{"id":"dab87729-1fe4-438d-b23b-43ea70df8b52","arxiv_id":"2607.22446","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Rendering with deformable, non-convex triangle primitives improves novel-view synthesis quality and expressiveness over fixed-shape splatting.","lead":"Deformable Triangle Splatting lets each triangular rendering primitive bend its edges inward or outward using learned control points, so one primitive can cover curved or concave surfaces. The method reports better view-synthesis quality than previous triangle splatting while rendering at interactive rates.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The view-independence claim fails under perspective: the barycentric frame defined by the projected triangle is itself view-dependent, so a fixed set of displacements does not define a fixed 3D shape.","rationale":"The reader's weakest_assumption identifies exactly the same load-bearing concern: the barycentric coordinate space derived from the projected triangle is not view-independent under perspective projection. This is the single most important flaw because the paper's theoretical novelty—the justification for using barycentric coordinates—rests on the claim of exact view-independence. If that claim falls, the method is essentially an image-space deformation with a different parameterization, and the paper's explanation for why it avoids multi-view gradient conflicts is incorrect. The empirical benchmark improvements (LPIPS 0.183 vs 0.191) may still be valid, and the method could be salvaged by redefining the primitive in true 3D barycentric coordinates and performing ray-triangle intersection, but as written the central assertion is wrong. Therefore the verdict should remain CONDITIONAL: the paper needs either a corrected view-independence proof or a revised claim. The R=2A/P inradius error is a secondary inaccuracy that does not threaten the core method, so we focus on the view-dependence issue.","tokens_in":18470,"tokens_out":5188,"duration_ms":64369,"concrete_test":"Construct a 3D triangle with non-trivial depth variation (e.g., vertices at depths 1, 2, 3 in camera coordinates) and a deformed boundary defined by fixed displacements d_i,k in the barycentric space of the frontal view. For two camera poses (frontal and, say, 60° rotation about the Y-axis), compute the 3D points on the triangle plane that project to a given set of barycentric vertices (using the inverse perspective projection onto the plane). Then compute their 2D barycentric coordinates via T^{-1} for each view. If the method were view-independent, these coordinates would match the original b values; in fact they will differ, with the difference increasing with viewpoint change. Plot the max |Δb| vs. rotation angle. This will quantitatively demonstrate that the deformed primitive's 3D footprint shifts across views, falsifying the 'exactly view-independent' claim.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The core theoretical justification of the method is that performing deformations in the barycentric coordinate system defined by the projected triangle 'ensur[es] view-independent deformations' and that the formulation is 'exactly view-independent by construction' (Sec. 3.1, 'Why Barycentric Space?'). This is not correct. In Eq. (1), the barycentric coordinates are computed via b = T^{-1}(p - p1), where T = [p2-p1, p3-p1] is built from the 2D projected positions of the 3D vertices. Under perspective projection, the mapping from a 3D point X on the triangle plane to its 2D barycentric coordinate b is a homography, not an affine map. Consequently, a fixed deformed polygon in (u, v) space (defined by fixed displacements d_i,k) corresponds to different sets of 3D points on the triangle plane for different viewpoints. In other words, the primitive's implied 3D shape changes with the camera. The paper's own critique of image-space deformations—'the same 3D triangle projects differently under each camera'—applies equally to this barycentric space, because the barycentric frame itself is derived from the projection. The paper's defense that 'all boundary tests are evaluated in a fixed reference frame' is misleading: the reference frame is not fixed in 3D; it is redefined per viewpoint from the projected vertices. This directly undermines the claim of view-consistent rendering (Abstract) and the assertion that multi-view gradient conflicts are eliminated. The empirical gains may still hold, but the central conceptual claim is false.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes DETRIS, a differentiable radiance-field renderer whose primitives are triangles with deformable edges. Each edge carries K learnable control points, each with a scalar displacement along the edge normal, defined in the barycentric coordinate system of the projected triangle. Rendering uses a winding-number inside test, a polynomial smooth-minimum distance field, and a power-law opacity falloff. The authors report improved LPIPS/PSNR/SSIM over Triangle Splatting on Mip-NeRF 360 and Tanks & Temples, improved Chamfer distance on DTU, and ablations showing that the deformation and regularization components contribute.","tokens_in":18952,"tokens_out":10437,"duration_ms":125322,"significance":"Non-convex, deformable triangle primitives are a useful step beyond fixed triangles and convex primitives. The paper is strong on empirical validation: per-scene tables, deformation contribution maps, control-point statistics, and a clear ablation suite. It also describes an efficient CUDA implementation and discusses stability under self-intersection. However, a central theoretical claim—that the barycentric-space formulation is exactly view-independent—is not correct under perspective, so the paper's main conceptual justification needs substantial rework.","major_comments":[{"comment":"The claim that the formulation is ‘exactly view-independent by construction’ is invalid. The map b=T^{-1}(p-p_1) is built from the 2D projected vertices p_i. Under perspective, a fixed 3D point X on the base triangle has 2D barycentric coordinates that change with viewpoint (b_i are projective, not affine, in the 3D barycentrics λ). A fixed deformed polygon in (u,v) therefore corresponds to different 3D regions on the primitive for different cameras. This is exactly the view-dependence the paper attributes to image-space deformations. The Abstract’s ‘view-consistent rendering’, §3.1’s ‘eliminating multi-view gradient conflict’, and the Conclusion’s ‘strictly view-independent’ are therefore unsupported. Figure 3 does not test 3D consistency: it compares two image-space parameterizations. The authors should either formulate the deformation in true 3D barycentric coordinates of the base tri","section":"Sec. 3.1, Eq. (1), ‘Why Barycentric Space?’"},{"comment":"R=2A/P is not, as stated, the inradius of a general convex polygon; it equals the inradius only for tangential polygons. For a 2×1 rectangle, R=2A/P=4/6≈0.667 while the inradius is 0.5. For non-convex polygons the claim that R is an upper bound on interior distances is not established, and φ≤1 is trivial because of the min(1,·) clamp. Since R sets the spatial scale of the opacity falloff in Eq. (6), the paper should either compute the true polygon inradius or explicitly present R as an area-perimeter heuristic and discuss the consequences.","section":"Eq. (5)"}],"minor_comments":[{"comment":"The loss in Eq. (7) includes L_d with weight λ3, but Table S1 sets λ_dist=0. If the distortion term is disabled, this should be stated in the main text.","section":"Sec. 3.3 and Table S1"},{"comment":"FPS and training-time footnotes are ambiguous: TS is reported with two FPS/Train values, and the paper’s average Mip-NeRF 360 FPS (55) is hard to reconcile with the per-scene Bonsai/Garden values (47/33). Please clarify hardware and averaging protocol.","section":"Table 2 and Table S2"},{"comment":"The units and color scale for |Δ| are not defined, and Fig. 3-right should state quantitatively what ‘consistent shape’ means; visual comparison alone is not a test of 3D consistency.","section":"Fig. 3"},{"comment":"Zeroing δ together with d means the figure does not isolate the displacement contribution; Table 3 is the cleaner ablation. The caption should acknowledge this.","section":"Fig. 5 and Fig. S2"},{"comment":"The statement that barycentric displacements are ‘scale-invariant with respect to the triangle’s image-space size’ is true only for uniform scaling of the projected triangle, not under perspective; the sentence should be qualified.","section":"Sec. 3.1"}],"recommendation":"major_revision","confidential_remarks":"The view-independence flaw is the main obstacle. If the authors rework the theoretical claim and clarify the R normalization, the empirical contribution is likely sufficient for publication. The current manuscript should not be accepted as-is."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a credible, well-ablated extension of Triangle Splatting, and the benchmark gains are plausible. The stress-test note is right: the central conceptual claim that deformations in barycentric coordinates are exactly view-independent is false under perspective.\n\nWhat's actually new and good: the deformable triangle primitive—three 3D vertices plus K learnable scalar displacements per edge in the triangle's barycentric space—is a real addition to the toolbox. The rasterization pipeline (winding test, polynomial smooth-minimum distance, power-law window) is a coherent way to handle non-convex, even self-intersecting polygons. The ablations are thorough: the K sweep, the deformation contribution maps, the curvature-loss analysis, and the warm-up delay study all support that the deformations do work. The single-primitive shape fitting (clover, heart, Pac-Man) makes the expressiveness point concretely. On Mip-NeRF 360 they beat TS on average LPIPS 0.183 vs 0.191 and on 9 of 11 scenes, and they honestly report the two scenes where they lose. That's good behavior.\n\nNow the soft spots, in proportion. The view-independence claim is load-bearing and wrong. The barycentric frame is built from the projected 2D vertices, so it is redefined per viewpoint. A fixed set of displacements does not pick out a fixed set of 3D points on the triangle plane; under perspective the same 2D barycentric offsets correspond to different 3D regions as the camera moves. The paper's own critique of image-space deformations applies verbatim to their construction. This does not necessarily sink the method—triangles are small and perspective is locally affine, so the effect may be minor in practice—but the 'exactly view-independent by construction' statement in Sec 3.1 and the conclusion is simply not true and needs to be replaced with an honest approximation statement.\n\nSecond, Eq. (5) states that for a convex polygon R=2A/P equals the true inradius. That is only true for tangential polygons, not general convex ones (a rectangle breaks it). Since R is only a normalization heuristic, this is a minor error, but it is a geometric misstatement.\n\nThird, no code is released—only a project page. The CUDA rasterizer is the method's engine; without it, the empirical results are hard to verify. I'd want the code as a condition for acceptance.\n\nWho gets value: anyone working on primitive-based radiance field rendering, especially real-time splatting. It deserves a serious referee; desk reject would be wrong. I'd engage with it, but I'd require the theoretical overclaims fixed and the code released.","headline":"DETRIS is a credible incremental extension of Triangle Splatting with plausible gains, but the 'exactly view-independent by construction' claim does not hold under perspective projection.","tokens_in":19371,"tokens_out":4055,"would_cite":true,"duration_ms":46514,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that adding K learnable edge displacements to each triangle in a splatting renderer produces a single primitive that can represent non-convex shapes and improves novel-view quality over rigid triangle splatting.","keywords":["deformable triangles","non-convex primitives","barycentric coordinates","radiance fields","splatting","differentiable rendering","winding number","novel view synthesis"],"falsifier":"Render a single deformed primitive (e.g., a heart or arrow) with fixed displacements and corner smoothness from several camera angles spanning 0°–60° slant, extract the screen-space silhouette each time, and unproject it to 3D using the rendered depth. If the reconstructed 3D boundary differs between views beyond numerical precision, the claimed view-independence fails; equivalently, compute the 3D barycentric coordinates of the ray–plane intersection and compare them to the 2D pixel barycentric coordinates used by the rasterizer, and show the discrepancy grows with slant.","tokens_in":18378,"feed_emoji":"🔺","tokens_out":10100,"duration_ms":95303,"temperature":0.7,"pith_summary":"The paper sets out to give radiance-field rendering a primitive that is not forced to be convex. Its proposal: start from the standard triangle used in Triangle Splatting, but let each edge be deformed by K control points, each carrying one learnable scalar displacement along the edge normal, evaluated in the triangle's own barycentric coordinate space. A single such deformable triangle can take the shape of a circle, a heart, an arrow, or a crescent, which previously required many rigid triangles or soft Gaussian blobs. The authors report that on real scenes this lowers perceptual error (LPIPS 0.183 vs. 0.191 on Mip-NeRF 360) and improves mesh geometry (DTU Chamfer distance 1.01 vs. 1.06) while keeping rendering real-time. The reason this matters: if true, curved and concave geometry no longer demands excessive primitive proliferation, and a unified primitive can adapt to whatever shape the data requires.","feed_headline":"Deformable triangles beat rigid ones at radiance field rendering","feed_subtitle":"K learnable edge bends per triangle capture curves and concavities with fewer primitives, still real time","key_machinery":"The load-bearing machinery is the barycentric coordinate map b = T^{-1}(p - p1) with T = [p2 - p1, p3 - p1], which sends every pixel inside the projected triangle to the unit triangle in (u,v) space. Control points are placed at b_{i,k} = b_start + (k/(K+1)) e_i + d_{i,k} nhat_i, where d_{i,k} is the single learnable scalar displacement along the edge normal nhat_i; this is the entire shape-adaptation mechanism, and it preserves the three base vertices that define the 3D plane. Inside/outside decisions use a non-zero winding-number rule via ray casting; the opacity falloff uses a polynomial smooth minimum over point-to-segment distances with smoothing radius g = delta * r_bary, followed by a","core_discovery":"On its own terms, the paper's discovery is that convexity is not a necessary property of a splatting primitive. By placing K control points per edge and letting each move by a single scalar displacement along the edge normal in barycentric coordinates, the boundary of a triangle becomes a piecewise-linear polygon that can bend inward and outward while the three base vertices still define a 3D plane. The rasterizer classifies pixels with a winding-number test, computes a C1-continuous distance field via a polynomial smooth minimum with a learnable corner-rounding radius, and converts it to opacity through a power-law window normalized by the deformed polygon's inradius. Because all deformatio","pith_inferences":["Inference: The paper leaves implicit that its view-independence claim holds for the affine barycentric map, but perspective projection is projective, not affine; the 2D barycentric coordinates of a pixel do not equal the 3D barycentric coordinates of the point where the viewing ray meets the triangle plane, so a direct slant test would quantify the approximation.","Inference: Because each primitive carries a well-defined face normal and a piecewise-linear boundary, the representation could be reused for surface editing, relighting, or level-of-detail by decimating control points; these are natural next steps the paper does not explore.","Inference: The curvature regularizer and the tolerance for self-intersecting boundaries suggest the primitive can act as a deformable template in optimization problems beyond radiance fields, such as image segmentation or shape fitting; the paper demonstrates only 2D shape fitting as a proof of concept.","Inference: The reported gains over Triangle Splatting are mostly perceptual (LPIPS) rather than PSNR, which the paper attributes to sharper boundaries; an evaluation protocol that weights high-frequency structure would be a more sensitive test of the advantage."],"forward_implications":["A single deformable triangle can reproduce both convex and concave 2D targets (circle, square, Gaussian, clover, arrow, Pac-Man, heart) that require three rigid triangles or eight Gaussians.","On average over Mip-NeRF 360, the method improves LPIPS to 0.183 from Triangle Splatting's 0.191, and on Tanks & Temples to 0.133 from 0.143, with best-in-class perceptual quality among non-volumetric primitives.","Zeroing the learned displacements after training increases mean absolute error by +0.052 on Bonsai and +0.029 on Bicycle, showing the deformations are what sharpen fine boundary structures.","The per-primitive overhead is small (3K+1 = 10 extra floats, about +17% per primitive), and rendering stays real-time though slower than rigid triangles (47/33 FPS vs. 63/49 on Bonsai/Garden), with the cost tunable through K.","Rendered normal maps are geometrically coherent as a by-product, enabling TSDF-based mesh extraction on DTU with Chamfer distance 1.01, better than the rigid-triangle baseline's 1.06."],"fun_headline_variants":["Triangle splats bend with learnable edge curves for radiance fields","Non-convex triangle splats: winding-number test for real-time radiance","Bendy triangles: flexible splats for higher-quality radiance fields","Radiance fields get curvy: deformable triangle splats","Fewer primitives: curved triangle splats for real-time radiance"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The load-bearing premise is that the 2D barycentric coordinates of a pixel, computed from the projected triangle, are an intrinsic and view-independent parameterization of the primitive's surface; because perspective projection is projective, not affine, a fixed deformed polygon in this coordinate space does not correspond to a fixed 3D region when the triangle is viewed obliquely.","fun_headline_variants_meta":{"raw":{"variants":["Triangle splats bend with learnable edge curves for radiance fields","Non-convex triangle splats: winding-number test for real-time radiance","Bendy triangles: flexible splats for higher-quality radiance fields","Radiance fields get curvy: deformable triangle splats","Fewer primitives: curved triangle splats for real-time radiance"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000676,"raw_usage":{"total_tokens":2904,"prompt_tokens":731,"completion_tokens":2173,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":475,"completion_tokens_details":{"reasoning_tokens":2079}},"tokens_in":475,"tokens_out":2173,"duration_ms":20322,"temperature":1.0,"reasoning_tokens":2079,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T04:43:27.884111+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Render a single deformed primitive (e.g., a heart or arrow) with fixed displacements and corner smoothness from several camera angles spanning 0°–60° slant, extract the screen-space silhouette each time, and unproject it to 3D using the rendered depth. If the reconstructed 3D boundary differs between views beyond numerical precision, the claimed view-independence fails; equivalently, compute the 3D barycentric coordinates of the ray–plane intersection and compare them to the 2D pixel barycentric coordinates used by the rasterizer, and show the discrepancy grows with slant.","supporting_citations":[],"review_version":1}