚ, φₚ], [θₓ, φₓ], [θy, φy])`, sample the result at the selected time steps and store the result in `geo`. The solution includes the geodesic which we extract and convert to a sequence of points digestible by `Makie.jl`, `geo_ps`. +`[θₚ, φₚ]` is the parametrization in chart (0, 0) of the starting point of the geodesic. +The direction of the geodesic is determined by `[θₓ, φₓ]`, coordinates of the tangent vector at the starting point expressed in the induced basis of chart `i_p0x` (which depends on the initial point). +Finally, `[θy, φy]` are the coordinates of the tangent vector that will be transported along the geodesic, which are also expressed in same basis as `[θₓ, φₓ]`. + +We won't draw the transported vector at every point as there would be too many arrows, which is why we select every 100th point only for that purpose with `pt_indices`. Then, `geo_ps_pt` contains points at which the transported vector is tangent to and `geo_Ys` the transported vector at that point, represented in the embedding. + +The logarithmic map will be solved between points with parametrization `bvp_a1` and `bvp_a2` in chart `bvp_i`. +The result is assigned to variable `bvp_sol` and then sampled with time step 0.05. The result of this sampling is converted from parameters in chart `bvp_i` to point in the embedding and stored in `geo_r`. +""" + +```{julia} +function solve_for(p0x, X_p0x, Y_transp, T) + p = [Manifolds._torus_param(M, p0x...)...] + i_p0x = Manifolds.get_chart_index(M, A, p) + p_exp = Manifolds.solve_chart_parallel_transport_ode( + M, + [0.0, 0.0], + X_p0x, + A, + i_p0x, + Y_transp; + final_time=T, + ) + return p_exp +end; +``` + + +### Solving parallel Transport ODE + +We set the end time `t_end` and time step `dt`. + +```{julia} +t_end = 2.0 +dt = 1e-1 +``` + +We also parametrise the start point and direction. + +```{julia} +θₚ = π/10 +φₚ = -π/4 +θₓ = π/2 +φₓ = 0.7 +θy = 0.2 +φy = -0.1 + +geo = solve_for([θₚ, φₚ], [θₓ, φₓ], [θy, φy], t_end)(0.0:dt:t_end) +geo_ps = [Point3f(s[1]) for s in geo] +pt_indices = 1:div(length(geo), 10):length(geo) +geo_ps_pt = [Point3f(s[1]) for s in geo[pt_indices]] +geo_Ys = [Point3f(s[3]) for s in geo[pt_indices]] + +ax1, fig1 = torus_figure() +arrows!(ax1, geo_ps_pt, geo_Ys, linewidth=0.05, color=:blue) +lines!(geo_ps; linewidth=4.0, color=:green) +fig1 +``` + +### Solving the logairthmic map ODE + +```{julia} +θ₁=π/2 +φ₁=-1.0 +θ₂=-π/8 +φ₂=π/2 + +bvp_i = (0, 0) +bvp_a1 = [θ₁, φ₁] +bvp_a2 = [θ₂, φ₂] +bvp_sol = Manifolds.solve_chart_log_bvp(M, bvp_a1, bvp_a2, A, bvp_i) +geo_r = [Point3f(get_point(M, A, bvp_i, p[1:2])) for p in bvp_sol(0.0:0.05:1.0)] + +ax2, fig2 = torus_figure() +lines!(geo_r; linewidth=4.0, color=:green) +fig2 +``` From 7cf5b34821aad0a8c90df87d45a7359e795eda3c Mon Sep 17 00:00:00 2001 From: Mateusz Baran Date: Sat, 1 Jul 2023 15:33:29 +0200 Subject: [PATCH 05/13] minor improvements --- docs/make.jl | 3 ++- tutorials/Project.toml | 6 ++++++ tutorials/working-in-charts.qmd | 5 +++-- 3 files changed, 11 insertions(+), 3 deletions(-) diff --git a/docs/make.jl b/docs/make.jl index 0a823698a3..80d0dc7d42 100755 --- a/docs/make.jl +++ b/docs/make.jl @@ -17,7 +17,7 @@ if Base.active_project() != joinpath(@__DIR__, "Project.toml") end # (b) Did someone say render? Then we render! -if "--quarto" ∈ ARGS +if true || "--quarto" ∈ ARGS using CondaPkg CondaPkg.withenv() do @info "Rendering Quarto" @@ -90,6 +90,7 @@ makedocs( "How to..." => [ "🚀 Get Started with `Manifolds.jl`" => "tutorials/getstarted.md", "Hand gesture analysis" => "tutorials/hand-gestures.md", + "Working in charts" => "tutorials/working-in-charts.md", ], "Manifolds" => [ "Basic manifolds" => [ diff --git a/tutorials/Project.toml b/tutorials/Project.toml index d97ef56bac..c37f29ac14 100644 --- a/tutorials/Project.toml +++ b/tutorials/Project.toml @@ -1,12 +1,18 @@ [deps] +BoundaryValueDiffEq = "764a87c0-6b3e-53db-9096-fe964310641d" CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b" DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0" +DiffEqCallbacks = "459566f4-90b8-5000-8ac3-15dfb0a30def" +GLMakie = "e9467ef8-e4e7-5192-8a1a-b1aee30e663a" IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a" +Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a" Manifolds = "1cead3c2-87b3-11e9-0ccd-23c62b72b94e" ManifoldsBase = "3362f125-f0bb-47a3-aa74-596ffd7ef2fb" Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a" MultivariateStats = "6f286f6a-111f-5878-ab1e-185364afe411" +OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" +RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd" [compat] IJulia = "1" diff --git a/tutorials/working-in-charts.qmd b/tutorials/working-in-charts.qmd index 7622cb7eb4..1484b03e9d 100644 --- a/tutorials/working-in-charts.qmd +++ b/tutorials/working-in-charts.qmd @@ -25,6 +25,7 @@ The second one is beneficital, if there exist a representation of points and tan In this tutorial we focus on chart-based computation. ```{julia} +#| output: false using Manifolds, RecursiveArrayTools, OrdinaryDiffEq, DiffEqCallbacks, BoundaryValueDiffEq ``` @@ -84,10 +85,10 @@ end ``` -## (Interactive) Values for the geodesic. +## Values for the geodesic `solve_for` is a helper function that solves a parallel transport along geodesic problem on the torus `M`. -`p0x` is the (ϴ, φ) parametrization of the point from which we will transport the vector. +`p0x` is the $(ϴ, φ)$ parametrization of the point from which we will transport the vector. We first calculate the coordinates in the embedding of `p0x` and store it as `p`, and then get the initial chart from atlas `A` appropriate for starting working at point `p`. The vector we transport has coordinates `Y_transp` in the induced tangent space basis of chart `i_p0x`. The function returns the full solution to the parallel transport problem, containing the sequence of charts that was used and solutions of differential equations computed using `OrdinaryDiffEq`. From 2728cb0ebfb63a6982eb39fa70992bd95a57789d Mon Sep 17 00:00:00 2001 From: Mateusz Baran Date: Sat, 1 Jul 2023 15:38:25 +0200 Subject: [PATCH 06/13] undo temporary change --- docs/make.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/make.jl b/docs/make.jl index 80d0dc7d42..71e91e2a32 100755 --- a/docs/make.jl +++ b/docs/make.jl @@ -17,7 +17,7 @@ if Base.active_project() != joinpath(@__DIR__, "Project.toml") end # (b) Did someone say render? Then we render! -if true || "--quarto" ∈ ARGS +if "--quarto" ∈ ARGS using CondaPkg CondaPkg.withenv() do @info "Rendering Quarto" From ba93dcee203fa76020d5e3c683a499f76f598355 Mon Sep 17 00:00:00 2001 From: Mateusz Baran Date: Sat, 1 Jul 2023 19:10:38 +0200 Subject: [PATCH 07/13] don't use Makie --- tutorials/Project.toml | 2 -- tutorials/working-in-charts.qmd | 36 ++++++++++++++++++--------------- 2 files changed, 20 insertions(+), 18 deletions(-) diff --git a/tutorials/Project.toml b/tutorials/Project.toml index c37f29ac14..5297394c51 100644 --- a/tutorials/Project.toml +++ b/tutorials/Project.toml @@ -3,9 +3,7 @@ BoundaryValueDiffEq = "764a87c0-6b3e-53db-9096-fe964310641d" CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b" DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0" DiffEqCallbacks = "459566f4-90b8-5000-8ac3-15dfb0a30def" -GLMakie = "e9467ef8-e4e7-5192-8a1a-b1aee30e663a" IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a" -Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a" Manifolds = "1cead3c2-87b3-11e9-0ccd-23c62b72b94e" ManifoldsBase = "3362f125-f0bb-47a3-aa74-596ffd7ef2fb" Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a" diff --git a/tutorials/working-in-charts.qmd b/tutorials/working-in-charts.qmd index 1484b03e9d..d5dda8c418 100644 --- a/tutorials/working-in-charts.qmd +++ b/tutorials/working-in-charts.qmd @@ -45,11 +45,11 @@ We will first set up our plot with an empty torus. `param_points` are points on the surface of the torus that will be used for basic surface shape in `Makie.jl`. The torus will be colored according to its Gaussian curvature stored in `gcs`. We later want to have a color scale that has negative curvature blue, zero curvature white and positive curvature red so `gcs_mm` is the largest absolute value of the curvature that will be needed to properly set range of curvature values. -In the documentation this tutorial represents a static situation (without interactivity). +In the documentation this tutorial represents a static situation (without interactivity). `Makie.jl` rendering is turned off. ```{julia} -using GLMakie, Makie -GLMakie.activate!() +# using GLMakie, Makie +# GLMakie.activate!() """ torus_figure() @@ -144,17 +144,19 @@ We also parametrise the start point and direction. φy = -0.1 geo = solve_for([θₚ, φₚ], [θₓ, φₓ], [θy, φy], t_end)(0.0:dt:t_end) -geo_ps = [Point3f(s[1]) for s in geo] -pt_indices = 1:div(length(geo), 10):length(geo) -geo_ps_pt = [Point3f(s[1]) for s in geo[pt_indices]] -geo_Ys = [Point3f(s[3]) for s in geo[pt_indices]] - -ax1, fig1 = torus_figure() -arrows!(ax1, geo_ps_pt, geo_Ys, linewidth=0.05, color=:blue) -lines!(geo_ps; linewidth=4.0, color=:green) -fig1 +# geo_ps = [Point3f(s[1]) for s in geo] +# pt_indices = 1:div(length(geo), 10):length(geo) +# geo_ps_pt = [Point3f(s[1]) for s in geo[pt_indices]] +# geo_Ys = [Point3f(s[3]) for s in geo[pt_indices]] + +# ax1, fig1 = torus_figure() +# arrows!(ax1, geo_ps_pt, geo_Ys, linewidth=0.05, color=:blue) +# lines!(geo_ps; linewidth=4.0, color=:green) +# fig1 ``` +![fig-pt]{tutorials/working-in-charts-transport.png} + ### Solving the logairthmic map ODE ```{julia} @@ -167,9 +169,11 @@ bvp_i = (0, 0) bvp_a1 = [θ₁, φ₁] bvp_a2 = [θ₂, φ₂] bvp_sol = Manifolds.solve_chart_log_bvp(M, bvp_a1, bvp_a2, A, bvp_i) -geo_r = [Point3f(get_point(M, A, bvp_i, p[1:2])) for p in bvp_sol(0.0:0.05:1.0)] +# geo_r = [Point3f(get_point(M, A, bvp_i, p[1:2])) for p in bvp_sol(0.0:0.05:1.0)] -ax2, fig2 = torus_figure() -lines!(geo_r; linewidth=4.0, color=:green) -fig2 +# ax2, fig2 = torus_figure() +# lines!(geo_r; linewidth=4.0, color=:green) +# fig2 ``` + 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We first calculate the coordinates in the embedding of `p0x` and store it as `p`, and then get the initial chart from atlas `A` appropriate for starting working at point `p`. The vector we transport has coordinates `Y_transp` in the induced tangent space basis of chart `i_p0x`. The function returns the full solution to the parallel transport problem, containing the sequence of charts that was used and solutions of differential equations computed using `OrdinaryDiffEq`. @@ -104,7 +104,7 @@ We won't draw the transported vector at every point as there would be too many a The logarithmic map will be solved between points with parametrization `bvp_a1` and `bvp_a2` in chart `bvp_i`. The result is assigned to variable `bvp_sol` and then sampled with time step 0.05. The result of this sampling is converted from parameters in chart `bvp_i` to point in the embedding and stored in `geo_r`. -""" + ```{julia} function solve_for(p0x, X_p0x, Y_transp, T) From 7f58dd30c6d6c36f3d78a566950e21eadfbf5368 Mon Sep 17 00:00:00 2001 From: Mateusz Baran Date: Wed, 5 Jul 2023 12:19:11 +0200 Subject: [PATCH 10/13] Apply suggestions from code review Co-authored-by: Ronny Bergmann --- docs/make.jl | 4 ++-- tutorials/hand-gestures.qmd | 15 ++++----------- tutorials/working-in-charts.qmd | 1 - 3 files changed, 6 insertions(+), 14 deletions(-) diff --git a/docs/make.jl b/docs/make.jl index 71e91e2a32..bc38f2c19c 100755 --- a/docs/make.jl +++ b/docs/make.jl @@ -89,8 +89,8 @@ makedocs( "Home" => "index.md", "How to..." => [ "🚀 Get Started with `Manifolds.jl`" => "tutorials/getstarted.md", - "Hand gesture analysis" => "tutorials/hand-gestures.md", - "Working in charts" => "tutorials/working-in-charts.md", + "work in charts" => "tutorials/working-in-charts.md", + "perform Hand gesture analysis" => "tutorials/hand-gestures.md", ], "Manifolds" => [ "Basic manifolds" => [ diff --git a/tutorials/hand-gestures.qmd b/tutorials/hand-gestures.qmd index 4290346ce3..5fede3fd02 100644 --- a/tutorials/hand-gestures.qmd +++ b/tutorials/hand-gestures.qmd @@ -16,11 +16,7 @@ using Markdown ```{julia} -using Manifolds -using CSV -using DataFrames -using Plots -using MultivariateStats +using Manifolds, CSV, DataFrames, Plots, MultivariateStats function load_hands() hands_url = "https://raw.githubusercontent.com/geomstats/geomstats/master/geomstats/datasets/data/hands/hands.txt" @@ -46,7 +42,7 @@ Mshape = KendallsShapeSpace(3, 22) ``` Hands read from the dataset are projected to the shape space to remove translation -and scaling variability. Rotational variability is then handled using quotient +and scaling variability. Rotational variability is then handled using the quotient structure of ``[`KendallsShapeSpace`](@ref)``{=commonmark} ```{julia} #| output: false @@ -61,10 +57,10 @@ mean_hand = mean(Mshape, hands_projected) hand_logs = [log(Mshape, mean_hand, p) for p in hands_projected] ``` -For tangent PCA, we need coordinates in a basis. +For a tangent PCA, we need coordinates in a basis. Some libraries skip this step because the representation of tangent vectors forms a linear subspace of an Euclidean space so PCA automatically detects -which directions have no variance but this is a more principled way to solve +which directions have no variance but this is a more generic way to solve this issue. ```{julia} #| output: false @@ -75,16 +71,13 @@ hand_log_coordinates = [get_coordinates(Mshape, mean_hand, X, B) for X in hand_l This code prepares data for MultivariateStats -- `mean=0` is set because we've centered the data geometrically to `mean_hand` in the code above. ```{julia} - red_coords = reduce(hcat, hand_log_coordinates) fp = fit(PCA, red_coords; mean=0) ``` Now let's show explained variance of each principal component. ```{julia} - plot(principalvars(fp), title="explained variance", label="Tangent PCA") - ``` Also, let's look at how projections on the first two pricipal components look like. diff --git a/tutorials/working-in-charts.qmd b/tutorials/working-in-charts.qmd index 348382da06..65d967e9b5 100644 --- a/tutorials/working-in-charts.qmd +++ b/tutorials/working-in-charts.qmd @@ -14,7 +14,6 @@ Pkg.activate("."); # for reproducibility use the local tutorial environment. using Markdown ``` -## Working in Charts: the embedded Torus There are two conceptually different approaches to working on a manifold: working in charts and chart-free representations. From e61bd3b717fd2f26a1a6fc22d05be93b4b084a3f Mon Sep 17 00:00:00 2001 From: Mateusz Baran Date: Wed, 5 Jul 2023 12:32:47 +0200 Subject: [PATCH 11/13] Address review comments --- tutorials/Project.toml | 3 +++ tutorials/hand-gestures.qmd | 19 +++++++++++-------- tutorials/working-in-charts.qmd | 4 +++- 3 files changed, 17 insertions(+), 9 deletions(-) diff --git a/tutorials/Project.toml b/tutorials/Project.toml index 5297394c51..1d0d4c7d2f 100644 --- a/tutorials/Project.toml +++ b/tutorials/Project.toml @@ -13,6 +13,9 @@ Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd" [compat] +CSV = "0.10" +DataFrames = "1" IJulia = "1" Manifolds = "0.8.46" ManifoldsBase = "0.14.5" +MultivariateStats = "0.10" diff --git a/tutorials/hand-gestures.qmd b/tutorials/hand-gestures.qmd index 5fede3fd02..c591f46975 100644 --- a/tutorials/hand-gestures.qmd +++ b/tutorials/hand-gestures.qmd @@ -14,9 +14,15 @@ Pkg.activate("."); # for reproducibility use the local tutorial environment. using Markdown ``` +Let's start by loading libraries required for our work. ```{julia} using Manifolds, CSV, DataFrames, Plots, MultivariateStats +``` + +Our first function loads dataset of hand gestures, described [here](https://geomstats.github.io/notebooks/14_real_world_applications__hand_poses_analysis_in_kendall_shape_space.html). + +```{julia} function load_hands() hands_url = "https://raw.githubusercontent.com/geomstats/geomstats/master/geomstats/datasets/data/hands/hands.txt" @@ -29,8 +35,7 @@ function load_hands() end ``` -Let's load dataset of hand gestures, described [here](https://geomstats.github.io/notebooks/14_real_world_applications__hand_poses_analysis_in_kendall_shape_space.html) -and plot a sample gesture as a 3D scatter plot of points. +The following code plots a sample gesture as a 3D scatter plot of points. ```{julia} hands, hand_labels = load_hands() scatter3d(hands[1, 1, :], hands[1, 2, :], hands[1, 3, :]) @@ -49,7 +54,7 @@ structure of ``[`KendallsShapeSpace`](@ref)``{=commonmark} hands_projected = [project(Mshape, hands[i, :, :]) for i in axes(hands, 1)] ``` -Now let's do tangent space PCA. This starts with computing a mean point and computing +In the next part let's do tangent space PCA. This starts with computing a mean point and computing logithmic maps at mean to each point in the dataset. ```{julia} #| output: false @@ -80,10 +85,8 @@ Now let's show explained variance of each principal component. plot(principalvars(fp), title="explained variance", label="Tangent PCA") ``` -Also, let's look at how projections on the first two pricipal components look like. +The next plot shows how projections on the first two pricipal components look like. ```{julia} - - fig = plot(; title="coordinates per gesture of the first two principal components") for label_num in [0, 1] mask = hand_labels .== label_num @@ -96,8 +99,8 @@ ylabel!(fig, "principal component 2") fig ``` -Now let's compute pairwise distances between gestures -we can use them for clustering, classification, etc. +The following heatmap displays pairwise distances between gestures. +We can use them for clustering, classification, etc. ```{julia} hand_distances = [ distance(Mshape, hands_projected[i], hands_projected[j]) for diff --git a/tutorials/working-in-charts.qmd b/tutorials/working-in-charts.qmd index 65d967e9b5..16f85e91a2 100644 --- a/tutorials/working-in-charts.qmd +++ b/tutorials/working-in-charts.qmd @@ -2,7 +2,7 @@ title: Working in charts --- -In this tutorial we will learn how to use Kendall's shape space to analyze hand gesture data. +In this tutorial we will learn how to use charts for basic geometric operations like exponential map, logarithmic map and parallel transport. ```{julia} #| echo: false @@ -176,3 +176,5 @@ bvp_sol = Manifolds.solve_chart_log_bvp(M, bvp_a1, bvp_a2, A, bvp_i); ``` ![fig-geodesic](working-in-charts/working-in-charts-geodesic.png) + +An interactive Pluto version of this tutorial is available in file `tutorials/working-in-charts.jl`. From e5a966e3b9bb2d781367e4ab3b787b9d7ebcd9b6 Mon Sep 17 00:00:00 2001 From: Mateusz Baran Date: Tue, 11 Jul 2023 17:43:53 +0200 Subject: [PATCH 12/13] Add link --- tutorials/working-in-charts.qmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/tutorials/working-in-charts.qmd b/tutorials/working-in-charts.qmd index 16f85e91a2..7c3eebe36e 100644 --- a/tutorials/working-in-charts.qmd +++ b/tutorials/working-in-charts.qmd @@ -177,4 +177,4 @@ bvp_sol = Manifolds.solve_chart_log_bvp(M, bvp_a1, bvp_a2, A, bvp_i); ![fig-geodesic](working-in-charts/working-in-charts-geodesic.png) -An interactive Pluto version of this tutorial is available in file `tutorials/working-in-charts.jl`. +An interactive Pluto version of this tutorial is available in file [`tutorials/working-in-charts.jl`](https://github.com/JuliaManifolds/Manifolds.jl/blob/616855447996fb1ee7dfb2a779341b962a1323f8/tutorials/working-in-charts.jl). From 8af3b5b746c0dbf78985d499070640af7dd94e4e Mon Sep 17 00:00:00 2001 From: Mateusz Baran Date: Tue, 11 Jul 2023 21:09:13 +0200 Subject: [PATCH 13/13] bump version --- Project.toml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Project.toml b/Project.toml index ccd59e9305..0612503698 100644 --- a/Project.toml +++ b/Project.toml @@ -1,7 +1,7 @@ name = "Manifolds" uuid = "1cead3c2-87b3-11e9-0ccd-23c62b72b94e" authors = ["Seth Axen ", "Mateusz Baran ", "Ronny Bergmann ", "Antoine Levitt "] -version = "0.8.73" +version = "0.8.74" [deps] Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"