Compact light field photography towards versatile three-dimensional vision

Principle of compact light field photography

In linear systems, the image acquisition process can be written in a general matrix formalism as

$${{{{{\bf{f}}}}}}={{{{{\bf{Ah}}}}}}+{{{{{\boldsymbol{\sigma }}}}}}{{{{{\boldsymbol{,}}}}}}$$

(1)

where \({{{{{\boldsymbol{\sigma }}}}}}\) is the measurement noise, h and f are the vectorized image and measurement, respectively. A is the m × N2 system matrix (for an image resolution of N × N throughout the manuscript), which is square (m = N2) for full-rate sampling and rectangular (m < N2) under compressive sensing. This formulation, though general, typically assumes all m measurements of the scene are obtained from a single view and hence possessing no light field capability. To record light fields with an angular resolution of l, the measurement procedure must be repeated either parallelly (via a lens array32) or sequentially at l different views33, leading to a measurement dataset of size m × l. In CLIP, we break this convention by employing nonlocal acquisition for the row entries of matrix A and splitting the m measurements into l different views, thereby compactly recording light field data with an angular resolution of l. As derived in Supplementary Note 5, this transforms the image model into:

$${{{{{\bf{f}}}}}}=\left[\begin{array}{ccc}{{{{{{\bf{A}}}}}}}_{{{{{{\bf{1}}}}}}} & \cdots & {{{{{\boldsymbol{0}}}}}}\\ \vdots & {{{{{{\bf{A}}}}}}}_{{{{{{\bf{2}}}}}}} & \vdots \\ {{{{{\boldsymbol{0}}}}}} & \ddots & {{{{{\boldsymbol{0}}}}}}\\ {{{{{\boldsymbol{0}}}}}} & \cdots & {{{{{{\bf{A}}}}}}}_{l}\end{array}\right]\left[\begin{array}{c}{{{{{{\bf{P}}}}}}}_{{{{{{\bf{1}}}}}}}\\ {{{{{{\bf{P}}}}}}}_{{{{{{\bf{2}}}}}}}\\ \vdots \\ {{{{{{\bf{P}}}}}}}_{{{{{{\boldsymbol{l}}}}}}}\end{array}\right]+{{{{{\boldsymbol{\sigma }}}}}}={{{{{{\bf{A}}}}}}}^{{\prime}} \left[\begin{array}{c}{{{{{{\bf{P}}}}}}}_{{{{{{\bf{1}}}}}}}\\ {{{{{{\bf{P}}}}}}}_{{{{{{\bf{2}}}}}}}\\ \vdots \\ {{{{{{\bf{P}}}}}}}_{{{{{{\boldsymbol{l}}}}}}}\end{array}\right]+{{{{{\boldsymbol{\sigma }}}}}}={{{{{{\bf{A}}}}}}}^{{\prime} }{{{{{\bf{P}}}}}}+{{{{{\boldsymbol{\sigma }}}}}}{{{{{\boldsymbol{,}}}}}}$$

(2)

where \({{{{{{\bf{A}}}}}}}_{{{{{{\bf{k}}}}}}}\) is the kth sub-matrix such that \({{{{{\bf{A}}}}}}=\left[{{{{{{\bf{A}}}}}}}_{{{{{{\bf{1}}}}}}}{{;}}\,{{{{{{\bf{A}}}}}}}_{{{{{{\bf{2}}}}}}}{{;}}\,{{{\cdots }}{{,}}\,{{{{{\bf{A}}}}}}}_{{{{{{\bf{l}}}}}}}\right]\), \({{{{{{\bf{A}}}}}}}^{{{{\prime} }}}\) is the transformed block-diagonal matrix and \({{{{{\bf{P}}}}}}=\left[{{{{{{\bf{P}}}}}}}_{{{{{{\bf{1}}}}}}}{{{{{\rm{;}}}}}}\,{{{{{{\bf{P}}}}}}}_{{{{{{\bf{2}}}}}}}{{{{{\rm{;}}}}}}\,{\cdots ,{{{{{\bf{P}}}}}}}_{{{{{{\rm{l}}}}}}}\right]\) is the 4D light field. While one can exploit the sparisity prior to compressively recover a 4D light field at this stage, CLIP can further retrieve a refocused image directly by explicitly modeling the correlations in the 4D light field to better cope with complex scenes (see Supplementary Note 8 for comparisons).

This is inspired by the observation that images of the same scene acquired from different views share the same content in photographic applications (Supplementary Note 1): there is only a depth-dependent disparity between any two sub-aperture images, as illustrated in Fig. 1a. Therefore, one can explicitly model the correlations among the sub-aperture images by digitally propagating the light field, which relates the sub-aperture image at view k (denoted as \({{{{{{\bf{P}}}}}}}_{{k}}\)) to a reference sub-aperture image h via an invertible shearing operator \({{{{{{\bf{B}}}}}}}_{{k}}\) as \({{{{{{\bf{P}}}}}}}_{{k}}={{{{{{\bf{B}}}}}}}_{{k}}{{{{{\bf{h}}}}}}\) (Supplementary Note 1) and the m measurement data acquired from l views now becomes:

$${{{{{\bf{f}}}}}}=\left[\begin{array}{c}{{{{{{\bf{f}}}}}}}_{{{{{{\bf{1}}}}}}}\\ {{{{{{\bf{f}}}}}}}_{{{{{{\bf{2}}}}}}}\\ \vdots \\ {{{{{{\bf{f}}}}}}}_{{{{{{\bf{l}}}}}}}\end{array}\right]=\left[\begin{array}{ccc}{{{{{{\bf{A}}}}}}}_{{{{{{\bf{1}}}}}}} & \cdots & {{{{{\boldsymbol{0}}}}}}\\ \vdots & {{{{{{\bf{A}}}}}}}_{{{{{{\bf{2}}}}}}} & \vdots \\ {{{{{\boldsymbol{0}}}}}} & \ddots & {{{{{\boldsymbol{0}}}}}}\\ {{{{{\boldsymbol{0}}}}}} & \cdots & {{{{{{\bf{A}}}}}}}_{l}\end{array}\right]\left[\begin{array}{c}{{{{{{\bf{B}}}}}}}_{{{{{{\bf{1}}}}}}}{{{{{\bf{h}}}}}}\\ {{{{{{\bf{B}}}}}}}_{{{{{{\bf{2}}}}}}}{{{{{\bf{h}}}}}}\\ \vdots \\ {{{{{{\bf{B}}}}}}}_{l}{{{{{\bf{h}}}}}}\end{array}\right]+{{{{{\boldsymbol{\sigma }}}}}}=\left[\begin{array}{c}{{{{{{\bf{A}}}}}}}_{{{{{{\bf{1}}}}}}}{{{{{{\bf{B}}}}}}}_{{{{{{\bf{1}}}}}}}\\ {{{{{{\bf{A}}}}}}}_{{{{{{\bf{2}}}}}}}{{{{{{\bf{B}}}}}}}_{{{{{{\bf{2}}}}}}}\\ \vdots \\ {{{{{{\bf{A}}}}}}}_{{{{{{\bf{l}}}}}}}{{{{{{\bf{B}}}}}}}_{{{{{{\bf{l}}}}}}}\end{array}\right]{{{{{\bf{h}}}}}}+{{{{{\boldsymbol{\sigma }}}}}}={{{{{\bf{F}}}}}}\left({{{{{\bf{d}}}}}}\right){{{{{\bf{h}}}}}}+{{{{{\boldsymbol{\sigma }}}}}},$$

(3)

where \({{{{{{\bf{f}}}}}}}_{{k}}\) is a vector that contains mk measurements at view k, and the total number of measurements in \({{{{{\bf{f}}}}}}\) is \(m=\mathop{\sum }\limits_{k=1}^{l}{m}_{k}\). The whole system model \({{{{{\bf{F}}}}}}{(}{d}{)}\) becomes a function of the depth d, which is the key to recover the image h with different focal settings—by applying the shearing matrix \({{{{{{\bf{B}}}}}}}_{{k}}\) (hence \({{{{{\bf{F}}}}}}{{{{{\boldsymbol{(}}}}}}{{{{{\bf{d}}}}}}{{{{{\boldsymbol{)}}}}}}\)) to depth d as in light field cameras, the reconstructed image will be correspondingly focused thereon. Supplementary Note 2 details the workflow for image refocusing, novel view synthesis, extending the depth of field, and 3D imaging via depth-from-focus. CLIP thus can attain light field imaging (conventionally of a data size m × l) with a measurement data size of only m. It is worth noting that further reduction of the measurement data is possible by multiplexing the measurement from all the views onto a single measurement vector: \({{{{{{\bf{f}}}}}}}^{{{{{{\bf{c}}}}}}}={{{{{\bf{Tf}}}}}}\), with \({{{{{\bf{T}}}}}}\) being the integration operator. Supplementary Note 3 illustrates such a design strategy for a CLIP camera using 2D area detectors.

a A conventional light field camera captures the scene from different views with a lens array and records all sub-aperture images. In contrast, CLIP records (operator \({{{{{{\bf{A}}}}}}}_{{k}}\)) only a few nonlocal measurements (\({{{{{{\bf{f}}}}}}}_{{k}}\) to fn) from each sub-aperture image and exploits the depth-dependent disparity (modeled by Bk) to relate the sub-aperture images for gathering enough information to reconstruct the scene computationally. Refocusing is achieved by varying the depth-dependent disparity model Bk. b Seeing through severe occlusions by CLIP as a camera array, with each camera only recording partial nonlocal information of the scene. A obscured object (from the camera with black rays) remains partially visible to some other views (with green rays), whose nonlocal and complementary information enables compressive retrieval of the object. c Illustration of instantaneous compressibility of the time-of-flight measurements for a 3D scene in a flash LiDAR setup, where a transient illumination and measurement slice the crowded 3D scene along the depth (time) direction into a sequence of simpler instantaneous 2D images. d–f CLIP embodiments that directly perform nonlocal image acquisitions with a single-pixel, a linear array, and 2D area detectors, respectively. A single pixel utilizes a defocused spherical lens to integrate a coded image, with u and v behind the lnes being the angular dimension. A cylindrical lens yields along its invariant axis a radon transformation of the en-face image onto a 1D sensor. The complex-valued mask such as a random lens produces a random, wide-field PSF that varies with object depth to allow light field imaging. PSF point spread function, CLIP compact light field photography, LiDAR light detection and ranging, 1D, 2D, 3D one, two, and three-dimensional.

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The nonlocal acquisition strategy is pivotal to encode all scene points of the image into each view’s smaller sub-measurement vector fk (i.e., \({m}_{k}\ll {N}^{2}\)) for attaining an effective angular resolution of l. This is similar to the incoherent multiplexing requirement in compressive sensing, where a rich pool of nonlocal acquisition schemes has been developed for a range of applications during the past decades, benefiting CLIP. Such a nonlocal acquisition also endows CLIP with imaging robustness against defective pixels or scene occlusions. Because the complete scene is encoded in any subset of the measurements, image recovery is not substantially affected by a fraction of defective pixel readings, despite that the conditioning of image reconstruction might deteriorate (Supplementary Note 9). Similarly, an object that is completely blocked in certain views by its surrounding objects, as in Fig. 1b, could be partially visible to the remaining views, which contain incomplete but complementarily global information of the object to enable its retrieval (Supplementary Note 10). Furthermore, CLIP’s nonlocal acquisition can take advantage of the compressibility of natural photographs for compressive imaging (m < N2) to minimize data load, particularly when coupled with time-of-flight imaging. As illustrated in Fig. 1c for a point-scanning-based LiDAR imaging of a crowded office scene, the camera captures only a thin slice of the 3D volume at each time bin under an ultrashort illumination. As a result, the crowded 3D scene is decomposed into a sequence of instantaneous 2D images that are far simpler than its continuously-wave-illuminated photograph. Such instantaneous compressibility also holds for NLOS imaging, albeit in a different representation basis12.

Three exemplar CLIP embodiments utilizing a single pixel element (0D), a linear array (1D), and a 2D area detector are illustrated in Fig. 1d–f, respectively. The single-pixel camera34,35 (Fig. 1d) sequentially encrypts the scene with different random codes and measures light intensities with a bucket detector. To sample light fields without redundant data, CLIP splits the measurements by scanning the detector during code update along the u−v direction (u, v, angular axis behind the collection lens) into l positions. With random binary codes, each measurement integrates ~50% of the image pixels, and mk ≥ 7 measurements in each view cover every pixel with a high probability (\(p=1-{0.5}^{7} \, > \, 99 \%\)). For CLIP with 1D sensors, the x-ray CT imaging model is transformed by using a cylindrical lens to cast along the lens’ invariant axis (the axis without optical power) a line-integral of the image onto an individual pixel as in Fig. 1e, allowing a 1D detector array to parallelly records mk = N measurements to cover all image pixels. Light fields of the scene are then acquired with an array of cylindrical lenses, each being oriented at a distinct angle with respect to the 1D sensor (see the “Methods” section).

For CLIP imaging with 2D detectors (of various sparsity), one can design a complex-valued mask to produce a wide-field, depth-dependent point spread function (PSF) (Fig. 1f) to multiplex sub-aperture measurements (i.e., \({{{{{{\bf{f}}}}}}}^{{{{{{\bf{c}}}}}}}={{{{{\bf{Tf}}}}}}\)). Moreover, we can unify wavefront coding36,37, coded-aperture38 techniques, and diffuser cameras23,24 into the CLIP framework, where the full recovery of 4D light fields is unnecessary25. Detailed formulations and synthetic imaging results for CLIP with 2D detectors, along with additional 1D-sensor-based designs with provably close-to-optimal performances, are provided in Supplementary Notes 3 and 4, respectively. Adaption to camera array systems can be readily accomplished by making each camera (of any dimension) record a few nonlocal coefficients of the scene and sufficiently overlapping individual cameras’ fields of view.

We quantified the efficacy of CLIP for light field imaging experimentally with a 0D sensor in Supplementary Note 7, and further evaluated the CLIP reconstruction accuracy synthetically with both 0D and 1D sensors in Supplementary Note 11, which employs CLIP to represent custom-acquired 4D light field data for scenes of different complexities and BRDF characteristics.

3D imaging through occlusions

Seeing through occlusions has been previously achieved by dense camera array systems16, which apply synthetic aperture processing to blur down the occluder while keeping the object of interest coherently enhanced. However, a clear separation of the object and occluder in 3D is difficult due to the defocused background and the limited depth sectioning capacity of camera array systems. We show here background-free 3D vision through severe occlusion with time-of-flight (ToF) CLIP imaging. For the proof-of-concept demonstration, we built a ToF-CLIP system with a streak camera as the 1D ultrafast sensor for snapshot acquisition of large scale 3D time-of-flight data. The streak camera is spatially multiplexed by seven customized plano-convex cylindrical lenslets (diameter of 2 mm and a focal length of 4 mm) along its entrance slit at distinct orientations to mimic a camera array system (see the “Methods” section). The baseline of the camera is 15 mm, and the field of view is 30 mm at a distance of 60 mm. With ~1000 pixels, CLIP implicitly recorded a 125 × 125 × 7 light field dataset and streamed a temporal sequence of 1016 points (i.e., 1000 spatial × 1016 temporal) at a 100 Hz repetition rate for high-speed imaging. A femtosecond laser was modulated by a motorized assembly consisting of a concave lens and a diffuser for programmable illumination between a diverged and a collimated light. The diverged laser shines from an oblique angle to cover both the object and occluder. In practice, an array of synchronized laser diodes is typically employed, with each camera having its own laser source as illustrated in Supplementary Note 10.

Background-free 3D imaging through severe occlusions for three different scenes is shown in Fig. 2a–c. In all cases, the objects that are completely blocked by their preceding items, as rendered in the front view images emulating what a conventional camera would capture, can be well retrieved by the ToF-CLIP camera with correct 3D locations and geometric shapes. For larger objects such as the letter V in Fig. 2b that remain partially visible, its occluded parts are recovered with a weaker intensity. This is because the occluded parts contribute less effective measurement signals for the image reconstruction, equivalent to imaging with a smaller synthetic aperture. Trackings through occlusions is demonstrated in Fig. 2d, where a 2 × 2 grid pattern made of white foam was mounted on a translation stage behind a rectangular obscurer and moved back and forth across the camera field of view. Motion of the grid pattern varied the severity of occlusion smoothly from none to a complete obscurance as shown in the representative frames. Except for a weaker intensity caused by occlusion, the grid pattern is adequately recovered at all the time instances. The complete video of tracking through occlusion is provided in Supplementary Movie 1 along with reference photographs.

a–c Reconstructed 3D images rendered in different perspective for three scenes: circular plate (a) and letter V (b) behind the letter N, and letter X (c) blocked by a rectangular plate. The severe occlusions are evident from the front view images, with the larger objects in the front completely blocked the object right behind them. In contrast, CLIP is able to unambiguously reconstruct the obstructed objects in 3D without any defocusing signals from the preceding occluder. d Three representative frames of imaging a 2 × 2 grid pattern moving across the CLIP camera FOV behind a rectangular occluder. Note that signals from the black occluders are enhanced relative to the objects for better visualization.

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It is noteworthy that a clear separation between the objects and occluder is consistently achieved in all the scenes. No defocused background signals from the occluder are discernible on the blocked object, highlighting the benefits of merging dense multi-view measurement with ToF by CLIP. Because an occluder reduces the number of measurements for the blocked object, and the current CLIP camera has a compression factor of ~20 (with respect to a single sub-aperture image), the occluded objects that can be well recovered are restricted to be relatively simple in geometry. Nonetheless, the imaging outcomes are still remarkable, considering the reduction of measurements against camera array systems of the same resolution is more than 100 folds, and conventional compressive imaging using the same amount of data shows similar imaging characteristics but lacks light field capability to see through occlusions. We further quantified the accuracy of CLIP imaging through occlusions via synthetic studies in Supplementary Note 10, which shows a small imaging error (<10%) can be obtained by CLIP despite of a large reduction (>100 times) in light field measurement data.

Flash LiDAR within an extended depth range

For high-quality 3D imaging of indoor scenes, multi-view methods require an unwieldy system baseline apart from their dependence on object texture. By contrast, flash LiDAR imaging can maintain a high precision at longer distances in a compact form but suffers from a stringent tradeoff between the sensing range and light throughput15,39. To demonstrate that CLIP is well-posed to lift such a tradeoff, we tuned the camera’s field of view to 1.5 m × 1.5 m at a nominal distance of 3.0 m by moving the lenslet array closer to the slit and aligned the laser to be approximately confocal with the camera while providing a diverged illumination after passing through the motorized assembly.

An example of single-shot flash LiDAR imaging with an extended depth range is shown in Fig. 3a, where several texture-less letters were placed at different depths spanning a range of ~2 m. The extended depth of field is highlighted in Fig. 3b by computationally refocusing the camera from far to near, as indicated in the top view image. The resultant LiDAR projection photograph clearly renders the defocusing blur for objects that deviate from their actual focal settings, whereas an all-in-focus image generated by CLIP in Fig. 3c allows a sharper portrait of the entire 3D scene. The flash LiDAR imaging resolution was estimated to be about 30 mm laterally and ~10 mm axially (depth direction). While this example features a relatively simple scene to facilitate the comparison between the reference photograph and LiDAR images, additional results for handling more complex scenes are presented in Supplementary Note 14.

a Flash LiDAR imaging of a letter scene. From left to right are the reference photographs, a projected two-dimensional LiDAR images along the depth direction, and the 3D (three-dimensional) point-cloud representation of the scene. b flash LiDAR of the same 3D scene without extending the imaging depth of field, obtained by refocusing the camera onto a single focal plane. Note the defocus blur in the near and far objects. c Computational all-in-focus image. d and e Two representative frames for the dynamic imaging of a manually rotated letter V in a simple and cluttered scene, respectively.

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We demonstrated ToF-CLIP in dynamic imaging of a 3D scene by mounting a letter V on a rotation stage and manually rotating it at an irregular speed against a simple and cluttered background, respectively. The resultant motions were filmed by the CLIP-ToF camera at a 100 Hz frame rate and a reference video camera at 60 Hz. The two videos were then numerically synchronized after temporally downsampling the LiDAR results to 60 Hz for comparison. Representative frames of the dynamic results are shown in Fig. 3d and e for the simple and cluttered background, respectively, and the full comparison videos are provided in Supplementary Movies 2 and 3. To better visualize the rotating dynamics of the letter V in the cluttered scene, we isolated it in a magnified view in the projection image in Fig. 3e. CLIP captured the motion of the letter faithfully in both LiDAR videos and reproduced the letter’s small vibrations during rotation. We also recovered the unobstructed hand in the simple scene and the dynamic shadows cast by the letter V on the background walls in the cluttered scene, despite of compressive data acquisition in the current ToF-CLIP camera.

NLOS imaging with curved and disconnected surfaces

Unlike LiDAR that detects the directly scattered photons, NLOS imaging analyzes multiply scattered light from a diffusive surface to reveal objects hidden from direct line-of-sight. A key ingredient for such an analysis is the precise knowledge of the relaying surface’s 3D geometry, which was previously obtained via nontrivial calibrations by a stereo26 camera or scanning-based LiDAR27,40 ranger, hampering applications in the field where the relay surface evolves with the camera’s viewpoint and 3D surroundings. The ToF-CLIP camera addresses this critical need for real-time mapping of the relay surface via built-in flash LiDAR imaging. More importantly, it can accommodate a non-planar surface geometry for NLOS imaging using array detectors with its light field capability. Paired with a proposed hybrid time-frequency domain reconstruction algorithm, which can handle general surfaces with a computational complexity of o(N4) (see the “Methods“ section), ToF-CLIP can attain real-time NLOS imaging with arbitrary curved surfaces. While NLOS imaging with a dynamic and curved surface has been demonstrated by Manna et al. 40, its reception point was fixed at a stationary point rather than being on the dynamic surface, making it inapplicable for real-time imaging with array detectors. Similarly, the preprocessing step41 proposed by Lindell et al. that adapts the f−k migration reconstruction algorithm to deal with slightly curved surfaces in confocal NLOS imaging has a computational complexity of o(N5 log N), which is higher than the time-domain phasor field method and thus inefficient for real-time reconstruction.

To demonstrate our approach, we directed the CLIP-ToF camera towards a scattering wall with a fixed focus. The field of view is tuned to be ~0.5 m × 0.5 m at a standoff distance of ~1 m. The geometry of the wall was mapped by the flash LiDAR, and NLOS signal reception was delayed accordingly to avoid the strong reflections from the collimated laser spot on the wall. The hidden scene was then reconstructed in real-time by the hybrid time–frequency domain algorithm.

We demonstrated NLOS imaging with planar, disconnected, and curved walls in Fig. 4a–c. For all the relay walls, the hidden scenes were placed over 1 m away from the laser spot on the wall and then imaged with a single laser shot at an average laser power of 700 mW. The 3D flash LiDAR measurement of the walls are shown in the first column, and the NLOS imaging results for two example objects in each category were rendered in a 2D front view (from the wall’s perspective) and a 3D point cloud format in the following columns. Both the 3D positions and morphological structures of the hidden objects were decently recovered for NLOS imaging with all the relay walls. The importance of an extended depth-of-field to cope with disconnected and curved surfaces is illustrated in Fig. 4d, e, respectively, where the camera’s extended depth of field is disabled by computationally refocusing the camera onto different planes (from rear to the front) before reconstructing the hidden scenes. Due to defocus effects that blur the spatiotemporal data on the walls, the reconstruction quality degrades noticeably compared with the images reconstructed with an extended depth of field (highlighted by the green boxes). It is worth noting that NLOS imaging with the curved surface suffered from secondary laser inter-reflections (i.e., laser reflections between the surface parts before incident onto the hidden objects) during the experiments, which caused the imaging artifacts in Fig. 4c, despite that the phasor field method is robust against multiple inter-reflections. This is primarily because the secondary laser reflection is much stronger than the inter-reflections of the weaker NLOS photons. Still, CLIP’s capability to handle disconnected and curved surfaces is an important step to achieve point-and-shoot NLOS imaging in the field.

a–c Imaging with planar, disconnected, and curved surfaces, respectively. From left to right are the flash LiDAR imaging of the relay surfaces, and two example hidden objects rendered as a projection image in the front view, and a 3D (three-dimensional) point cloud. Ground truth photographs of the object are shown in the inset of the front view image. d, e Reconstructed NLOS images for the disconnected and curved surfaces, respectively, with defocus errors on the relay wall, and those recovered with extended depth of field (highlighted by the green box). The quality of reconstruction degrades when the camera’s extended depth of field is disabled.

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Models are very helpful, but they also have limitations.

Details—Models cannot include all the details of the objects that they represent. For example, maps cannot include all the details of the features of the earth such as mountains, valleys, etc.

Approximations—Most models include some approximations as a convenient way to describe something that happens in nature. These approximations are not exact, so predictions based on them tend to be a little bit different from what you actually observe. Models do not behave exactly like the things they represent.

Accuracy—In order to make models simplistic enough to communicate ideas some accuracy is lost. For example, ball and stick models of atoms do not show all the details that scientists know about the structure of the atom.